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Tang, Yun. "Hierarchical Generalization Models for Cognitive Decision-making Processes." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1370560139.
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Schoergendorfer, Angela. "BAYESIAN SEMIPARAMETRIC GENERALIZATIONS OF LINEAR MODELS USING POLYA TREES." UKnowledge, 2011. http://uknowledge.uky.edu/gradschool_diss/214.
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In a Bayesian framework, prior distributions on a space of nonparametric continuous distributions may be defined using Polya trees. This dissertation addresses statistical problems for which the Polya tree idea can be utilized to provide efficient and practical methodological solutions.
One problem considered is the estimation of risks, odds ratios, or other similar measures that are derived by specifying a threshold for an observed continuous variable. It has been previously shown that fitting a linear model to the continuous outcome under the assumption of a logistic error distribution leads to more efficient odds ratio estimates. We will show that deviations from the assumption of logistic error can result in great bias in odds ratio estimates. A one-step approximation to the Savage-Dickey ratio will be presented as a Bayesian test for distributional assumptions in the traditional logistic regression model. The approximation utilizes least-squares estimates in the place of a full Bayesian Markov Chain simulation, and the equivalence of inferences based on the two implementations will be shown. A framework for flexible, semiparametric estimation of risks in the case that the assumption of logistic error is rejected will be proposed.
A second application deals with regression scenarios in which residuals are correlated and their distribution evolves over an ordinal covariate such as time. In the context of prediction, such complex error distributions need to be modeled carefully and flexibly. The proposed model introduces dependent, but separate Polya tree priors for each time point, thus pooling information across time points to model gradual changes in distributional shapes. Theoretical properties of the proposed model will be outlined, and its potential predictive advantages in simulated scenarios and real data will be demonstrated.
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Nearing, Grey Stephen. "Diagnostics and Generalizations for Parametric State Estimation." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293533.
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This dissertation is comprised of a collection of five distinct research projects which apply, evaluate and extend common methods for land surface data assimilation. The introduction of novel diagnostics and extensions of existing algorithms is motivated by an example, related to estimating agricultural productivity, of failed application of current methods. We subsequently develop methods, based on Shannon's theory of communication, to quantify the contributions from all possible factors to the residual uncertainty in state estimates after data assimilation, and to measure the amount of information contained in observations which is lost due to erroneous assumptions in the assimilation algorithm. Additionally, we discuss an appropriate interpretation of Shannon information which allows us to measure the amount of information contained in a model, and use this interpretation to measure the amount of information introduced during data assimilation-based system identification. Finally, we propose a generalization of the ensemble Kalman filter designed to alleviate one of the primary assumptions - that the observation function is linear.
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Schustek, Philipp. "Probabilistic models for human judgments about uncertainty in intuitive inference tasks." Doctoral thesis, Universitat Pompeu Fabra, 2018. http://hdl.handle.net/10803/586057.
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Updating beliefs to maintain coherence with observational evidence is a cornerstone of rationality. This entails the compliance with probabilistic principles which acknowledge that real-world observations are consistent with several possible interpretations. This work presents two novel experimental paradigms and computational analyses of how human participants quantify uncertainty in perceptual inference tasks. Their behavioral responses feature non-trivial patterns of probabilistic inference such as reliability-based belief updating over hierarchical state representations of the environment. Despite characteristic generalization biases, behavior cannot be explained well by alternative heuristic accounts. These results suggest that uncertainty is an integral part of our inferences and that we indeed have the potential to resort to rational inference mechanisms that adhere to probabilistic principles. Furthermore, they appear consistent with ubiquitous representations of uncertainty posited by framework theories such as Bayesian hierarchical modeling and predictive coding.<br>Un pilar fundamental de la racionalidad es actualizar las creencias con la finalidad de mantener la coherencia con la evidencia observacional. Esto implica cumplir con principios probabilísticos, los cuales reconocen que las observaciones del mundo real son consistentes con varias interpretaciones posibles. Este estudio presenta dos novedosas pruebas experimentales, así como análisis computacionales, de cómo participantes humanos cuantifican la incertidumbre en tareas de inferencia perceptiva. Sus respuestas conductuales muestran patrones no triviales de inferencia probabilística, tales como la actualización de creencias basadas en la confiabilidad sobre las representaciones jerárquicas del estado del entorno. A pesar de los sesgos característicos de generalización, el comportamiento no puede ser correctamente explicado con descripciones heurísticas alternativas. Estos resultados sugieren que la incertidumbre es una parte integral de nuestras inferencias y que efectivamente tenemos el potencial para recurrir a mecanismos de inferencia racional, los cuales adhieren a principios probabilísticos. Además, dichos resultados son compatibles con la idea de que representaciones de incertidumbre internas son ubicuas, lo cual presuponen teorías generales como Bayesian hierarchical modeling y predictive coding.
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Matsuoka, Yoky 1971. "Models of generalization in motor control." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/9634.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.<br>Includes bibliographical references (p. 207-215).<br>Motor learning for humans is based on the capacity of the central nervous system (CNS) to perform computation and build an internal model for a task. This thesis investigates the CNS's ability to generalize a learned motor skill throughout neighboring spatial locations, its ability to divide the spatial generalization with variation of context, and proposes models of how these generalizations might be implemented. The investigation involved human psychophysics and simulations. The experimental paradigm was to study human neuromuscular adaptation to viscous force perturbation. When external perturbations were applied to the hand during a reaching task, the movement became distorted. This distortion motivated the CNS to produce counterbalancing forces, which resulted in the modification of the internal model for the task. Experimental results indicated that the introduction of interfering perturbations near the trained location disturbed the learned skill. In addition, if the same movement was perturbed in two opposite directions in sequence, neither of the forces are learned. Conversely, the adaptation to two opposite forces was possible within the same space when the forces were applied to two contextually distinguished movements. This was possible only when these movements were interleaved fairly regularly. During the adaptation to a difficult task, such as contextual distinction in the same spatial location, humans often used other strategies to avoid learning the actual paradigm. These strategies allowed subjects to perform the task -- without changing their internal models appropriately, and thus this was also investigated as a part of the learning process. Finally, a multiple function model was constructed which allowed multiple contextually dependent functions to co-exist within one state space. The sensory feedback affected all functions, however, only one function was active to output a motor command. This model supported the experimental data presented. The results of the psychophysical experiments as well as an explanation of the simulations and models that were developed will be presented in this thesis.<br>by Yoky Matsuoka.<br>Ph.D.
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Kim, Yong Ku. "Bayesian multiresolution dynamic models." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1180465799.
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Quintana, José Mario. "Multivariate Bayesian forecasting models." Thesis, University of Warwick, 1987. http://wrap.warwick.ac.uk/34805/.
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This thesis concerns theoretical and practical Bayesian modelling of multivariate time series. Our main goal is to intruduce useful, flexible and tractable multivariate forecasting models and provide the necessary theory for their practical implementation. After a brief review of the dynamic linear model we formulate a new matrix-v-ariate generalization in which a significant part of the variance-covariance structure is unknown. And a new general algorithm, based on the sweep operator is provided for its recursive implementation. This enables important advances to be made in long-standing problems related with the specification of the variances. We address the problem of plug-in estimation and apply our results in the context of dynamic linear models. We extend our matrix-variate model by considering the unknown part of the variance-covariance structure to be dynamic. Furthermore, we formulate the dynamic recursive model which is a general counterpart of fully recursive econometric models. The latter part of the dissertation is devoted to modelling aspects. The usefulness of the methods proposed is illustrated with several examples involving real and simulated data.
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McDonald, Daniel J. "Generalization Error Bounds for Time Series." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/184.
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In this thesis, I derive generalization error bounds — bounds on the expected inaccuracy of the predictions — for time series forecasting models. These bounds allow forecasters to select among competing models, and to declare that, with high probability, their chosen model will perform well — without making strong assumptions about the data generating process or appealing to asymptotic theory. Expanding upon results from statistical learning theory, I demonstrate how these techniques can help time series forecasters to choose models which behave well under uncertainty. I also show how to estimate the β-mixing coefficients for dependent data so that my results can be used empirically. I use the bound explicitly to evaluate different predictive models for the volatility of IBM stock and for a standard set of macroeconomic variables. Taken together my results show how to control the generalization error of time series models with fixed or growing memory.
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Ridgeway, Gregory Kirk. "Generalization of boosting algorithms and applications of Bayesian inference for massive datasets /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/8986.
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Michel, Axel. "Personalising privacy contraints in Generalization-based Anonymization Models." Thesis, Bourges, INSA Centre Val de Loire, 2019. http://www.theses.fr/2019ISAB0001/document.
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Les bénéfices engendrés par les études statistiques sur les données personnelles des individus sont nombreux, que ce soit dans le médical, l'énergie ou la gestion du trafic urbain pour n'en citer que quelques-uns. Les initiatives publiques de smart-disclosure et d'ouverture des données rendent ces études statistiques indispensables pour les institutions et industries tout autour du globe. Cependant, ces calculs peuvent exposer les données personnelles des individus, portant ainsi atteinte à leur vie privée. Les individus sont alors de plus en plus réticent à participer à des études statistiques malgré les protections garanties par les instituts. Pour retrouver la confiance des individus, il devient nécessaire de proposer dessolutions de user empowerment, c'est-à-dire permettre à chaque utilisateur de contrôler les paramètres de protection des données personnelles les concernant qui sont utilisées pour des calculs.Cette thèse développe donc un nouveau concept d'anonymisation personnalisé, basé sur la généralisation de données et sur le user empowerment.En premier lieu, ce manuscrit propose une nouvelle approche mettant en avant la personnalisation des protections de la vie privée par les individus, lors de calculs d'agrégation dans une base de données. De cette façon les individus peuvent fournir des données de précision variable, en fonction de leur perception du risque. De plus, nous utilisons une architecture décentralisée basée sur du matériel sécurisé assurant ainsi les garanties de respect de la vie privée tout au long des opérations d'agrégation.En deuxième lieu, ce manuscrit étudie la personnalisations des garanties d'anonymat lors de la publication de jeux de données anonymisés. Nous proposons l'adaptation d'heuristiques existantes ainsi qu'une nouvelle approche basée sur la programmation par contraintes. Des expérimentations ont été menées pour étudier l'impact d’une telle personnalisation sur la qualité des données. Les contraintes d’anonymat ont été construites et simulées de façon réaliste en se basant sur des résultats d'études sociologiques<br>The benefit of performing Big data computations over individual’s microdata is manifold, in the medical, energy or transportation fields to cite only a few, and this interest is growing with the emergence of smart-disclosure initiatives around the world. However, these computations often expose microdata to privacy leakages, explaining the reluctance of individuals to participate in studies despite the privacy guarantees promised by statistical institutes. To regain indivuals’trust, it becomes essential to propose user empowerment solutions, that is to say allowing individuals to control the privacy parameter used to make computations over their microdata.This work proposes a novel concept of personalized anonymisation based on data generalization and user empowerment.Firstly, this manuscript proposes a novel approach to push personalized privacy guarantees in the processing of database queries so that individuals can disclose different amounts of information (i.e. data at different levels of accuracy) depending on their own perception of the risk. Moreover, we propose a decentralized computing infrastructure based on secure hardware enforcing these personalized privacy guarantees all along the query execution process.Secondly, this manuscript studies the personalization of anonymity guarantees when publishing data. We propose the adaptation of existing heuristics and a new approach based on constraint programming. Experiments have been done to show the impact of such personalization on the data quality. Individuals’privacy constraints have been built and realistically using social statistic studies
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Gramacy, Robert B. "Bayesian treed Gaussian process models /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2005. http://uclibs.org/PID/11984.
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Husain, Syeda Tasmine. "Bayesian analysis of longitudinal models /." Internet access available to MUN users only, 2003. http://collections.mun.ca/u?/theses,163598.
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Ozbozkurt, Pelin. "Bayesian Inference In Anova Models." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611532/index.pdf.
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Estimation of location and scale parameters from a random sample of size n is of paramount importance in Statistics. An estimator is called fully efficient if it attains the Cramer-Rao minimum variance bound besides being unbiased. The method that yields such estimators, at any rate for large n, is the method of modified maximum likelihood estimation. Apparently, such estimators cannot be made more efficient by using sample based classical methods. That makes room for Bayesian method of estimation which engages prior distributions and likelihood functions. A formal combination of the prior knowledge and the sample information is called posterior distribution. The posterior distribution is maximized with respect to the unknown parameter(s). That gives HPD (highest probability density) estimator(s). Locating the maximum of the posterior distribution is, however, enormously difficult (computationally and analytically) in most situations. To alleviate these difficulties, we use modified likelihood function in the posterior distribution instead of the likelihood function. We derived the HPD estimators of location and scale parameters of distributions in the family of Generalized Logistic. We have extended the work to experimental design, one way ANOVA. We have obtained the HPD estimators of the block effects and the scale parameter (in the distribution of errors)<br>they have beautiful algebraic forms. We have shown that they are highly efficient. We have given real life examples to illustrate the usefulness of our results. Thus, the enormous computational and analytical difficulties with the traditional Bayesian method of estimation are circumvented at any rate in the context of experimental design.
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Osuna, Echavarría Leyre Estíbaliz. "Semiparametric Bayesian Count Data Models." Diss., lmu, 2004. http://nbn-resolving.de/urn:nbn:de:bvb:19-25573.
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Mohamed, Shakir. "Generalised Bayesian matrix factorisation models." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/237246.
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Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.
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Shon, Aaron P. "Bayesian cognitive models for imitation /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/7013.
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Xiang, Fei. "Bayesian consistency for regression models." Thesis, University of Kent, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587522.
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Bayesian consistency is an important issue in the context of non- parametric problems. The posterior consistency is a validation of a Bayesian approach and guarantees the posterior mass accumulates around the true density, which" is unknown in most circumstances, as the number of observations goes to infinity. This thesis mainly considers the consistency for nonparametric regression models over both random and non random covariates. The techniques to achieve consistency under random covariates are similar to that derived in Walker (2003, 2004) which is designed for the consistency of independent and identically distributed variables. We contribute a new idea to deal with the supremum metric over covariates when the regression model is with non random covariates. That is, if a regression density is away from the true density in the Hellinger sense, then there is a covariate, whose value is picked from a specific design, such that the density indexed by this value is also away from the true density. As a result, the posterior concentrates in the supremum Hellinger neighbourhood of the real model under conditions on the prior such as the Kullback-Leibler property and the summability of the square rooted prior mass on Hellinger covering balls. Furthermore, the predictive is also shown to be consistent and we illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. We also investigate conditions under which a piecewise density model is consistent.
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Young, Simon Christopher. "Bayesian models and repeated games." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/55723/.
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A game is a theoretical model of a social situation where the people involved have individually only partial control over the outcomes. Game theory is then the method used to analyse these models. As a player's outcome from a game depends upon the actions of his opponents, there is some uncertainty in these models. This uncertainty is described probabilistically, in terms of a player's subjective beliefs about the future play of his opponent. Any additional information that is acquired by the player can be incorporated into the analysis and these subjective beliefs are revised. Hence, the approach taken is `Bayesian'. Each outcome from the game has a value to each of the players, and the measure of merit from an outcome is referred to as a player's utility. This concept of utility is combined with a player's subjective probabilities to form an expected utility, and it is assumed that each player is trying to maximise his expected utility. Bayesian models for games are constructed in order to determine strategies for the players that are expected utility maximising. These models are guided by the belief that the other players are also trying to maximise their own expected utilities. It is shown that a player's beliefs about the other players form an infinite regress. This regress can be truncated to a finite number of levels of beliefs, under some assumptions about the utility functions and beliefs of the other players. It is shown how the dichotomy between prescribed good play and observed good play exists because of the lack of assumptions about the rationality of the opponents (i. e. the ability of the opponents to be utility maximising). It is shown how a model for a game can be built which is both faithful to the observed common sense behaviour of the subjects of an experimental game, and is also rational (in a Bayesian sense). It is illustrated how the mathematical form of an optimal solution to a game can be found, and then used with an inductive algorithm to determine an explicit optimal strategy. It is argued that the derived form of the optimal solution can be used to gain more insight into the game, and to determine whether an assumed model is realistic. It is also shown that under weak regularity conditions, and assuming that an opponent is playing a strategy from a given class of strategies, S, it is not optimal for the player to adopt any strategy from S, thus compromising the chosen model.
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Wiseman, Scott. "Bayesian learning in graphical models." Thesis, University of Kent, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.311261.
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Kadir, Dler. "Bayesian inference of autoregressive models." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/20610/.
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The principles, models and steps of Bayesian time series analysis and forecasting have been developed extensively during the past forty years. In order to estimate parameters of an autoregressive (AR) model we develop Markov chain Monte Carlo (MCMC) schemes for inference of AR model. It is our interest to propose a new prior distribution placed directly on the AR parameters of the model. Thus, we revisit the stationarity conditions to determine a flexible prior for AR model parameters.
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Gulam, Razul Sirajudeen. "Bayesian methods for unified models." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619713.
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Van, Gael Jurgen. "Bayesian nonparametric hidden Markov models." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610196.
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Streftaris, George. "Bayesian methods for Poisson models." Thesis, University of Edinburgh, 2000. http://hdl.handle.net/1842/14505.
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To account for overdispersion in count data, that is variation in excess of that justified from the assumed model, one may consider an additional source of variation, by assuming that each observation, <i>Y<sub>i</sub>, i = </i>1, ..., <i>m</i>, arises from a conditionally independent Poisson distribution, given its respective mean <i>q<sub>i</sub>, i = </i>1, ..., <i>m</i>. We review various frequentist methods for the estimation of the Poisson parameters <i>q<sub>i</sub>, i = </i>1, ..., <i>m</i>, which are based on the inadmissibility of the usual unbiased maximum likelihood estimator, in terms of the associated risk in dimensions greater than two. The so called shrinkage estimators adjust the maximum likelihood estimates towards a fixed or data-determined point, abandoning unbiasedness in favour of lower risk. Inferences for the parameters of interest can also be drawn employing Bayesian methods. Conjugate models are often adopted to facilitate the computational procedure. In this thesis we assume a nonconjugate log-normal prior distribution, which allows for more dispersion in the Poisson means and can also accommodate a correlation structure. We derive two empirical Bayes estimators, which approximate the posterior mean. The first is based on a linear shrinkage rule, while the second employs a non-iterative importance sampling technique. The frequency properties of the two estimators in terms of average risk are assessed and compared to other estimating approaches proposed in the literature. A full hierarchical Bayes analysis is also considered, assuming both informative and non-informative prior distributions at the lower stage of the hierarchy. Some analytical posterior inferences, based on simple approximations are obtained. We then employ stochastic simulation techniques, suggesting two Markov chain Monte Carlo methods which involve the Gibbs sampler and a hybrid strategy. They rely on a log-normal/gamma mixture approximation to the full conditional posterior distribution of the parameters <i>q<sub>i</sub></i>, <i>i </i>= 1, ,..., <i>m</i>. The shrinkage behaviour of the hierarchical Bayes estimator is explored, and its average risk is examined through frequency simulations. Examples and applications of the considered methods are given throughout the thesis.
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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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Bush, Christopher A. "Semi-parametric Bayesian linear models /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487856076417948.
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Kunkel, Deborah Elizabeth. "Anchored Bayesian Gaussian Mixture Models." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524134234501475.
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Bouda, Milan. "Bayesian Estimation of DSGE Models." Doctoral thesis, Vysoká škola ekonomická v Praze, 2012. http://www.nusl.cz/ntk/nusl-200007.
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Thesis is dedicated to Bayesian Estimation of DSGE Models. Firstly, the history of DSGE modeling is outlined as well as development of this macroeconometric field in the Czech Republic and in the rest of the world. Secondly, the comprehensive DSGE framework is described in detail. It means that everyone is able to specify or estimate arbitrary DSGE model according to this framework. Thesis contains two empirical studies. The first study describes derivation of the New Keynesian DSGE Model and its estimation using Bayesian techniques. This model is estimated with three different Taylor rules and the best performing Taylor rule is identified using the technique called Bayesian comparison. The second study deals with development of the Small Open Economy Model with housing sector. This model is based on previous study which specifies this model as a closed economy model. I extended this model by open economy features and government sector. Czech Republic is generally considered as a small open economy and these extensions make this model more applicable to this economy. Model contains two types of households. The first type of consumers is able to access the capital markets and they can smooth consumption across time by buying or selling financial assets. These households follow the permanent income hypothesis (PIH). The other type of household uses rule of thumb (ROT) consumption, spending all their income to consumption. Other agents in this economy are specified in standard way. Outcomes of this study are mainly focused on behavior of house prices. More precisely, it means that all main outputs as Bayesian impulse response functions, Bayesian prediction and shock decomposition are focused mainly on this variable. At the end of this study one macro-prudential experiment is performed. This experiment comes up with answer on the following question: is the higher/lower Loan to Value (LTV) ratio better for the Czech Republic? This experiment is very conclusive and shows that level of LTV does not affect GDP. On the other hand, house prices are very sensitive to this LTV ratio. The recommendation for the Czech National Bank could be summarized as follows. In order to keep house prices less volatile implement rather lower LTV ratio than higher.
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KIM, DONG-HYUK. "Bayesian Econometrics for Auction Models." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/193663.
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This dissertation develops Bayesian methods to analyze data from auctions and produce policy recommendations for auction design. The essay, "Auction Design Using Bayesian Methods," proposes a decision theoretic method to choose a reserve price in an auction using data from past auctions. Our method formally incorporates parameter uncertainty and the payoff structure into the decision procedure. When the sample size is modest, it produces higher expected revenue than the plug-in methods. Monte Carlo evidence for this is provided. The second essay, "Flexible Bayesian Analysis of First Price Auctions Using Simulated Likelihood," develops an empirical framework that fully exploits all the shape restrictions arising from economic theory: bidding monotonicity and density affiliation. We directly model the valuation density so that bidding monotonicity is automatically satisfied, and restrict the parameter space to rule out all the nonaffiliated densities. Our method uses a simulated likelihood to allow for a very exible specification, but the posterior analysis is exact for the chosen likelihood. Our method controls the smoothness and tail behavior of the valuation density and provides a decision theoretic framework for auction design. We reanalyze a dataset of auctions for drilling rights in the Outer Continental Shelf that has been widely used in past studies. Our approach gives significantly different policy prescriptions on the choice of reserve price than previous methods, suggesting the importance of the theoretical shape restrictions. Lastly, in the essay, "Simple Approximation Methods for Bayesian Auction Design," we propose simple approximation methods for Bayesian decision making in auction design problems. Asymptotic posterior distributions replace the true posteriors in the Bayesian decision framework, which are typically a Gaussian model (second price auction) or a shifted exponential model (first price auction). Our method first approximates the posterior payoff using the limiting models and then maximizes the approximate posterior payoff. Both the approximate and exact Bayes rules converge to the true revenue maximizing reserve price under certain conditions. Monte Carlo studies show that my method closely approximates the exact procedure even for fairly small samples.
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Rolfe, Margaret Irene. "Bayesian models for longitudinal data." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/34435/1/Margaret_Rolfe_Thesis.pdf.
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Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.
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Foreman, Lindsay Anne. "Bayesian computation for hidden Markov models." Thesis, Imperial College London, 1994. http://hdl.handle.net/10044/1/11490.
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Campolieti, Michele. "Bayesian estimation of discrete duration models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0001/NQ27884.pdf.
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Bennett, James Elston. "Bayesian analysis of population pharmacokinetic models." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363017.
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Östling, Robert. "Bayesian Models for Multilingual Word Alignment." Doctoral thesis, Stockholms universitet, Institutionen för lingvistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-115541.
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In this thesis I explore Bayesian models for word alignment, how they can be improved through joint annotation transfer, and how they can be extended to parallel texts in more than two languages. In addition to these general methodological developments, I apply the algorithms to problems from sign language research and linguistic typology. In the first part of the thesis, I show how Bayesian alignment models estimated with Gibbs sampling are more accurate than previous methods for a range of different languages, particularly for languages with few digital resources available—which is unfortunately the state of the vast majority of languages today. Furthermore, I explore how different variations to the models and learning algorithms affect alignment accuracy. Then, I show how part-of-speech annotation transfer can be performed jointly with word alignment to improve word alignment accuracy. I apply these models to help annotate the Swedish Sign Language Corpus (SSLC) with part-of-speech tags, and to investigate patterns of polysemy across the languages of the world. Finally, I present a model for multilingual word alignment which learns an intermediate representation of the text. This model is then used with a massively parallel corpus containing translations of the New Testament, to explore word order features in 1001 languages.
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Kaufmann, Sylvia, and Sylvia Frühwirth-Schnatter. "Bayesian Analysis of Switching ARCH Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/744/1/document.pdf.
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We consider a time series model with autoregressive conditional heteroskedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov Chain Monte Carlo simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by combining the candidate's formula with importance sampling. The usefulness of the sampler is demonstrated by applying it to the dataset previously used by Hamilton and Susmel who investigated models with switching autoregressive conditional heteroskedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model select ion, and to potential straightforward extensions of the model presented here. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
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Wakefield, Jon. "The Bayesian analysis of pharmacokinetic models." Thesis, University of Nottingham, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334806.
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Giles, Philip R. "Bayesian inference for stochastic epidemic models." Thesis, University of Newcastle Upon Tyne, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420008.
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Grigsby, Mark Edwin. "Bayesian inference for log-linear models." Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393934.
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HUAMANI, LUIS ALBERTO NAVARRO. "BAYESIAN INFERENCE ON MULTIVARIATE ARCH MODELS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2001. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=1868@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>O objetivo deste trabalho é desenvolver uma estratégia
Metropolis-Hastings para inferência Bayesiana, usando a
estrutura ARCH multivatriada com representação BEKK.Em
problemas complexos, como a generalização ARCH/GARCH
univariadas para estruturas multivariadas, o processo de
inferência é dificultado por causa do número de
parâmetros
envolvidos e das restrições a que eles estão sujeitos.
Neste trabalho desenvolvemos uma estratégia Metropolis-
Hastings para inferência Bayesiana, usando uma estrutura
ARCH multivariada com representação BEKK.<br>The objective of this work is to develop Metropolis-Hasting
for strategy Bayesian Inference, based on a Multivariate
ARCH model with BEKK representation. In complex problems,
such as the multivariate generalization of ARCH/GARCH
structures, the inference process in complicated, due to
the large number of parameters involved and to the
restrictions they must satisfy. We propose Metropolis-
Hastings structure to provide inference, in a Bayesian
framework, for a multivariate ARCH model with BEKK
representation.<br>EL objetivo de este trabajo es desarrollar una estrategia Metropolis-Hastings para inferencia
Bayesiana, usando La extructura ARCH multivatriada con representación BEKK.En problemas
complejos, como la generalización ARCH/GARCH univariadas para extructuras multivariadas, el
proceso de inferencia se hace dificil por causa del número de parámetros involucrados y de las
restricciones a que ellos están sujetos. En este trabajo desarrollamos una estrategia Metropolis-
Hastings para inferencia Bayesiana, usando una extructura ARCH multivariada con representación
BEKK.
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Mestre, María del Rosario. "Bayesian predictive models of user intention." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708641.
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Al-Kaabawi, Zainab A. A. "Bayesian hierarchical models for linear networks." Thesis, University of Plymouth, 2018. http://hdl.handle.net/10026.1/12829.
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A motorway network is handled as a linear network. The purpose of this study is to highlight dangerous motorways via estimating the intensity of accidents and study its pattern across the UK motorway network. Two mechanisms have been adopted to achieve this aim. The first, the motorway-specific intensity is estimated by modelling the point pattern of the accident data using a homogeneous Poisson process. The homogeneous Poisson process is used to model all intensities but heterogeneity across motorways is incorporated using two-level hierarchical models. The data structure is multilevel since each motorway consists of junctions that are joined by grouped segments. In the second mechanism, the segment-specific intensity is estimated by modelling the point pattern of the accident data. The homogeneous Poisson process is used to model accident data within segments but heterogeneity across segments is incorporated using three-level hierarchical models. A Bayesian method via Markov Chain Monte Carlo simulation algorithms is used in order to estimate the unknown parameters in the models and a sensitivity analysis to the prior choice is assessed. The performance of the proposed models is checked through a simulation study and an application to traffic accidents in 2016 on the UK motorway network. The performance of the three-level frequentist model was poor. The deviance information criterion (DIC) and the widely applicable information criterion (WAIC) are employed to choose between the two-level Bayesian hierarchical model and the three-level Bayesian hierarchical model, where the results showed that the best fitting model was the three-level Bayesian hierarchical model.
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Umaras, Jonas Radvilas. "Bayesian Parametrisation ofIn Silico Tumour Models." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-382536.
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Technological progress in recent decades has allowed researchers to utilise accurate but computationally demanding models. One example of this development is the adoption of the multi-scale modelling technique for simulating various tissues. These models can then be utilised to test the efficacy of new drugs, e.g., for cancer treatment. Though multi-scale models can produce accurate representations of complex systems, their parameters often cannot be measured directly and have to be inferred using experimental data, which is a challenge yet to be solved. The goal of this work is to investigate the possibility of parametrising a specific high-performance tumour growth model using a likelihood-free method called Approximate Bayesian Computation (ABC). The first objective is to understand the effect that parameters of the model have on its behaviour. Then, by using the insights gained from the first step, define a set of summary statistics and a distance metric capable of capturing the impact of parameter variations on the growth of simulated tumours. Finally, assess the landscapes of the parameter space by utilising the statistics and the metric. The obtained results indicate that some of the parameters can be inferred by applying an ABC-style method, which motivates to further investigate the prospect of applying ABC for parametrising the model in question. However, the computational costs of such techniques are expected to be high, putting its execution time in the order of weeks, thus requiring future performance improvements of the model and highly efficient implementations of the parametrisation procedure.
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Lu, Peter Guang Yi. "Bayesian inference of stochastic dynamical models." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/79265.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 165-175).<br>A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.<br>by Peter Lu.<br>S.M.
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Vasconcelos, Nuno Miguel Borges de Pinho Cruz de. "Bayesian models for visual information retrieval." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/62947.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2000.<br>Includes bibliographical references (leaves 192-208).<br>This thesis presents a unified solution to visual recognition and learning in the context of visual information retrieval. Realizing that the design of an effective recognition architecture requires careful consideration of the interplay between feature selection, feature representation, and similarity function, we start by searching for a performance criteria that can simultaneously guide the design of all three components. A natural solution is to formulate visual recognition as a decision theoretical problem, where the goal is to minimize the probability of retrieval error. This leads to a Bayesian architecture that is shown to generalize a significant number of previous recognition approaches, solving some of the most challenging problems faced by these: joint modeling of color and texture, objective guidelines for controlling the trade-off between feature transformation and feature representation, and unified support for local and global queries without requiring image segmentation. The new architecture is shown to perform well on color, texture, and generic image databases, providing a good trade-off between retrieval accuracy, invariance, perceptual relevance of similarity judgments, and complexity. Because all that is needed to perform optimal Bayesian decisions is the ability to evaluate beliefs on the different hypothesis under consideration, a Bayesian architecture is not restricted to visual recognition. On the contrary, it establishes a universal recognition language (the language of probabilities) that provides a computational basis for the integration of information from multiple content sources and modalities. In result, it becomes possible to build retrieval systems that can simultaneously account for text, audio, video, or any other content modalities. Since the ability to learn follows from the ability to integrate information over time, this language is also conducive to the design of learning algorithms. We show that learning is, indeed, an important asset for visual information retrieval by designing both short and long-term learning mechanisms. Over short time scales (within a retrieval session), learning is shown to assure faster convergence to the desired target images. Over long time scales (between retrieval sessions), it allows the retrieval system to tailor itself to the preferences of particular users. In both cases, all the necessary computations are carried out through Bayesian belief propagation algorithms that, although optimal in a decision-theoretic sense, are extremely simple, intuitive, and easy to implement.<br>by Nuno Miguel Borges de Pinho Cruz de Vasconcelos.<br>Ph.D.
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Evans, Owain Rhys. "Bayesian computational models for inferring preferences." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101522.
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Thesis: Ph. D. in Linguistics, Massachusetts Institute of Technology, Department of Linguistics and Philosophy, 2015.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 130-131).<br>This thesis is about learning the preferences of humans from observations of their choices. It builds on work in economics and decision theory (e.g. utility theory, revealed preference, utilities over bundles), Machine Learning (inverse reinforcement learning), and cognitive science (theory of mind and inverse planning). Chapter 1 lays the conceptual groundwork for the thesis and introduces key challenges for learning preferences that motivate chapters 2 and 3. I adopt a technical definition of 'preference' that is appropriate for inferring preferences from choices. I consider what class of objects preferences should be defined over. I discuss the distinction between actual preferences and informed preferences and the distinction between basic/intrinsic and derived/instrumental preferences. Chapter 2 focuses on the challenge of human 'suboptimality'. A person's choices are a function of their beliefs and plans, as well as their preferences. If they have inaccurate beliefs or make inefficient plans, then it will generally be more difficult to infer their preferences from choices. It is also more difficult if some of their beliefs might be inaccurate and some of their plans might be inefficient. I develop models for learning the preferences of agents subject to false beliefs and to time inconsistency. I use probabilistic programming to provide a concise, extendable implementation of preference inference for suboptimal agents. Agents performing suboptimal sequential planning are represented as functional programs. Chapter 3 considers how preferences vary under different combinations (or &compositions') of outcomes. I use simple mathematical functional forms to model composition. These forms are standard in microeconomics, where the outcomes in question are quantities of goods or services. These goods may provide the same purpose (and be substitutes for one another). Alternatively, they may combine together to perform some useful function (as with complements). I implement Bayesian inference for learning the preferences of agents making choices between different combinations of goods. I compare this procedure to empirical data for two different applications.<br>by Owain Rhys Evans.<br>Ph. D. in Linguistics
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Williamson, Sinead Anne. "Nonparametric Bayesian models for dependent data." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610373.
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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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Bracegirdle, C. I. "Inference in Bayesian time-series models." Thesis, University College London (University of London), 2013. http://discovery.ucl.ac.uk/1383529/.
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Time series-data accompanied with a sequential ordering-occur and evolve all around us. Analysing time series is the problem of trying to discern and describe a pattern in the sequential data that develops in a logical way as the series continues, and the study of sequential data has occurred for a long period across a vast array of fields, including signal processing, bioinformatics, and finance-to name but a few. Classical approaches are based on estimating the parameters of temporal evolution of the process according to an assumed model. In econometrics literature, the field is focussed on parameter estimation of linear (regression) models with a number of extensions. In this thesis, I take a Bayesian probabilistic modelling approach in discrete time, and focus on novel inference schemes. Fundamentally, Bayesian analysis replaces parameter estimates by quantifying uncertainty in the value, and probabilistic inference is used to update the uncertainty based on what is observed in practice. I make three central contributions. First, I discuss a class of latent Markov model which allows a Bayesian approach to internal process resets, and show how inference in such a model can be performed efficiently, before extending the model to a tractable class of switching time series models. Second, I show how inference in linear-Gaussian latent models can be extended to allow a Bayesian approach to variance, and develop a corresponding variance-resetting model, the heteroskedastic linear-dynamical system. Third, I turn my attention to cointegration-a headline topic in finance-and describe a novel estimation scheme implied by Bayesian analysis, which I show to be empirically superior to the classical approach. I offer example applications throughout and conclude with a discussion.
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Frank, Stella Christina. "Bayesian models of syntactic category acquisition." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/6693.
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Discovering a word’s part of speech is an essential step in acquiring the grammar of a language. In this thesis we examine a variety of computational Bayesian models that use linguistic input available to children, in the form of transcribed child directed speech, to learn part of speech categories. Part of speech categories are characterised by contextual (distributional/syntactic) and word-internal (morphological) similarity. In this thesis, we assume language learners will be aware of these types of cues, and investigate exactly how they can make use of them. Firstly, we enrich the context of a standard model (the Bayesian Hidden Markov Model) by adding sentence type to the wider distributional context.We show that children are exposed to a much more diverse set of sentence types than evident in standard corpora used for NLP tasks, and previous work suggests that they are aware of the differences between sentence type as signalled by prosody and pragmatics. Sentence type affects local context distributions, and as such can be informative when relying on local context for categorisation. Adding sentence types to the model improves performance, depending on how it is integrated into our models. We discuss how to incorporate novel features into the model structure we use in a flexible manner, and present a second model type that learns to use sentence type as a distinguishing cue only when it is informative. Secondly, we add a model of morphological segmentation to the part of speech categorisation model, in order to model joint learning of syntactic categories and morphology. These two tasks are closely linked: categorising words into syntactic categories is aided by morphological information, and finding morphological patterns in words is aided by knowing the syntactic categories of those words. In our joint model, we find improved performance vis-a-vis single-task baselines, but the nature of the improvement depends on the morphological typology of the language being modelled. This is the first token-based joint model of unsupervised morphology and part of speech category learning of which we are aware.
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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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Rios, Felix Leopoldo. "Bayesian structure learning in graphical models." Licentiate thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-179852.
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This thesis consists of two papers studying structure learning in probabilistic graphical models for both undirected graphs anddirected acyclic graphs (DAGs). Paper A, presents a novel family of graph theoretical algorithms, called the junction tree expanders, that incrementally construct junction trees for decomposable graphs. Due to its Markovian property, the junction tree expanders are shown to be suitable for proposal kernels in a sequential Monte Carlo (SMC) sampling scheme for approximating a graph posterior distribution. A simulation study is performed for the case of Gaussian decomposable graphical models showing efficiency of the suggested unified approach for both structural and parametric Bayesian inference. Paper B, develops a novel prior distribution over DAGs with the ability to express prior knowledge in terms of graph layerings. In conjunction with the prior, a search and score algorithm based on the layering property of DAGs, is developed for performing structure learning in Bayesian networks. A simulation study shows that the search and score algorithm along with the prior has superior performance for learning graph with a clearly layered structure compared with other priors.<br><p>QC 20160111</p>