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1
Moustaki, Irini. "Latent variable models for mixed manifest variables." Thesis, London School of Economics and Political Science (University of London), 1996. http://etheses.lse.ac.uk/78/.
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Latent variable models are widely used in social sciences in which interest is centred on entities such as attitudes, beliefs or abilities for which there e)dst no direct measuring instruments. Latent modelling tries to extract these entities, here described as latent (unobserved) variables, from measurements on related manifest (observed) variables. Methodology already exists for fitting a latent variable model to manifest data that is either categorical (latent trait and latent class analysis) or continuous (factor analysis and latent profile analysis). In this thesis a latent trait and a latent class model are presented for analysing the relationships among a set of mixed manifest variables using one or more latent variables. The set of manifest variables contains metric (continuous or discrete) and binary items. The latent dimension is continuous for the latent trait model and discrete for the latent class model. Scoring methods for allocating individuals on the identified latent dimen-sions based on their responses to the mixed manifest variables are discussed. ' Item nonresponse is also discussed in attitude scales with a mixture of binary and metric variables using the latent trait model. The estimation and the scoring methods for the latent trait model have been generalized for conditional distributions of the observed variables given the vector of latent variables other than the normal and the Bernoulli in the exponential family. To illustrate the use of the naixed model four data sets have been analyzed. Two of the data sets contain five memory questions, the first on Thatcher's resignation and the second on the Hillsborough football disaster; these five questions were included in BMRBI's August 1993 face to face omnibus survey. The third and the fourth data sets are from the 1990 and 1991 British Social Attitudes surveys; the questions which have been analyzed are from the sexual attitudes sections and the environment section respectively.
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Xiong, Hao. "Diversified Latent Variable Models." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/18512.
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Latent variable model is a common probabilistic framework which aims to estimate the hidden states of observations. More specifically, the hidden states can be the position of a robot, the low dimensional representation of an observation. Meanwhile, various latent variable models have been explored, such as hidden Markov models (HMM), Gaussian mixture model (GMM), Bayesian Gaussian process latent variable model (BGPLVM), etc. Moreover, these latent variable models have been successfully applied to a wide range of fields, such as robotic navigation, image and video compression, natural language processing. So as to make the learning of latent variable more efficient and robust, some approaches seek to integrate latent variables with related priors. For instance, the dynamic prior can be incorporated so that the learned latent variables take into account the time sequence. Besides, some methods introduce inducing points as a small set representing the large size latent variable to enhance the optimization speed of the model. Though those priors are effective to facilitate the robustness of the latent variable models, the learned latent variables are inclined to be dense rather than diverse. This is to say that there are significant overlapping between the generated latent variables. Consequently, the latent variable model will be ambiguous after optimization. Clearly, a proper diversity prior play a pivotal role in having latent variables capture more diverse features of the observations data. In this thesis, we propose diversified latent variable models incorporated by different types of diversity priors, such as single/dual diversity encouraging prior, multi-layered DPP prior, shared diversity prior. Furthermore, we also illustrate how to formulate the diversity priors in different latent variable models and perform learning, inference on the reformulated latent variable models.
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Creagh-Osborne, Jane. "Latent variable generalized linear models." Thesis, University of Plymouth, 1998. http://hdl.handle.net/10026.1/1885.
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Generalized Linear Models (GLMs) (McCullagh and Nelder, 1989) provide a unified framework for fixed effect models where response data arise from exponential family distributions. Much recent research has attempted to extend the framework to include random effects in the linear predictors. Different methodologies have been employed to solve different motivating problems, for example Generalized Linear Mixed Models (Clayton, 1994) and Multilevel Models (Goldstein, 1995). A thorough review and classification of this and related material is presented. In Item Response Theory (IRT) subjects are tested using banks of pre-calibrated test items. A useful model is based on the logistic function with a binary response dependent on the unknown ability of the subject. Item parameters contribute to the probability of a correct response. Within the framework of the GLM, a latent variable, the unknown ability, is introduced as a new component of the linear predictor. This approach affords the opportunity to structure intercept and slope parameters so that item characteristics are represented. A methodology for fitting such GLMs with latent variables, based on the EM algorithm (Dempster, Laird and Rubin, 1977) and using standard Generalized Linear Model fitting software GLIM (Payne, 1987) to perform the expectation step, is developed and applied to a model for binary response data. Accurate numerical integration to evaluate the likelihood functions is a vital part of the computational process. A study of the comparative benefits of two different integration strategies is undertaken and leads to the adoption, unusually, of Gauss-Legendre rules. It is shown how the fitting algorithms are implemented with GLIM programs which incorporate FORTRAN subroutines. Examples from IRT are given. A simulation study is undertaken to investigate the sampling distributions of the estimators and the effect of certain numerical attributes of the computational process. Finally a generalized latent variable model is developed for responses from any exponential family distribution.
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Dallaire, Patrick. "Bayesian nonparametric latent variable models." Doctoral thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/26848.
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L’un des problèmes importants en apprentissage automatique est de déterminer la complexité du modèle à apprendre. Une trop grande complexité mène au surapprentissage, ce qui correspond à trouver des structures qui n’existent pas réellement dans les données, tandis qu’une trop faible complexité mène au sous-apprentissage, c’est-à-dire que l’expressivité du modèle est insuffisante pour capturer l’ensemble des structures présentes dans les données. Pour certains modèles probabilistes, la complexité du modèle se traduit par l’introduction d’une ou plusieurs variables cachées dont le rôle est d’expliquer le processus génératif des données. Il existe diverses approches permettant d’identifier le nombre approprié de variables cachées d’un modèle. Cette thèse s’intéresse aux méthodes Bayésiennes nonparamétriques permettant de déterminer le nombre de variables cachées à utiliser ainsi que leur dimensionnalité. La popularisation des statistiques Bayésiennes nonparamétriques au sein de la communauté de l’apprentissage automatique est assez récente. Leur principal attrait vient du fait qu’elles offrent des modèles hautement flexibles et dont la complexité s’ajuste proportionnellement à la quantité de données disponibles. Au cours des dernières années, la recherche sur les méthodes d’apprentissage Bayésiennes nonparamétriques a porté sur trois aspects principaux : la construction de nouveaux modèles, le développement d’algorithmes d’inférence et les applications. Cette thèse présente nos contributions à ces trois sujets de recherches dans le contexte d’apprentissage de modèles à variables cachées. Dans un premier temps, nous introduisons le Pitman-Yor process mixture of Gaussians, un modèle permettant l’apprentissage de mélanges infinis de Gaussiennes. Nous présentons aussi un algorithme d’inférence permettant de découvrir les composantes cachées du modèle que nous évaluons sur deux applications concrètes de robotique. Nos résultats démontrent que l’approche proposée surpasse en performance et en flexibilité les approches classiques d’apprentissage. Dans un deuxième temps, nous proposons l’extended cascading Indian buffet process, un modèle servant de distribution de probabilité a priori sur l’espace des graphes dirigés acycliques. Dans le contexte de réseaux Bayésien, ce prior permet d’identifier à la fois la présence de variables cachées et la structure du réseau parmi celles-ci. Un algorithme d’inférence Monte Carlo par chaîne de Markov est utilisé pour l’évaluation sur des problèmes d’identification de structures et d’estimation de densités. Dans un dernier temps, nous proposons le Indian chefs process, un modèle plus général que l’extended cascading Indian buffet process servant à l’apprentissage de graphes et d’ordres. L’avantage du nouveau modèle est qu’il admet les connections entres les variables observables et qu’il prend en compte l’ordre des variables. Nous présentons un algorithme d’inférence Monte Carlo par chaîne de Markov avec saut réversible permettant l’apprentissage conjoint de graphes et d’ordres. L’évaluation est faite sur des problèmes d’estimations de densité et de test d’indépendance. Ce modèle est le premier modèle Bayésien nonparamétrique permettant d’apprendre des réseaux Bayésiens disposant d’une structure complètement arbitraire.<br>One of the important problems in machine learning is determining the complexity of the model to learn. Too much complexity leads to overfitting, which finds structures that do not actually exist in the data, while too low complexity leads to underfitting, which means that the expressiveness of the model is insufficient to capture all the structures present in the data. For some probabilistic models, the complexity depends on the introduction of one or more latent variables whose role is to explain the generative process of the data. There are various approaches to identify the appropriate number of latent variables of a model. This thesis covers various Bayesian nonparametric methods capable of determining the number of latent variables to be used and their dimensionality. The popularization of Bayesian nonparametric statistics in the machine learning community is fairly recent. Their main attraction is the fact that they offer highly flexible models and their complexity scales appropriately with the amount of available data. In recent years, research on Bayesian nonparametric learning methods have focused on three main aspects: the construction of new models, the development of inference algorithms and new applications. This thesis presents our contributions to these three topics of research in the context of learning latent variables models. Firstly, we introduce the Pitman-Yor process mixture of Gaussians, a model for learning infinite mixtures of Gaussians. We also present an inference algorithm to discover the latent components of the model and we evaluate it on two practical robotics applications. Our results demonstrate that the proposed approach outperforms, both in performance and flexibility, the traditional learning approaches. Secondly, we propose the extended cascading Indian buffet process, a Bayesian nonparametric probability distribution on the space of directed acyclic graphs. In the context of Bayesian networks, this prior is used to identify the presence of latent variables and the network structure among them. A Markov Chain Monte Carlo inference algorithm is presented and evaluated on structure identification problems and as well as density estimation problems. Lastly, we propose the Indian chefs process, a model more general than the extended cascading Indian buffet process for learning graphs and orders. The advantage of the new model is that it accepts connections among observable variables and it takes into account the order of the variables. We also present a reversible jump Markov Chain Monte Carlo inference algorithm which jointly learns graphs and orders. Experiments are conducted on density estimation problems and testing independence hypotheses. This model is the first Bayesian nonparametric model capable of learning Bayesian learning networks with completely arbitrary graph structures.
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Christmas, Jacqueline. "Robust spatio-temporal latent variable models." Thesis, University of Exeter, 2011. http://hdl.handle.net/10036/3051.
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Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are widely-used mathematical models for decomposing multivariate data. They capture spatial relationships between variables, but ignore any temporal relationships that might exist between observations. Probabilistic PCA (PPCA) and Probabilistic CCA (ProbCCA) are versions of these two models that explain the statistical properties of the observed variables as linear mixtures of an alternative, hypothetical set of hidden, or latent, variables and explicitly model noise. Both the noise and the latent variables are assumed to be Gaussian distributed. This thesis introduces two new models, named PPCA-AR and ProbCCA-AR, that augment PPCA and ProbCCA respectively with autoregressive processes over the latent variables to additionally capture temporal relationships between the observations. To make PPCA-AR and ProbCCA-AR robust to outliers and able to model leptokurtic data, the Gaussian assumptions are replaced with infinite scale mixtures of Gaussians, using the Student-t distribution. Bayesian inference calculates posterior probability distributions for each of the parameter variables, from which we obtain a measure of confidence in the inference. It avoids the pitfalls associated with the maximum likelihood method: integrating over all possible values of the parameter variables guards against overfitting. For these new models the integrals required for exact Bayesian inference are intractable; instead a method of approximation, the variational Bayesian approach, is used. This enables the use of automatic relevance determination to estimate the model orders. PPCA-AR and ProbCCA-AR can be viewed as linear dynamical systems, so the forward-backward algorithm, also known as the Baum-Welch algorithm, is used as an efficient method for inferring the posterior distributions of the latent variables. The exact algorithm is tractable because Gaussian assumptions are made regarding the distribution of the latent variables. This thesis introduces a variational Bayesian forward-backward algorithm based on Student-t assumptions. The new models are demonstrated on synthetic datasets and on real remote sensing and EEG data.
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Paquet, Ulrich. "Bayesian inference for latent variable models." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613111.
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O'Sullivan, Aidan Michael. "Bayesian latent variable models with applications." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/19191.
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The massive increases in computational power that have occurred over the last two decades have contributed to the increasing prevalence of Bayesian reasoning in statistics. The often intractable integrals required as part of the Bayesian approach to inference can be approximated or estimated using intensive sampling or optimisation routines. This has extended the realm of applications beyond simple models for which fully analytic solutions are possible. Latent variable models are ideally suited to this approach as it provides a principled method for resolving one of the more difficult issues associated with this class of models, the question of the appropriate number of latent variables. This thesis explores the use of latent variable models in a number of different settings employing Bayesian methods for inference. The first strand of this research focusses on the use of a latent variable model to perform simultaneous clustering and latent structure analysis of multivariate data. In this setting the latent variables are of key interest providing information on the number of sub-populations within a heterogeneous data set and also the differences in latent structure that define them. In the second strand latent variable models are used as a tool to study relational or network data. The analysis of this type of data, which describes the interconnections between different entities or nodes, is complicated due to the dependencies between nodes induced by these connections. The conditional independence assumptions of the latent variable framework provide a means of taking these dependencies into account, the nodes are independent conditioned on an associated latent variable. This allows us to perform model based clustering of a network making inference on the number of clusters. Finally the latent variable representation of the network, which captures the structure of the network in a different form, can be studied as part of a latent variable framework for detecting differences between networks. Approximation schemes are required as part of the Bayesian approach to model estimation. The two methods that are considered in this thesis are stochastic Markov chain Monte Carlo methods and deterministic variational approximations. Where possible these are extended to incorporate model selection over the number of latent variables and a comparison, the first of its kind in this setting, of their relative performance in unsupervised model selection for a range of different settings is presented. The findings of the study help to ascertain in which settings one method may be preferred to the other.
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Zhang, Cheng. "Structured Representation Using Latent Variable Models." Doctoral thesis, KTH, Datorseende och robotik, CVAP, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-191455.
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Over the past two centuries the industrial revolution automated a great part of work that involved human muscles. Recently, since the beginning of the 21st century, the focus has shifted towards automating work that is involving our brain to further improve our lives. This is accomplished by establishing human-level intelligence through machines, which lead to the growth of the field of artificial intelligence. Machine learning is a core component of artificial intelligence. While artificial intelligence focuses on constructing an entire intelligence system, machine learning focuses on the learning ability and the ability to further use the learned knowledge for different tasks. This thesis targets the field of machine learning, especially structured representation learning, which is key for various machine learning approaches. Humans sense the environment, extract information and make action decisions based on abstracted information. Similarly, machines receive data, abstract information from data through models and make decisions about the unknown through inference. Thus, models provide a mechanism for machines to abstract information. This commonly involves learning useful representations which are desirably compact, interpretable and useful for different tasks. In this thesis, the contribution relates to the design of efficient representation models with latent variables. To make the models useful, efficient inference algorithms are derived to fit the models to data. We apply our models to various applications from different domains, namely E-health, robotics, text mining, computer vision and recommendation systems. The main contribution of this thesis relates to advancing latent variable models and deriving associated inference schemes for representation learning. This is pursued in three different directions. Firstly, through supervised models, where better representations can be learned knowing the tasks, corresponding to situated knowledge of humans. Secondly, through structured representation models, with which different structures, such as factorized ones, are used for latent variable models to form more efficient representations. Finally, through non-parametric models, where the representation is determined completely by the data. Specifically, we propose several new models combining supervised learning and factorized representation as well as a further model combining non-parametric modeling and supervised approaches. Evaluations show that these new models provide generally more efficient representations and a higher degree of interpretability. Moreover, this thesis contributes by applying these proposed models in different practical scenarios, demonstrating that these models can provide efficient latent representations. Experimental results show that our models improve the performance for classical tasks, such as image classification and annotations, robotic scene and action understanding. Most notably, one of our models is applied to a novel problem in E-health, namely diagnostic prediction using discomfort drawings. Experimental investigation show here that our model can achieve significant results in automatic diagnosing and provides profound understanding of typical symptoms. This motivates novel decision support systems for healthcare personnel.<br><p>QC 20160905</p>
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Surian, Didi. "Novel Applications Using Latent Variable Models." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14014.
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Latent variable models have achieved a great success in many research communities, including machine learning, information retrieval, data mining, natural language processing, etc. Latent variable models use an assumption that the data, which is observable, has an affinity to some hidden/latent variables. In this thesis, we present a suite of novel applications using latent variable models. In particular, we (i) extend topic models using directional distributions, (ii) propose novel solutions using latent variable models to detect outliers (anomalies) and (iii) to answer cross-modal retrieval problem. We present a study of directional distributions in modeling data. Specifically, we implement the von Mises-Fisher (vMF) distribution and develop latent variable models which are based on directed graphical models. The directed graphical models are commonly used to represent the conditional dependency among the variables. Under Bayesian treatment, we propose approximate posterior inference algorithms using variational methods for the models. We show that by incorporating the vMF distribution, the quality of clustering is improved rather than by using word count-based topic models. Furthermore, with the properties of directional distributions in hand, we extend the applications to detect outliers in various data sets and settings. Finally, we present latent variable models that are based on supervised learning to answer the cross-modal retrieval problem. In the cross-modal retrieval problem, the objective is to find matching content across different modalities such as text and image. We explore various approaches such as by using one-class learning methods, generating negative instances and using ranking methods. We show that our models outperform generic approaches such as Canonical Correlation Analysis (CCA) and its variants.
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Parsons, S. "Approximation methods for latent variable models." Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1513250/.
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Modern statistical models are often intractable, and approximation methods can be required to perform inference on them. Many different methods can be employed in most contexts, but not all are fully understood. The current thesis is an investigation into the use of various approximation methods for performing inference on latent variable models. Composite likelihoods are used as surrogates for the likelihood function of state space models (SSM). In chapter 3, variational approximations to their evaluation are investigated, and the interaction of biases as composite structure changes is observed. The bias effect of increasing the block size in composite likelihoods is found to balance the statistical benefit of including more data in each component. Predictions and smoothing estimates are made using approximate Expectation- Maximisation (EM) techniques. Variational EM estimators are found to produce predictions and smoothing estimates of a lesser quality than stochastic EM estimators, but at a massively reduced computational cost. Surrogate latent marginals are introduced in chapter 4 into a non-stationary SSM with i.i.d. replicates. They are cheap to compute, and break functional dependencies on parameters for previous time points, giving estimation algorithms linear computational complexity. Gaussian variational approximations are integrated with the surrogate marginals to produce an approximate EM algorithm. Using these Gaussians as proposal distributions in importance sampling is found to offer a positive trade-off in terms of the accuracy of predictions and smoothing estimates made using estimators. A cheap to compute model based hierarchical clustering algorithm is proposed in chapter 5. A cluster dissimilarity measure based on method of moments estimators is used to avoid likelihood function evaluation. Computation time for hierarchical clustering sequences is further reduced with the introduction of short-lists that are linear in the number of clusters at each iteration. The resulting clustering sequences are found to have plausible characteristics in both real and synthetic datasets.
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Oldmeadow, Christopher. "Latent variable models in statistical genetics." Thesis, Queensland University of Technology, 2009. https://eprints.qut.edu.au/31995/1/Christopher_Oldmeadow_Thesis.pdf.
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Understanding the complexities that are involved in the genetics of multifactorial diseases is still a monumental task. In addition to environmental factors that can influence the risk of disease, there is also a number of other complicating factors. Genetic variants associated with age of disease onset may be different from those variants associated with overall risk of disease, and variants may be located in positions that are not consistent with the traditional protein coding genetic paradigm. Latent Variable Models are well suited for the analysis of genetic data. A latent variable is one that we do not directly observe, but which is believed to exist or is included for computational or analytic convenience in a model. This thesis presents a mixture of methodological developments utilising latent variables, and results from case studies in genetic epidemiology and comparative genomics. Epidemiological studies have identified a number of environmental risk factors for appendicitis, but the disease aetiology of this oft thought useless vestige remains largely a mystery. The effects of smoking on other gastrointestinal disorders are well documented, and in light of this, the thesis investigates the association between smoking and appendicitis through the use of latent variables. By utilising data from a large Australian twin study questionnaire as both cohort and case-control, evidence is found for the association between tobacco smoking and appendicitis. Twin and family studies have also found evidence for the role of heredity in the risk of appendicitis. Results from previous studies are extended here to estimate the heritability of age-at-onset and account for the eect of smoking. This thesis presents a novel approach for performing a genome-wide variance components linkage analysis on transformed residuals from a Cox regression. This method finds evidence for a dierent subset of genes responsible for variation in age at onset than those associated with overall risk of appendicitis. Motivated by increasing evidence of functional activity in regions of the genome once thought of as evolutionary graveyards, this thesis develops a generalisation to the Bayesian multiple changepoint model on aligned DNA sequences for more than two species. This sensitive technique is applied to evaluating the distributions of evolutionary rates, with the finding that they are much more complex than previously apparent. We show strong evidence for at least 9 well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least 7 classes in an alignment of four mammals, including human. A pattern of enrichment and depletion of genic regions in the profiled segments suggests they are functionally significant, and most likely consist of various functional classes. Furthermore, a method of incorporating alignment characteristics representative of function such as GC content and type of mutation into the segmentation model is developed within this thesis. Evidence of fine-structured segmental variation is presented.
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Ridall, Peter Gareth. "Bayesian Latent Variable Models for Biostatistical Applications." Thesis, Queensland University of Technology, 2004. https://eprints.qut.edu.au/16164/1/Peter_Ridall_Thesis.pdf.
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In this thesis we develop several kinds of latent variable models in order to address
three types of bio-statistical problem. The three problems are the treatment
effect of carcinogens on tumour development, spatial interactions between plant
species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting
of measurements of compound muscle action potential (CMAP) area and amplitude.
Chapter 1 sets out the structure and the development of ideas presented
in this thesis from the point of view of: model structure, model selection, and
efficiency of estimation. Chapter 2 is an introduction to the relevant literature
that has in influenced the development of this thesis. In Chapter 3 we use the EM
algorithm for an application of an autoregressive hidden Markov model to describe
longitudinal counts. The data is collected from experiments to test the
effect of carcinogens on tumour growth in mice. Here we develop forward and
backward recursions for calculating the likelihood and for estimation. Chapter 4
is the analysis of a similar kind of data using a more sophisticated model, incorporating
random effects, but estimation this time is conducted from the Bayesian
perspective. Bayesian model selection is also explored. In Chapter 5 we move
to the two dimensional lattice and construct a model for describing the spatial
interaction of tree types. We also compare the merits of directed and undirected
graphical models for describing the hidden lattice. Chapter 6 is the application
of a Bayesian hierarchical model (MUNE), where the latent variable this time is
multivariate Gaussian and dependent on a covariate, the stimulus. Model selection
is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we
approach the same problem by using the reversible jump methodology (Green,
1995) where this time we use a dual Gaussian-Binary representation of the latent
data. We conclude in Chapter 8 with suggestions for the direction of new
work. In this thesis, all of the estimation carried out on real data has only been
performed once we have been satisfied that estimation is able to retrieve the parameters
from simulated data.
Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov
models (HMM), latent variable models, longitudinal data analysis, motor unit
disease (MND), partially ordered Markov models (POMMs), the pseudo auto-
logistic model, reversible jump, spatial interactions.
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Ridall, Peter Gareth. "Bayesian Latent Variable Models for Biostatistical Applications." Queensland University of Technology, 2004. http://eprints.qut.edu.au/16164/.
Full textAbstract:
In this thesis we develop several kinds of latent variable models in order to address three types of bio-statistical problem. The three problems are the treatment effect of carcinogens on tumour development, spatial interactions between plant species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting of measurements of compound muscle action potential (CMAP) area and amplitude. Chapter 1 sets out the structure and the development of ideas presented in this thesis from the point of view of: model structure, model selection, and efficiency of estimation. Chapter 2 is an introduction to the relevant literature that has in influenced the development of this thesis. In Chapter 3 we use the EM algorithm for an application of an autoregressive hidden Markov model to describe longitudinal counts. The data is collected from experiments to test the effect of carcinogens on tumour growth in mice. Here we develop forward and backward recursions for calculating the likelihood and for estimation. Chapter 4 is the analysis of a similar kind of data using a more sophisticated model, incorporating random effects, but estimation this time is conducted from the Bayesian perspective. Bayesian model selection is also explored. In Chapter 5 we move to the two dimensional lattice and construct a model for describing the spatial interaction of tree types. We also compare the merits of directed and undirected graphical models for describing the hidden lattice. Chapter 6 is the application of a Bayesian hierarchical model (MUNE), where the latent variable this time is multivariate Gaussian and dependent on a covariate, the stimulus. Model selection is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we approach the same problem by using the reversible jump methodology (Green, 1995) where this time we use a dual Gaussian-Binary representation of the latent data. We conclude in Chapter 8 with suggestions for the direction of new work. In this thesis, all of the estimation carried out on real data has only been performed once we have been satisfied that estimation is able to retrieve the parameters from simulated data. Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto- logistic model, reversible jump, spatial interactions.
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Dominicus, Annica. "Latent variable models for longitudinal twin data." Doctoral thesis, Stockholm : Mathematical statistics, Dept. of mathematics, Stockholm university, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-848.
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Burridge, C. Y. "Latent variable models for genotype-environment interaction." Thesis, University of Reading, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383469.
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Albanese, Maria Teresinha. "Latent variable models for binary response data." Thesis, London School of Economics and Political Science (University of London), 1990. http://etheses.lse.ac.uk/1220/.
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Most of the results in this thesis are obtained for the logit/probit model for binary response data given by Bartholomew (1980), which is sometimes called the two-parameter logistic model. In most the cases the results also hold for other common binary response models. By profiling and an approximation, we investigate the behaviour of the likelihood function, to see if it is suitable for ML estimation. Particular attention is given to the shape of the likelihood around the maximum point in order to see whether the information matrix will give a good guide to the variability of the estimates. The adequacy of the asymptotic variance-covariance matrix is inwestigated through jackknife and bootstrap techniques. We obtain the marginal ML estimators for the Rasch model and compare them with those obtained from conditional ML estimation. We also test the fit of the Rasch model against a logit/probit model with a likelihood ratio test, and investigate the behaviour of the likelihood function for the Rasch model and its bootstrap estimates together with approximate methods. For both fixed and decreasing sample size, we investigate the stability of the discrimination parameter estimates ai, 1 when the number of items is reduced. We study the conditions which give rise to large discrimination parameter estimates. This leads to a method for the generation of a (p+1)th item with any fixed ap+1,1 and ap+1,0. In practice it is importante to measure the latent variable and this is usually done by using the posterior mean or the component scores. We give some theoretical and applied results for the relation between the linearity of the plot of the posterior mean latent variable values, the component scores and the normality of those posterior distributions.
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Fusi, Nicolo. "Probabilistic latent variable models in statistical genomics." Thesis, University of Sheffield, 2015. http://etheses.whiterose.ac.uk/8326/.
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In this thesis, we propose different probabilistic latent variable mod- els to identify and capture the hidden structure present in commonly studied genomics datasets. We start by investigating how to cor- rect for unwanted correlations due to hidden confounding factors in gene expression data. This is particularly important in expression quantitative trait loci (eQTL) studies, where the goal is to identify associations between genetic variants and gene expression levels. We start with a na¨ ıve approach, which estimates the latent factors from the gene expression data alone, ignoring the genetics, and we show that it leads to a loss of signal in the data. We then highlight how, thanks to the formulation of our model as a probabilistic model, it is straightforward to modify it in order to take into account the specific properties of the data. In particular, we show that in the na¨ ıve ap- proach the latent variables ”explain away” the genetic signal, and that this problem can be avoided by jointly inferring these latent variables while taking into account the genetic information. We then extend this, so far additive, model to additionally detect interactions between the latent variables and the genetic markers. We show that this leads to a better reconstruction of the latent space and that it helps dis- secting latent variables capturing general confounding factors (such as batch effects) from those capturing environmental factors involved in genotype-by-environment interactions. Finally, we investigate the effects of misspecifications of the noise model in genetic studies, show- ing how the probabilistic framework presented so far can be easily ex- tended to automatically infer non-linear monotonic transformations of the data such that the common assumption of Gaussian distributed residuals is respected.
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Ruffini, Matteo. "Learning latent variable models : efficient algorithms and applications." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/665817.
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Learning latent variable models is a fundamental machine learning problem, and the models belonging to this class - which include topic models, hidden Markov models, mixture models and many others - have a variety of real-world applications, like text mining, clustering and time series analysis.
For many practitioners, the decade-old Expectation Maximization method (EM) is still the tool of choice, despite its known proneness to local minima and long running times. To overcome these issues, algorithms based on the spectral method of moments have been recently proposed. These techniques recover the parameters of a latent variable model by solving - typically via tensor decomposition - a system of non-linear equations relating the low-order moments of the observable data with the parameters of the model to be learned. Moment-based algorithms are in general faster than EM as they require a single pass over the data, and have provable guarantees of learning accuracy in polynomial time. Nevertheless, methods of moments have room for improvements: their ability to deal with real-world data is often limited by a lack of robustness to input perturbations. Also, almost no theory studies their behavior when some of the model assumptions are violated by the input data. Extending the theory of methods of moments to learn latent variable models and providing meaningful applications to real-world contexts is the focus of this thesis.
ssuming data to be generated by a certain latent variable model, the standard approach of methods of moments consists of two steps: first, finding the equations that relate the moments of the observable data with the model parameters and then, to solve these equations to retrieve estimators of the parameters of the model. In Part I of this thesis we will focus on both steps, providing and analyzing novel and improved model-specific moments estimators and techniques to solve the equations of the moments. In both the cases we will introduce theoretical results, providing guarantees on the behavior of the proposed methods, and we will perform experimental comparisons with existing algorithms. In Part II, we will analyze the behavior of methods of moments when data violates some of the model assumptions performed by a user. First, we will observe that in this context most of the theoretical infrastructure underlying methods of moments is not valid anymore, and consequently we will develop a theoretical foundation to methods of moments in the misspecified setting, developing efficient methods, guaranteed to provide meaningful results even when some of the model assumptions are violated.
During all the thesis, we will apply the developed theoretical results to challenging real-world applications, focusing on two main domains: topic modeling and healthcare analytics. We will extend the existing theory of methods of moments to learn models that are traditionally used to do topic modeling – like the single-topic model and Latent Dirichlet Allocation – providing improved learning techniques and comparing them with existing methods, which we prove to outperform in terms of speed and learning accuracy. Furthermore, we will propose applications of latent variable models to the analysis of electronic healthcare records, which, similarly to text mining, are very likely to become massive datasets; we will propose a method to discover recurrent phenotypes in populations of patients and to cluster them in groups with similar clinical profiles - a task where the efficiency properties of methods of moments will constitute a competitive advantage over traditional approaches.<br>Aprender modelos de variable latente es un problema fundamental de machine learning, y los modelos que pertenecen a esta clase, como topic models, hidden Markov models o mixture models, tienen muchas aplicaciones en el mundo real, por ejemplo text mining, clustering y time series analysis. El método de Expectation Maximization (EM) sigue siendo la herramienta más utilizada, a pesar de su conocida tendencia a producir soluciones subóptimas y sus largos tiempos de ejecución. Para superar estos problemas, se han propuesto recientemente algoritmos basados en el método de los momentos. Estas técnicas aprenden los parámetros de un modelo resolviendo un sistema de ecuaciones no lineales que relacionan los momentos de los datos observables con los parámetros del modelo que se debe aprender. Los métodos de los momentos son en general más rápidos que EM, ya que requieren una sola pasada sobre los datos y tienen garantías de producir estimadores consistentes en tiempo polinomial. A pesar de estas ventajas, los métodos de los momentos todavía tienen margen de mejora: cuando se utilizan con datos reales, los métodos de los momentos se revelan inestables, con una fuerte sensibilidad a las perturbaciones. Además, las garantías de estos métodos son válidas solo si el usuario conoce el modelo probabilístico que genera los datos, y no existe alguna teoría que estudie lo que pasa cuando ese modelo es desconocido o no correctamente especificado. El objetivo de esta tesis es ampliar la teoría de métodos de los momentos, estudiar sus aplicaciones para aprender modelos de variable latente, extendiendo la teoría actual. Además se proporcionarán aplicaciones significativas a contextos reales. Típicamente, el método de los momentos consta de de dos partes: primero, encontrar las ecuaciones que relacionan los momentos de los datos observables con los parámetros del modelo y segundo, resolver estas ecuaciones para recuperar estimadores consistentes de los parámetros del modelo. En la Parte I de esta tesis, nos centraremos en ambos pasos, proporcionando y analizando nuevos estimadores de momentos para una variedad de modelos, y técnicas para resolver las ecuaciones de los momentos. En ambos casos, introduciremos resultados teóricos, proporcionaremos garantías sobre el comportamiento de los métodos propuestos y realizaremos comparaciones experimentales con algoritmos existentes. En la Parte II, analizaremos el comportamiento de los métodos de los momentos cuando algunas de las hipótesis de modelo se encuentran violadas por los datos. Como primera cosa, observaremos que en este contexto, la mayoría de la infraestructura teórica que subyace a estos métodos pierde de validez y, por lo tanto, desarrollaremos una base teórica nueva, presentando métodos eficientes, garantizados para proporcionar resultados razonables incluso cuando algunas de las hipótesis del modelo son violadas. En toda la tesis aplicamos los resultados obtenidos a nivel teórico a aplicaciones del mundo real, centrándonos en dos áreas principales: topic modeling y healthcare analytics. Ampliamos la teoría existente de los métodos de momentos para aprender los modelos que se usan tradicionalmente en el ámbito de topic modeling, como el single-topic model y la Latent Dirichlet Allocation, proporcionando nuevas técnicas de aprendizaje y comparándolas con los métodos existentes. Además, estudiamos aplicaciones de modelos de variable latente en el análisis de datos del ámbito healthcare; proponemos un método para descubrir fenotipos recurrentes en poblaciones de pacientes y agruparlos en clusters con perfiles clínicos similares, una tarea donde las propiedades de eficiencia de los métodos de los momentos constituyen una ventaja competitiva sobre los métodos tradicionales.
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Rastelli, Riccardo, and Nial Friel. "Optimal Bayesian estimators for latent variable cluster models." Springer Nature, 2018. http://dx.doi.org/10.1007/s11222-017-9786-y.
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In cluster analysis interest lies in probabilistically
capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.
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Qiu, David. "Embedding and latent variable models using maximal correlation." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/108977.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 45-46).<br>Finding low dimensional latent variable models is a useful technique in inferring unobserved affinity between unobserved co-occurrences. We explore using maximal correlation and the alternating conditional expectation algorithm to construct embeddings one dimensional at a time to maximally preserve the linear correlation in the embedding space. Each dimension is enforced to be orthogonal to all other dimensions to not encode redundant information. Intuitively, we want to map objects that frequently co-occur to be close in the embedding space. However, often there are unobserved or under-sampled pairs that skew the result. We derive simple regularization techniques to compensate for those outliers. Additionally, optimizing for the preservation of maximal correlations after processing lets us induce informative soft clustering and mixture models. Empirical results on natural language processing datasets show that our technique performs comparably to popular word embedding algorithms.<br>by David Qiu.<br>S.M.
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Harvey, Morgan A. "Bayesian latent variable models for the collaborative Web." Thesis, University of Strathclyde, 2011. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=16822.
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Svebrant, Henrik. "Latent variable neural click models for web search." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-232311.
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User click modeling in web search is most commonly done through probabilistic graphical models. Due to the successful use of machine learning techniques in other fields of research, it is interesting to evaluate how machine learning can be applied to click modeling. In this thesis, modeling is done using recurrent neural networks trained on a distributed representation of the state of the art user browsing model (UBM). It is further evaluated how extending this representation with a set of latent variables that are easily derivable from click logs, can affect the model's prediction performance. Results show that a model using the original representation does not perform very well. However, the inclusion of simple variables can drastically increase the performance regarding the click prediction task. For which it manages to outperform the two chosen baseline models, which themselves are well performing already. It also leads to increased performance for the relevance prediction task, although the results are not as significant. It can be argued that the relevance prediction task is not a fair comparison to the baseline functions, due to them needing more significant amounts of data to learn the respective probabilities. However, it is favorable that the neural models manage to perform quite well using smaller amounts of data. It would be interesting to see how well such models would perform when trained on far greater data quantities than what was used in this project. Also tailoring the model for the use of LSTM, which supposedly could increase performance even more. Evaluating other representations than the one used would also be of interest, as this representation did not perform remarkably on its own.<br>Klickmodellering av användare i söksystem görs vanligtvis med hjälp av probabilistiska modeller. På grund av maskininlärningens framgångar inom andra områden är det intressant att undersöka hur dessa tekniker kan appliceras för klickmodellering. Detta examensarbete undersöker klickmodellering med hjälp av recurrent neural networks tränade på en distribuerad representation av en populär och välpresterande klickmodell benämnd user browsing model (UBM). Det undersöks vidare hur utökandet av denna representation med statistiska variabler som enkelt kan utvinnas från klickloggar, kan påverka denna modells prestanda. Resultaten visar att grundrepresentationen inte presterar särskilt bra. Däremot har användningen av simpla variabler visats medföra drastiska prestandaökningar när det kommer till att förutspå en användares klick. I detta syfte lyckas modellerna prestera bättre än de två baselinemodeller som valts, vilka redan är välpresterande för syftet. De har även lyckats förbättra modellernas förmåga att förutspå relevans, fastän skillnaderna inte är lika drastiska. Relevans utgör inte en lika jämn jämförelse gentemot baselinemodellerna, då dessa kräver mycket större datamängder för att nå verklig prestanda. Det är däremot fördelaktigt att de neurala modellerna når relativt god prestanda för datamängden som använts. Det vore intressant att undersöka hur dessa modeller skulle prestera när de tränas på mycket större datamängder än vad som använts i detta projekt. Även att skräddarsy modellerna för LSTM, vilket borde kunna öka prestandan ytterligare. Att evaluera andra representationer än den som användes i detta projekt är också av intresse, då den använda representationen inte presterade märkvärdigt i sin grundform.
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Katsikatsou, Myrsini. "Composite Likelihood Estimation for Latent Variable Models with Ordinal and Continuous, or Ranking Variables." Doctoral thesis, Uppsala universitet, Statistiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-188342.
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The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator. The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters. In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones. The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper. The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11).
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Heiss, Florian. "Essays on Specification and Estimation of Latent Variable Models." [S.l. : s.n.], 2005. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11947811.
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Newman, Keith. "Bayesian modelling of latent Gaussian models featuring variable selection." Thesis, University of Newcastle upon Tyne, 2017. http://hdl.handle.net/10443/3700.
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Latent Gaussian models are popular and versatile models for performing Bayesian inference. In many cases, these models will be analytically intractable creating a need for alternative inference methods. Integrated nested Laplace approximations (INLA) provides fast, deterministic inference of approximate posterior densities by exploiting sparsity in the latent structure of the model. Markov chain Monte Carlo (MCMC) is often used for Bayesian inference by sampling from a target posterior distribution. This suffers poor mixing when many variables are correlated, but careful reparameterisation or use of blocking methods can mitigate these issues. Blocking comes with additional computational overheads due to the matrix algebra involved; these costs can be limited by harnessing the same latent Markov structures and sparse precision matrix properties utilised by INLA, with particular attention paid to efficient matrix operations. We discuss how linear and latent Gaussian models can be constructed by combining methods for linear Gaussian models with Gaussian approximations. We then apply these ideas to a case study in detecting genetic epistasis between telomere defects and deletion of non-essential genes in Saccharomyces cerevisiae, for an experiment known as Quantitative Fitness Analysis (QFA). Bayesian variable selection is included to identify which gene deletions cause a genetic interaction. Previous Bayesian models have proven successful in detecting interactions but time-consuming due to the complexity of the model and poor mixing. Linear and latent Gaussian models are created to pursue more efficient inference over standard Gibbs samplers, but we find inference methods for latent Gaussian models can struggle with increasing dimension. We also investigate how the introduction of variable selection provides opportunities to reduce the dimension of the latent model structure for potentially faster inference. Finally, we discuss progress on a new follow-on experiment, Mini QFA, which attempts to find epistasis between telomere defects and a pair of gene deletions.
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Lu, Yu. "Statistical and Computational Guarantees for Learning Latent Variable Models." Thesis, Yale University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10783452.
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<p> Latent variable models are widely used to capture the underlying structures of the data, for example, Gaussian mixture models for speech recognition, stochastic block models for community detection and topic models for information retrieval. While alternative minimization based algorithms such as EM algorithm and Lloyd's algorithm performs well in practice, there has been little theoretical advancement in explaining the effectiveness of these algorithms. In this thesis, we investigate the performance of Lloyd's algorithm and EM algorithm on clustering two-mixture of Gaussians. With an initializer slightly better than random guess, we are able to show the linear converge of Lloyd's and EM iterations to the statistical optimal estimator. These results shed light on the global convergence of more general non-convex optimizations.</p><p> We generalized the results to arbitrary number of sub-Gaussian mixtures. Motivated by the Lloyd's algorithm, we propose new algorithms for other latent variable models including sparse gaussian mixture model, stochastic block model. biclustering model and Dawid-Skene model. The proposed algorithms are computationally efficient and shown to be rate-optimal under mild signal-to-noise ratio conditions. The highlight of our theoretical analysis is to develop new proof techniques to handle the dependency between iterations, which can be applied to other iterative algorithms with explicit iteration formulas. </p><p>
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Hore, Victoria. "Latent variable models for analysing multidimensional gene expression data." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:ec62bc11-5c3f-467d-9ff3-f3c4eb29d140.
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Multi-tissue gene expression studies give rise to 3D arrays of data. These experiments make it possible to study the tissue-specific nature of gene regulation and also the relationship between genotypes and higher level traits such as disease status. Analysing these multidimensional data sets is a statistical challenge, as they contain high noise levels and missing data. In this thesis I introduce a new approach for analysing multidimensional gene expression data sets called SPIDER (SParse Integrated DEcomposition for RNA-sequencing). SPIDER is a sparse Bayesian tensor decomposition that models the data as a sum of components (or factors). Each component consists of three vectors of scores or loadings that describe modes of variation across individuals, genes and tissues. Sparsity is induced in the components using a spike and slab prior, allowing for recovery of sparse structure in the data. The decomposition is easily extended to jointly decompose several data types, handle missing data and allow for relatedness between individuals, another common problem in genetics. Inference for the model is performed using variational Bayes. SPIDER is compared to existing approaches for decomposing multidimensional data via simulations. Results suggest that SPIDER performs comparably to, or better than, existing approaches and particularly well when the underlying signals are very sparse. Additional simulations designed to contain realistic levels of signal and noise suggest that SPIDER has the power to recover gene networks from gene expression data. I have applied SPIDER to gene expression data measured using RNA-sequencing for 845 individuals in three tissues from the TwinsUK cohort. Estimated components were tested for association with genetic variation genome-wide. Five signals describing gene regulation networks driven by genetic variants are uncovered, building on the current understanding of these pathways. In addition, components uncovering effects of experimental artefacts and covariates were also recovered from the data.
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SIMONETTO, ANNA. "Estimation procedures for latent variable models with psychological traits." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/17370.
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The starting point for this thesis is a concrete problem: to measure, using
statistical models, aspects of subjective perceptions and assessments and to
understand their dependencies. The objective is to study the
statistical properties of some estimators of the parameters of regression models
with variables affected by measurement errors. These models are widely
used in surveys based on questionnaires developed to detect subjective assessments
and perceptions with Likert-type scales. It is a highly debated topic,
as many of the relevant aspects in this field are not directly observable and
therefore the variables used to estimate them are affected by measurement
errors. The models with measurement errors were very thorough in literature. In this work we will
developed two of the most used approaches that the authors have with this topic. Obviously, according to the approach chosen,
different models were proposed to estimate the relationships between
variables affected by measurement error. After exposing the main features
of these models, the thesis focuses on providing an original contribution to
comparative analysis of the two presented approaches.
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Kaban, Ata. "Latent variable models with application to text based document representation." Thesis, University of the West of Scotland, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365082.
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Das, Dipanjan. "Semi-Supervised and Latent-Variable Models of Natural Language Semantics." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/342.
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This thesis focuses on robust analysis of natural language semantics. A primary bottleneck for semantic processing of text lies in the scarcity of high-quality and large amounts of annotated data that provide complete information about the semantic structure of natural language expressions. In this dissertation, we study statistical models tailored to solve problems in computational semantics, with a focus on modeling structure that is not visible in annotated text data. We first investigate supervised methods for modeling two kinds of semantic phenomena in language. First, we focus on the problem of paraphrase identification, which attempts to recognize whether two sentences convey the same meaning. Second, we concentrate on shallow semantic parsing, adopting the theory of frame semantics (Fillmore, 1982). Frame semantics offers deep linguistic analysis that exploits the use of lexical semantic properties and relationships among semantic frames and roles. Unfortunately, the datasets used to train our paraphrase and frame-semantic parsing models are too small to lead to robust performance. Therefore, a common trait in our methods is the hypothesis of hidden structure in the data. To this end, we employ conditional log-linear models over structures, that are firstly capable of incorporating a wide variety of features gathered from the data as well as various lexica, and secondly use latent variables to model missing information in annotated data. Our approaches towards solving these two problems achieve state-of-the-art accuracy on standard corpora. For the frame-semantic parsing problem, we present fast inference techniques for jointly modeling the semantic roles of a given predicate. We experiment with linear program formulations, and use a commercial solver as well as an exact dual decomposition technique that breaks the role labeling problem into several overlapping components. Continuing with the theme of hypothesizing hidden structure in data for modeling natural language semantics, we present methods to leverage large volumes of unlabeled data to improve upon the shallow semantic parsing task. We work within the framework of graph-based semi-supervised learning, a powerful method that associates similar natural language types, and helps propagate supervised annotations to unlabeled data. We use this framework to improve frame-semantic parsing performance on unknown predicates that are absent in annotated data. We also present a family of novel objective functions for graph-based learning that result in sparse probability measures over graph vertices, a desirable property for natural language types. Not only are these objectives easier to numerically optimize, but also they result in smoothed distributions over predicates that are smaller in size. The experiments presented in this dissertation empirically demonstrates that missing information in text corpora contain considerable semantic information that can be incorporated into structured models for semantics, to significant benefit over the current state of the art. The methods in this thesis were originally presented by Das and Smith (2009, 2011, 2012), and Das et al. (2010, 2012). The thesis gives a more thorough exposition, relating and comparing the methods, and also presents several extensions of the aforementioned papers.
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Humphreys, Keith. "Latent variable models for discrete longitudinal data with measurement error." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295045.
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Saeedi, Ardavan. "Latent variable models for understanding user behavior in software applications." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115779.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 147-157).<br>Understanding user behavior in software applications is of significant interest to software developers and companies. By having a better understanding of the user needs and usage patterns, the developers can design a more efficient workflow, add new features, or even automate the user's workflow. In this thesis, I propose novel latent variable models to understand, predict and eventually automate the user interaction with a software application. I start by analyzing users' clicks using time series models; I introduce models and inference algorithms for time series segmentation which are scalable to large-scale user datasets. Next, using a conditional variational autoencoder and some related models, I introduce a framework for automating the user interaction with a software application. I focus on photo enhancement applications, but this framework can be applied to any domain where segmentation, prediction and personalization is valuable. Finally, by combining sequential Monte Carlo and variational inference, I propose a new inference scheme which has better convergence properties than other reasonable baselines.<br>by Ardavan Saeedi.<br>Ph. D.
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Xi, Nuo. "The Sample Average Approximation Method for Estimating Latent Variable Models." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1228060675.
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Ren, Chunfeng. "LATENT VARIABLE MODELS GIVEN INCOMPLETELY OBSERVED SURROGATE OUTCOMES AND COVARIATES." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3473.
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Latent variable models (LVMs) are commonly used in the scenario where the outcome of the main interest is an unobservable measure, associated with multiple observed surrogate outcomes, and affected by potential risk factors. This thesis develops an approach of efficient handling missing surrogate outcomes and covariates in two- and three-level latent variable models. However, corresponding statistical methodologies and computational software are lacking efficiently analyzing the LVMs given surrogate outcomes and covariates subject to missingness in the LVMs. We analyze the two-level LVMs for longitudinal data from the National Growth of Health Study where surrogate outcomes and covariates are subject to missingness at any of the levels. A conventional method for efficient handling of missing data is to reexpress the desired model as a joint distribution of variables, including the surrogate outcomes that are subject to missingness conditional on all of the covariates that are completely observable, and estimate the joint model by maximum likelihood, which is then transformed to the desired model. The joint model, however, identifies more parameters than desired, in general. The over-identified joint model produces biased estimates of LVMs so that it is most necessary to describe how to impose constraints on the joint model so that it has a one-to-one correspondence with the desired model for unbiased estimation. The constrained joint model handles missing data efficiently under the assumption of ignorable missing data and is estimated by a modified application of the expectation-maximization (EM) algorithm.
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PENNONI, FULVIA. "Issues on the Estimation of Latent Variable and Latent Class Models with Social Science Applications." Doctoral thesis, Università degli Studi di Firenze, 2004. http://hdl.handle.net/10281/46004.
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This Ph.D. work is made of different reseach problems which have in common the precence of latent variables.
Chapters 1 and 2 provide accessible primer on the models developped in the subsequent chapters. Chapters 3 and 4 are written in form of articles. A list of references at the end of each chapter is provided and a general bibliography is also reported as last part of the work.
The first chapter introduces the models of depedence and association and their interpretation using graphical models which have been proved useful to display in graphical form the essential relationships between variables. The structure of the graph yields direct information about various aspects related to the statistical analysis. At first we provide the necessary notation and background on graph theory. We describe the Markov properties that associate a set of conditional independence assumptions to an undirected and directed graph. Such definitions does not depend of any particular distributional form and hence can be applied to models with both discrete and continuous random variables. In particular we consider models for Gaussian continuous variables where the structure is assumed to be adequately described via a vector of means and by a covariance matrix. The concentration and the covariance graphs models are illustrated. The specification of the complex multivariate distribution through univariate regressions induced by a Directed Acyclic Graph (DAG) can be regarded as a simplification, as the single regression models typically involve considerably fewer variables than the whole multivariate vector.
In the present work it is shown that such models are a subclass of the structural equation models developed for linear analysis known as Structural Equation Models (SEM)
The chapter is concluded by some bibliographical notes.
Chapter 2 takes into account the latent class model for measuring one or more latent categorical variables by means of a set of observed categorical variables. After some notes on the model identifiability and estimation we consider the model extension to study latent changes over time when longitudinal studies are used. The hidden Markov model is presented cosisting of hidden state variables and observed variables both varying over time.
In Chapter 3 we consider in detail the DAG Gaussian models in which one of the variables is not observed. Once the condition for global identification has been satisfied, we show how the incomplete log-likelihood of the observed data can be maximize using the EM algorithm. As the EM does not provide the matrix of the second derivatives we propose a method for obtaining an explicit formula of the observed information matrix using the missing information principle. We illustrate the models with two examples on real data concerning the educational attainement and criminological research.
The first appendix of the chapter reports details on the calculations of the quantities necessary for the E-step of the EM algorithm. The second appendix reports the code of the statistical software R to get the estimated standard errors, which may implemented in the R package called ggm.
Chapter 4 starts from the practical problem of classifying criminal activity. The latent class cluster model is extended by proposing a latent class model that also incorporates the longitudinal structure of data using a method similar to a local likelihood approach. The data set which is taken from the Home Office Offenders Index of England and Wales. It contains the complete criminal histories of a sample of those born in 1953 and followed for forty years.
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Hagger-Johnson, Gareth. "Latent variable modelling of personality-health associations : measures, models and extensions." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/3490.
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Functional health status, morbidity and mortality are determined partly by health behaviours (World Health Organization, 2002), which have determinants of their own. Personality traits, such as Conscientiousness, have a strong association with health behaviours (Bogg & Roberts, 2004). There is a less consistent and generally weaker association between traits and health outcomes (e.g. Neuroticism and mortality). The central problem in this thesis is how to measure, model, maximize, and extend trait-health associations. Conceptual issues associated with modelling traits and health are discussed in chapter one. The next three chapters concern such measurement issues about: personality traits (chapter two), health behaviours (chapter three) and health outcomes, with particular reference to functional health status (chapter four). These chapters are followed by a move to modelling (chapter five), with particular reference to the generalized latent variable modelling (LVM) framework (Muth´en & Muth´en, 1998–2007). The HAPPLE study is introduced (chapter six) which is used to model associations between Conscientiousness and health criteria within the LVMframework (chapter seven). Moving beyond self-reported outcomes, which are a mono-method approach, the role of multiple health behaviours in predicting cardiovascular mortality is considered (chapter eight). In a third section, cortisol is introduced, which is a biomarker of stress reactivity. The diurnal profile of cortisol output is described (chapter nine). Latent growth curve modelling is used to illustrate its association with Neuroticism, in a sample of student volunteers (chapter 10). Taken together, the results highlight the need for a general framework of modelling techniques, in personality-health research. I conclude that biopsychosocial models with excellent explanatory power, which are still parsimonious, can be achieved with LVM and its extensions. However, trait researchers will need to state more clearly the intended destinations of their work in order to attract contributions from, and share knowledge with, other disciplines.
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Carreira-Perpinan, Miguel Angel. "Continuous latent variable models for dimensionality reduction and sequential data reconstruction." Thesis, University of Sheffield, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369991.
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Song, Dogyoon. "Blind regression : nonparametric regression for latent variable models via collaborative filtering." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105958.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 77-81).<br>Recommender systems are tools that provide suggestions for items that are most likely to be of interest to a particular user; they are central to various decision making processes so that recommender systems have become ubiquitous. We introduce blind regression, a framework motivated by matrix completion for recommender systems: given m users, n items, and a subset of user-item ratings, the goal is to predict the unobserved ratings given the data, i.e., to complete the partially observed matrix. We posit that user u and movie i have features x1(u) and x2(i) respectively, and their corresponding rating y(u, i) is a noisy measurement of f(x1(u), x2(i)) for some unknown function f. In contrast to classical regression, the features x = (x1(u), x2(i)) are not observed (latent), making it challenging to apply standard regression methods. We suggest a two-step procedure to overcome this challenge: 1) estimate distance for latent variables, and then 2) apply nonparametric regression. Applying this framework to matrix completion, we provide a prediction algorithm that is consistent for all Lipschitz functions. In fact, the analysis naturally leads to a variant of collaborative filtering, shedding insight into the widespread success of collaborative filtering. Assuming each entry is revealed independently with p = max(m-1+[delta], n-1/2+[delta]) for [delta] > 0, we prove that the expected fraction of our estimates with error greater than [epsilon] is less than [gamma]2/[epsilon]2, plus a polynomially decaying term, where [gamma]2 is the variance of the noise. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides principled improvements over basic collaborative filtering and is competitive with matrix factorization methods. The algorithm and analysis naturally extend to higher order tensor completion by simply flattening the tensor into a matrix. We show that our simple and principled approach is competitive with respect to state-of-art tensor completion algorithms when applied to image inpainting data. Lastly, we conclude this thesis by proposing various related directions for future research.<br>by Dogyoon Song.<br>S.M.
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Mccready, Carlyle. "Latent Variable Models for Longitudinal Outcomes from a Parenting Intervention Study." Master's thesis, Faculty of Science, 2019. https://hdl.handle.net/11427/31822.
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This research project analysed data collected with the use of self-reporting questionnaires and observational video scores in order to determine the level of success achieved by the Sinovuyo Caring Families Programme (SCFP). The SCFP aimed to reduce harsh parenting practices and child behavioural problems in high-risk South African families. This research project examined the use of structural equation modelling (SEM) for longitudinal profiles and latent growth mediation modelling. Improved behaviour was observed in terms of reported child behaviour problems and reported harsh parenting with differences between the intervention and control groups directly after the completion of the 3-month intervention program. Improved behaviour was also observed in terms of reported positive parenting with differences between the intervention and control groups directly after the completion of the 3- month intervention program and at the 12-month follow-up occasion. No improvement in observed child behaviour was mediated through reported positive parenting or reported harsh parenting. Furthermore, the intervention program led to improved positive parenting behaviour directly after the 3-month intervention period, however the improved behaviour of the parent did not act as a mediating variable and no improvement in child behaviour was observed as a result.
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Vegelius, Johan. "Non-Linear Latent Variable Models: A Study of Factor Score Approaches." Thesis, Uppsala universitet, Statistiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-326330.
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Non-linear latent variable models are associated with problems which are difficult to handle in applied sciences. Four methods for estimating factor scores, with the purpose of estimating latent variable models with an interaction term, were investigated. The LISREL procedure provided inconsistent estimates of the interaction term for all sample sizes and distributions of the latent exogenous variables. The Bartlett-Thompson approach yielded consistent estimates only when the distribution of the latent exogenous variables was normal, whereas the Hoshino-Bentler and adjusted LISREL approaches yielded consistency for all distributions of the latent exogenous variables. In the Bartlett-Thompson and LISREL approaches the interaction term is formed from multiplying latent variable scores, whereas in the Hoshino-Bentler and adjusted LISREL approaches the interaction term is treated as yet another factor which is freely estimated. It was, hence, concluded that the methods treating the interaction term as a factor were more appropriate (in terms of consistency and robustness) than those using products of factor scores for estimating the latent variable model.
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Aurstad, Tore. "Interactive removal of outlier points in latent variable models using virtual reality." Thesis, Norwegian University of Science and Technology, Department of Computer and Information Science, 2005. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9159.
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<p>This report investigates different methods in computer graphics and virtual reality that can be applied to develop a system that provides analysis for the changes that occur when removing outlier points in plots for principal component analysis. The main results of the report show that the use of animation gives a better understanding for the movement of individual points in the plots, before and after removal.</p>
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Köhler, Carmen [Verfasser]. "Isn’t Something Missing? Latent Variable Models Accounting for Item Nonresponse / Carmen Köhler." Berlin : Freie Universität Berlin, 2017. http://d-nb.info/112357216X/34.
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Foulds, James Richard. "Latent Variable Modeling for Networks and Text| Algorithms, Models and Evaluation Techniques." Thesis, University of California, Irvine, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3631094.
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<p> In the era of the internet, we are connected to an overwhelming abundance of information. As more facets of our lives become digitized, there is a growing need for automatic tools to help us find the content we care about. To tackle the problem of information overload, a standard machine learning approach is to perform dimensionality reduction, transforming complicated high-dimensional data into a manageable, low-dimensional form. Probabilistic latent variable models provide a powerful and elegant framework for performing this transformation in a principled way. This thesis makes several advances for modeling two of the most ubiquitous types of online information: networks and text data. </p><p> Our first contribution is to develop a model for social networks as they vary over time. The model recovers latent feature representations of each individual, and tracks these representations as they change dynamically. We also show how to use text information to interpret these latent features. </p><p> Continuing the theme of modeling networks and text data, we next build a model of citation networks. The model finds influential scientific articles and the influence relationships between the articles, potentially opening the door for automated exploratory tools for scientists. The increasing prevalence of web-scale data sets provides both an opportunity and a challenge. With more data we can fit more accurate models, as long as our learning algorithms are up to the task. To meet this challenge, we present an algorithm for learning latent Dirichlet allocation topic models quickly, accurately and at scale. The algorithm leverages stochastic techniques, as well as the collapsed representation of the model. We use it to build a topic model on 4.6 million articles from the open encyclopedia Wikipedia in a matter of hours, and on a corpus of 1740 machine learning articles from the NIPS conference in seconds. </p><p> Finally, evaluating the predictive performance of topic models is an important yet computationally difficult task. We develop one algorithm for comparing topic models, and another for measuring the progress of learning algorithms for these models. The latter method achieves better estimates than previous algorithms, in many cases with an order of magnitude less computational effort.</p>
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Foxall, Robert John. "Likelihood analysis of the multi-layer perceptron and related latent variable models." Thesis, University of Newcastle Upon Tyne, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327211.
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Farouni, Tarek. "Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1412374136.
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Yan, Xiaohong. "Latent variable models for multiple longitudinal outcomes with non-ignorable missing data." Diss., Restricted to subscribing institutions, 2007. http://proquest.umi.com/pqdweb?did=1472152481&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Giovinazzi, Francesco <1988>. "Solution Path Clustering for Fixed-Effects Models in a Latent Variable Context." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8740/1/giovinazzi_phdthesis.pdf.
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The main drawback of estimating latent variable models with fixed effects is the direct dependence between the number of free parameters and the number of observations. We propose to apply a well suited penalization technique in order to regularize the parameter estimates. In particular, we promote sparsity based on the pairwise differences of subject-specific parameters,
inducing the latter to shrink on each other. This method allows to group statistical units into clusters that are homogeneous with respect to a latent attribute, without the need to specify any distributional assumption,
and without adopting random effects. In practice, applying the proposed penalization, the number of free parameters is reduced and the adopted model becomes more parsimonious. The estimation of the fixed effects is based on an algorithm that builds a solution path, in the form of a hierarchical aggregation tree, whose outcome depends on a single tuning parameter. The method is intended to be general, and in principle it can be applied on the likelihood of any latent variable model with fixed effects. We describe in detail its application to the Rasch model, for which we provide a real data example and a simulation study. We then extend the method to the case of a latent variable model for continuous data, where the number of fixed effects to be estimated is higher.
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Maboudi, Afkham Heydar. "Improving Image Classification Performance using Joint Feature Selection." Doctoral thesis, KTH, Datorseende och robotik, CVAP, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-144896.
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In this thesis, we focus on the problem of image classification and investigate how its performance can be systematically improved. Improving the performance of different computer vision methods has been the subject of many studies. While different studies take different approaches to achieve this improvement, in this thesis we address this problem by investigating the relevance of the statistics collected from the image. We propose a framework for gradually improving the quality of an already existing image descriptor. In our studies, we employ a descriptor which is composed the response of a series of discriminative components for summarizing each image. As we will show, this descriptor has an ideal form in which all categories become linearly separable. While, reaching this form is not possible, we will argue how by replacing a small fraction of these components, it is possible to obtain a descriptor which is, on average, closer to this ideal form. To do so, we initially identify which components do not contribute to the quality of the descriptor and replace them with more robust components. As we will show, this replacement has a positive effect on the quality of the descriptor. While there are many ways of obtaining more robust components, we introduce a joint feature selection problem to obtain image features that retains class discriminative properties while simultaneously generalising between within class variations. Our approach is based on the concept of a joint feature where several small features are combined in a spatial structure. The proposed framework automatically learns the structure of the joint constellations in a class dependent manner improving the generalisation and discrimination capabilities of the local descriptor while still retaining a low-dimensional representations. The joint feature selection problem discussed in this thesis belongs to a specific class of latent variable models that assumes each labeled sample is associated with a set of different features, with no prior knowledge of which feature is the most relevant feature to be used. Deformable-Part Models (DPM) can be seen as good examples of such models. These models are usually considered to be expensive to train and very sensitive to the initialization. Here, we focus on the learning of such models by introducing a topological framework and show how it is possible to both reduce the learning complexity and produce more robust decision boundaries. We will also argue how our framework can be used for producing robust decision boundaries without exploiting the dataset bias or relying on accurate annotations. To examine the hypothesis of this thesis, we evaluate different parts of our framework on several challenging datasets and demonstrate how our framework is capable of gradually improving the performance of image classification by collecting more robust statistics from the image and improving the quality of the descriptor.<br><p>QC 20140506</p>
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Lee, Dong Hyung. "Testing executive function models of ADHD and its comorbid conditions: A latent variable approach." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/2801.
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Current theoretical models of ADHD (i.e., Disinhibition Model: Barkley, 1997; Working Memory Model: Rapport et al., 2001) conceptualize ADHD as the disorder of executive function (EF) with some variation in their emphases on particular components of the broadly-defined EF (e.g., working memory vs. inhibition) and in their postulated relationships with ADHD symptoms. Although these models provide systematic accounts of the manifestation of ADHD, they have not been extensively tested from an empirical standpoint. Moreover, despite the fact that ADHD is highly comorbid with other additional conditions such as learning and behavioral problems and EF deficits are found in individuals with these conditions as well as in those with ADHD, current EF models have not specified the developmental relationship between ADHD and its comorbid conditions. This study was: (1) to examine the extent to which two current models of ADHD are supported in a sample of 102 adults; (2) to present an ??integrated?? model by combining two current models of ADHD and linking them to recent research findings on two common comorbid conditions with ADHD (i.e., reading difficulty and substance abuse); and (3) to test and revise such an integrated model in the light of data using a latent variable analysis. Major findings provided a strong support for the Working Memory Model with a lesser degree of support for the Disinhibition Model. Preliminary evidence of working memory as the primary deficit in ADHD was also obtained in the present sample. Finally, the integrated EF model and its revised model (final model) demonstrated a very good fit to the data. These findings suggest that the integrated model provides a unified account of how EF deficits contribute to the manifestation of ADHD symptoms and comorbid conditions with ADHD. Given some limitations (e.g., sample size and scope) of the present study, current findings need to be replicated.
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Karipidou, Kelly. "Modelling the body language of a musical conductor using Gaussian Process Latent Variable Models." Thesis, KTH, Datorseende och robotik, CVAP, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-176101.
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Motion capture data of a musical conductor's movements when conducting a string quartet is analysed in this work using the Gaussian Process Latent Variable Model (GP-LVM) framework. A dimensionality reduction on the high dimensional motion capture data to a two dimensional representation using a GP-LVM is performed, followed by classification of conduction movements belonging to different interpretations of the same musical piece. A dynamical prior is used for the GP-LVM, resulting in a representative latent space for the sequential conduction motion data. Classification results with great performance for some of the interpretations are obtained. The GP-LVM with dynamical prior distribution is shown to be a reasonable choice when wanting to model conduction data, opening up the possibility for creating for example a "conduct-your-own-orchestra" system in a principled mathematical way, in the future.