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Dissertations / Theses on the topic 'Mixture models'
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1
Xiang, Sijia. "Semiparametric mixture models." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/17338.
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Doctor of Philosophy<br>Department of Statistics<br>Weixin Yao<br>This dissertation consists of three parts that are related to semiparametric mixture models.
In Part I, we construct the minimum profile Hellinger distance (MPHD) estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in biology and the sequential clustering algorithm.
In Part II, we propose a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both proposed EM-type algorithms preserve the asymptotic ascent property.
In Part III, we apply the idea of single-index model to the mixture of regression models and propose three new classes of models: the mixture of single-index models (MSIM), the mixture of regression models with varying single-index proportions (MRSIP), and the mixture of regression models with varying single-index proportions and variances (MRSIPV). Backfitting estimates and the corresponding algorithms have been proposed for the new models to achieve the optimal convergence rate for both the parameters and the nonparametric functions. We show that the nonparametric functions can be estimated as if the parameters were known and the parameters can be estimated with the same rate of convergence, n[subscript](-1/2), that is achieved in a parametric model.
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Haider, Peter. "Prediction with Mixture Models." Phd thesis, Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2014/6961/.
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Learning a model for the relationship between the attributes and the annotated labels of data examples serves two purposes. Firstly, it enables the prediction of the label for examples without annotation. Secondly, the parameters of the model can provide useful insights into the structure of the data. If the data has an inherent partitioned structure, it is natural to mirror this structure in the model. Such mixture models predict by combining the individual predictions generated by the mixture components which correspond to the partitions in the data.
Often the partitioned structure is latent, and has to be inferred when learning the mixture model. Directly evaluating the accuracy of the inferred partition structure is, in many cases, impossible because the ground truth cannot be obtained for comparison. However it can be assessed indirectly by measuring the prediction accuracy of the mixture model that arises from it.
This thesis addresses the interplay between the improvement of predictive accuracy by uncovering latent cluster structure in data, and further addresses the validation of the estimated structure by measuring the accuracy of the resulting predictive model.
In the application of filtering unsolicited emails, the emails in the training set are latently clustered into advertisement campaigns. Uncovering this latent structure allows filtering of future emails with very low false positive rates. In order to model the cluster structure, a Bayesian clustering model for dependent binary features is developed in this thesis.
Knowing the clustering of emails into campaigns can also aid in uncovering which emails have been sent on behalf of the same network of captured hosts, so-called botnets. This association of emails to networks is another layer of latent clustering. Uncovering this latent structure allows service providers to further increase the accuracy of email filtering and to effectively defend against distributed denial-of-service attacks. To this end, a discriminative clustering model is derived in this thesis that is based on the graph of observed emails. The partitionings inferred using this model are evaluated through their capacity to predict the campaigns of new emails.
Furthermore, when classifying the content of emails, statistical information about the sending server can be valuable. Learning a model that is able to make use of it requires training data that includes server statistics. In order to also use training data where the server statistics are missing, a model that is a mixture over potentially all substitutions thereof is developed.
Another application is to predict the navigation behavior of the users of a website. Here, there is no a priori partitioning of the users into clusters, but to understand different usage scenarios and design different layouts for them, imposing a partitioning is necessary. The presented approach simultaneously optimizes the discriminative as well as the predictive power of the clusters.
Each model is evaluated on real-world data and compared to baseline methods. The results show that explicitly modeling the assumptions about the latent cluster structure leads to improved predictions compared to the baselines. It is beneficial to incorporate a small number of hyperparameters that can be tuned to yield the best predictions in cases where the prediction accuracy can not be optimized directly.<br>Das Lernen eines Modells für den Zusammenhang zwischen den Eingabeattributen und annotierten Zielattributen von Dateninstanzen dient zwei Zwecken. Einerseits ermöglicht es die Vorhersage des Zielattributs für Instanzen ohne Annotation. Andererseits können die Parameter des Modells nützliche Einsichten in die Struktur der Daten liefern. Wenn die Daten eine inhärente Partitionsstruktur besitzen, ist es natürlich, diese Struktur im Modell widerzuspiegeln. Solche Mischmodelle generieren Vorhersagen, indem sie die individuellen Vorhersagen der Mischkomponenten, welche mit den Partitionen der Daten korrespondieren, kombinieren. Oft ist die Partitionsstruktur latent und muss beim Lernen des Mischmodells mitinferiert werden. Eine direkte Evaluierung der Genauigkeit der inferierten Partitionsstruktur ist in vielen Fällen unmöglich, weil keine wahren Referenzdaten zum Vergleich herangezogen werden können. Jedoch kann man sie indirekt einschätzen, indem man die Vorhersagegenauigkeit des darauf basierenden Mischmodells misst.
Diese Arbeit beschäftigt sich mit dem Zusammenspiel zwischen der Verbesserung der Vorhersagegenauigkeit durch das Aufdecken latenter Partitionierungen in Daten, und der Bewertung der geschätzen Struktur durch das Messen der Genauigkeit des resultierenden Vorhersagemodells.
Bei der Anwendung des Filterns unerwünschter E-Mails sind die E-Mails in der Trainingsmende latent in Werbekampagnen partitioniert. Das Aufdecken dieser latenten Struktur erlaubt das Filtern zukünftiger E-Mails mit sehr niedrigen Falsch-Positiv-Raten. In dieser Arbeit wird ein Bayes'sches Partitionierunsmodell entwickelt, um diese Partitionierungsstruktur zu modellieren.
Das Wissen über die Partitionierung von E-Mails in Kampagnen hilft auch dabei herauszufinden, welche E-Mails auf Veranlassen des selben Netzes von infiltrierten Rechnern, sogenannten Botnetzen, verschickt wurden. Dies ist eine weitere Schicht latenter Partitionierung. Diese latente Struktur aufzudecken erlaubt es, die Genauigkeit von E-Mail-Filtern zu erhöhen und sich effektiv gegen verteilte Denial-of-Service-Angriffe zu verteidigen. Zu diesem Zweck wird in dieser Arbeit ein diskriminatives Partitionierungsmodell hergeleitet, welches auf dem Graphen der beobachteten E-Mails basiert. Die mit diesem Modell inferierten Partitionierungen werden via ihrer Leistungsfähigkeit bei der Vorhersage der Kampagnen neuer E-Mails evaluiert.
Weiterhin kann bei der Klassifikation des Inhalts einer E-Mail statistische Information über den sendenden Server wertvoll sein. Ein Modell zu lernen das diese Informationen nutzen kann erfordert Trainingsdaten, die Serverstatistiken enthalten. Um zusätzlich Trainingsdaten benutzen zu können, bei denen die Serverstatistiken fehlen, wird ein Modell entwickelt, das eine Mischung über potentiell alle Einsetzungen davon ist.
Eine weitere Anwendung ist die Vorhersage des Navigationsverhaltens von Benutzern einer Webseite. Hier gibt es nicht a priori eine Partitionierung der Benutzer. Jedoch ist es notwendig, eine Partitionierung zu erzeugen, um verschiedene Nutzungsszenarien zu verstehen und verschiedene Layouts dafür zu entwerfen. Der vorgestellte Ansatz optimiert gleichzeitig die Fähigkeiten des Modells, sowohl die beste Partition zu bestimmen als auch mittels dieser Partition Vorhersagen über das Verhalten zu generieren.
Jedes Modell wird auf realen Daten evaluiert und mit Referenzmethoden verglichen. Die Ergebnisse zeigen, dass das explizite Modellieren der Annahmen über die latente Partitionierungsstruktur zu verbesserten Vorhersagen führt. In den Fällen bei denen die Vorhersagegenauigkeit nicht direkt optimiert werden kann, erweist sich die Hinzunahme einer kleinen Anzahl von übergeordneten, direkt einstellbaren Parametern als nützlich.
3
Qi, Meng. "Development in Normal Mixture and Mixture of Experts Modeling." UKnowledge, 2016. http://uknowledge.uky.edu/statistics_etds/15.
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In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational age data for the same model, whose purposes are to select model complexity from data.
4
Polsen, Orathai. "Nonparametric regression and mixture models." Thesis, University of Leeds, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.578651.
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Nonparametric regression estimation has become popular in the last 50 years. A commonly used nonparametric method for estimating the regression curve is the kernel estimator, exemplified by the Nadaraya- Watson estimator. The first part of thesis concentrates on the important issue of how to make a good choice of smoothing parameter for the Nadaraya- Watson estimator. In this study three types of smoothing parameter selectors are investigated: cross-validation, plug-in and bootstrap. In addition, two situations are examined: the same smoothing parameter and different smoothing parameters are employed for the estimates of the numerator and the denominator. We study the asymptotic bias and variance of the Nadaraya- Watson estimator when different smoothing parameters are used. We propose various plug-in methods for selecting smoothing parameter including a bootstrap smoothing parameter selector. The performances of the proposed selectors are investigated and also compared with cross-validation via a simulation study. Numerical results demonstrate that the proposed plug-in selectors outperform cross-validation when data is bivariate normal distributed. Numerical results also suggest that the proposed bootstrap selector with asymptotic pilot smoothing parameter compares favourably with cross-validation. We consider a circular-circular parametric regression model proposed by Taylor (2009), including parameter estimation and inference. In addition, we investigate diagnostic tools for circular regression which can be generally applied. A final thread is related to mixture models, in particular a mixture of linear regression models and a mixture of circular-circular regression models where there is unobserved group membership of the observation. We investigate methods for selecting starting values for EM algorithm which is used to fit mixture models and also the distributions of these values. Our experiments suggest that the proposed method compares favourably with the common method in mixture linear regression models.
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James, S. D. "Mixture models for times series." Thesis, Swansea University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637395.
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This thesis reviews some known results for the class of mixture models introduced by Jalali and Pemberton (1995) and presents two examples from the literature, which are based on the theory. The first has a countable number of mixture elements while the second has a finite number, <I>K</I>, and is called the Bernstein mixture model, since it involves the use of Bernstein polynomials in its construction. By including an additional parameter, λ, in the Binomial weights function, we obtain a parameterised version of the Bernstein model. The elements of the transition matrix for this model are polynomials in λ of degree <I>K</I> and the stationary distribution assumes a more complicated structure compared with its unparameterised counterpart. A series of elementary mathematical techniques is applied to reduce the elements of the transition matrix to much simpler polynomials and Cramer's Rule is adopted as a solution to obtain an explicit, analytical expression for the stationary distribution of the time series. Through maximum likelihood estimation of the parameters, λ, and <I>K</I>, in the parameterised Bernstein model, the solution developed using Cramer's Rule is compared with an alternative approach for evaluating the stationary distribution. This approach involves implementing a NAG subroutine based on Crout's factorisation method to solve the usual equations for the stationary probability row-vector. Finally, a relatively straightforward treatment of asymptotic maximum likelihood theory is given for the parameterised Bernstein model by employing regularity conditions stated in Billingsley (1961).
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Sandhu, Manjinder Kaur. "Optimal designs for mixture models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B31213583.
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Sánchez, Luis Enrique Benites. "Finite mixture of regression models." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-10052018-131627/.
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This dissertation consists of three articles, proposing extensions of finite mixtures in regression models. Here we consider a flexible class of both univariate and multivariate distributions, which allow adequate modeling of asymmetric data that have multimodality, heavy tails and outlying observations. This class has special cases such as skew-normal, skew-t, skew-slash and skew normal contaminated distributions, as well as symmetric cases. Initially, a model is proposed based on the assumption that the errors follow a finite mixture of scale mixture of skew-normal (FM-SMSN) distribution rather than the conventional normal distribution. Next, we have a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Next, we propose a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Finally, we consider a finite mixture of multivariate regression where the error has a multivariate SMSN distribution. For all proposed models, two R packages were developed, which are reported in the appendix.<br>Esta tese composta por três artigos, visa propor extensões das misturas finitas nos modelos de regressão. Aqui vamos considerar uma classe flexível de distribuições tanto univariada como multivariada, que permitem modelar adequadamente dados assimmétricos, que presentam multimodalidade, caldas pesadas e observações atípicas. Esta classe possui casos especiais tais como as distribuições skew-normal, skew-t, skew slash, skew normal contaminada, assim como os casos simétricos. Inicialmente, é proposto um modelo baseado na suposição de que os erros seguem uma mistura finita da distribuição mistura de escala skew-normal (SMSN) ao invés da convencional distribuição normal. Em seguida, temos um modelo de regressão censurado onde consideramos que o erro segue uma mistura finita da distribuição da mistura de escala normal (SMN). E por último, é considerada um mistura finita de regressão multivariada onde o erro tem uma distribuição SMSN multivariada. Para todos os modelos propostos foram desenvolvidos dois pacotes do software R, que estão exemplificados no apêndice.
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Li, Xiongya. "Robust multivariate mixture regression models." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38427.
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Doctor of Philosophy<br>Department of Statistics<br>Weixing Song<br>In this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution.
The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest.
A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure.
As an illustration, the proposed method is also applied to a real data set.
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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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Evers, Ludger. "Model fitting and model selection for 'mixture of experts' models." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445776.
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Heath, Jeffrey W. "Global optimization of finite mixture models." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7179.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Huang, Qingqing Ph D. Massachusetts Institute of Technology. "Efficient algorithms for learning mixture models." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/107337.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 261-274).<br>We study the statistical learning problems for a class of probabilistic models called mixture models. Mixture models are usually used to model settings where the observed data consists of different sub-populations, yet we only have access to a limited number of samples of the pooled data. It includes many widely used models such as Gaussian mixtures models, Hidden Markov Models, and topic models. We focus on parametric learning: given unlabeled data generated according to a mixture model, infer about the parameters of the underlying model. The hierarchical structure of the probabilistic model leads to non-convexity of the likelihood function in the model parameters, thus imposing great challenges in finding statistically efficient and computationally efficient solutions. We start with a simple, yet general setup of mixture model in the first part. We study the problem of estimating a low rank M x M matrix which represents a discrete distribution over M2 outcomes, given access to sample drawn according to the distribution. We propose a learning algorithm that accurately recovers the underlying matrix using 9(M) number of samples, which immediately lead to improved learning algorithms for various mixture models including topic models and HMMs. We show that the linear sample complexity is actually optimal in the min-max sense. There are "hard" mixture models for which there exist worst case lower bounds of sample complexity that scale exponentially in the model dimensions. In the second part, we study Gaussian mixture models and HMMs. We propose new learning algorithms with polynomial runtime. We leverage techniques in probabilistic analysis to prove that worst case instances are actually rare, and our algorithm can efficiently handle all the non-worst case instances. In the third part, we study the problem of super-resolution. Despite the lower bound for any deterministic algorithm, we propose a new randomized algorithm which complexity scales only quadratically in all dimensions, and show that it can handle any instance with high probability over the randomization.<br>by Qingqing Huang.<br>Ph. D.
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Nkadimeng, Calvin. "Language identification using Gaussian mixture models." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4170.
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Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT: The importance of Language Identification for African languages is seeing a
dramatic increase due to the development of telecommunication infrastructure
and, as a result, an increase in volumes of data and speech traffic in public
networks. By automatically processing the raw speech data the vital assistance
given to people in distress can be speeded up, by referring their calls to a person
knowledgeable in that language.
To this effect a speech corpus was developed and various algorithms were implemented
and tested on raw telephone speech data. These algorithms entailed
data preparation, signal processing, and statistical analysis aimed at discriminating
between languages. The statistical model of Gaussian Mixture Models
(GMMs) were chosen for this research due to their ability to represent an entire
language with a single stochastic model that does not require phonetic transcription.
Language Identification for African languages using GMMs is feasible, although
there are some few challenges like proper classification and accurate
study into the relationship of langauges that need to be overcome. Other methods
that make use of phonetically transcribed data need to be explored and
tested with the new corpus for the research to be more rigorous.<br>AFRIKAANSE OPSOMMING: Die belang van die Taal identifiseer vir Afrika-tale is sien ’n dramatiese toename
te danke aan die ontwikkeling van telekommunikasie-infrastruktuur en as gevolg
’n toename in volumes van data en spraak verkeer in die openbaar netwerke.Deur
outomaties verwerking van die ruwe toespraak gegee die noodsaaklike hulp verleen
aan mense in nood kan word vinniger-up ”, deur te verwys hul oproepe na
’n persoon ingelichte in daardie taal.
Tot hierdie effek van ’n toespraak corpus het ontwikkel en die verskillende algoritmes
is gemplementeer en getoets op die ruwe telefoon toespraak gegee.Hierdie
algoritmes behels die data voorbereiding, seinverwerking, en statistiese analise
wat gerig is op onderskei tussen tale.Die statistiese model van Gauss Mengsel
Modelle (GGM) was gekies is vir hierdie navorsing as gevolg van hul vermo
te verteenwoordig ’n hele taal met’ n enkele stogastiese model wat nodig nie
fonetiese tanscription nie.
Taal identifiseer vir die Afrikatale gebruik GGM haalbaar is, alhoewel daar
enkele paar uitdagings soos behoorlike klassifikasie en akkurate ondersoek na die
verhouding van TALE wat moet oorkom moet word.Ander metodes wat gebruik
maak van foneties getranskribeerde data nodig om ondersoek te word en getoets
word met die nuwe corpus vir die ondersoek te word strenger.
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Chanialidis, Charalampos. "Bayesian mixture models for count data." Thesis, University of Glasgow, 2015. http://theses.gla.ac.uk/6371/.
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Regression models for count data are usually based on the Poisson distribution. This thesis is concerned with Bayesian inference in more flexible models for count data. Two classes of models and algorithms are presented and studied in this thesis. The first employs a generalisation of the Poisson distribution called the COM-Poisson distribution, which can represent both overdispersed data and underdispersed data. We also propose a density regression technique for count data, which, albeit centered around the Poisson distribution, can represent arbitrary discrete distributions. The key contribution of this thesis are MCMC-based methods for posterior inference in these models. One key challenge in COM-Poisson-based models is the fact that the normalisation constant of the COM-Poisson distribution is not known in closed form. We propose two exact MCMC algorithms which address this problem. One is based on the idea of retrospective sampling; we sample the uniform random variable used to decide on the acceptance (or rejection) of the proposed new state of the unknown parameter first and then only evaluate bounds for the acceptance probability, in the hope that we will not need to know the acceptance probability exactly in order to come to a decision on whether to accept or reject the newly proposed value. This strategy is based on an efficient scheme for computing lower and upper bounds for the normalisation constant. This procedure can be applied to a number of discrete distributions, including the COM-Poisson distribution. The other MCMC algorithm proposed is based on an algorithm known as the exchange algorithm. The latter requires sampling from the COM-Poisson distribution and we will describe how this can be done efficiently using rejection sampling. We will also present simulation studies which show the advantages of using the COM-Poisson regression model compared to the alternative models commonly used in literature (Poisson and negative binomial). Three real world applications are presented: the number of emergency hospital admissions in Scotland in 2010, the number of papers published by Ph.D. students and fertility data from the second German Socio-Economic Panel. COM-Poisson distributions are also the cornerstone of the proposed density regression technique based on Dirichlet process mixture models. Density regression can be thought of as a competitor to quantile regression. Quantile regression estimates the quantiles of the conditional distribution of the response variable given the covariates. This is especially useful when the dispersion changes across the covariates. Instead of estimating the conditional mean , quantile regression estimates the conditional quantile function across different quantiles. As a result, quantile regression models both location and shape shifts of the conditional distribution. This allows for a better understanding of how the covariates affect the conditional distribution of the response variable. Almost all quantile regression techniques deal with a continuous response. Quantile regression models for count data have so far received little attention. A technique that has been suggested is adding uniform random noise ('jittering'), thus overcoming the problem that, for a discrete distribution, the conditional quantile function is not a continuous function of the parameters of interest. Even though this enables us to estimate the conditional quantiles of the response variable, it has disadvantages. For small values of the response variable Y, the added noise can have a large influence on the estimated quantiles. In addition, the problem of 'crossing quantiles' still exists for the jittering method. We eliminate all the aforementioned problems by estimating the density of the data, rather than the quantiles. Simulation studies show that the proposed approach performs better than the already established jittering method. To illustrate the new method we analyse fertility data from the second German Socio-Economic Panel.
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Tong, Edward N. C. "Mixture models for consumer credit risk." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/374795/.
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The three papers in this thesis comprise the development of three types of Basel models – a Probability of Default (PD), Loss Given Default (LGD) and Exposure at Default (EAD) model for consumer credit risk, using mixture model methods. Mixture models consider the underlying population as being composed of different sub-populations that are modelled separately. In the first paper (Chapter 2), mixture cure models are introduced to the area of PD/credit scoring. A large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. A mixture cure model predicting (time to) default on a UK personal loan portfolio was developed and its performance compared to industry standard models. The mixture cure model's ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower. The second paper (Chapter 3) considers LGD modelling. One of the key problems in building regression models to estimate loan-level LGD in retail portfolios such as mortgage loans relates to the difficulty in modelling its distribution, which typically contains an extensive amount of zeroes. An alternative approach is proposed in which a mixed discrete-continuous model for the total loss amount incurred on a defaulted loan is developed. The model simultaneously accommodates the probability of zero loss and the loss amount given that loss occurs. This zero-adjusted gamma model is shown to present an alternative and competitive approach to LGD modelling. The third paper (Chapter 4) considers EAD models for revolving credit facilities with variable exposure. The credit conversion factor (CCF), the proportion of the current undrawn amount that will be drawn down at time of default, is used to calculate the EAD and poses modelling challenges with challenging bimodal distributions. We explore alternative EAD models which ignore the CCF formulation and target the EAD distribution directly. We propose a mixture model with the zero-adjusted gamma distribution and compare performance with CCF based models. We find the mixture model to be more accurate in calibration than the CCF models and that segmented approaches offer further performance improvements.
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Schwander, Olivier. "Information-geometric methods for mixture models." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/93/17/22/PDF/these.pdf.
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Cette thèse présente de nouvelles méthodes pour l'apprentissage de modèles de mélanges basées sur la géométrie de l'information. Les modèles de mélanges considérés ici sont des mélanges de familles exponentielles, permettant ainsi d'englober une large part des modèles de mélanges utilisés en pratique. Grâce à la géométrie de l'information, les problèmes statistiques peuvent être traités avec des outils géométriques. Ce cadre offre de nouvelles perspectives permettant de mettre au point des algorithmes à la fois rapides et génériques. Deux contributions principales sont proposées ici. La première est une méthode de simplification d'estimateurs par noyaux. Cette simplification est effectuée à l'aide un algorithme de partitionnement, d'abord avec la divergence de Bregman puis, pour des raisons de rapidité, avec la distance de Fisher-Rao et des barycentres modèles. La seconde contribution est une généralisation de l'algorithme k-MLE permettant de traiter des mélanges où toutes les composantes ne font pas partie de la même famille: cette méthode est appliquée au cas des mélanges de Gaussiennes généralisées et des mélanges de lois Gamma et est plus rapide que les méthodes existantes. La description de ces deux méthodes est accompagnée d'une implémentation logicielle complète et leur efficacité est évaluée grâce à des applications en bio-informatique et en classification de textures<br>This thesis presents new methods for mixture model learning based on information geometry. We focus on mixtures of exponential families, which encompass a large number of mixtures used in practice. With information geometry, statistical problems can be studied with geometrical tools. This framework gives new perspectives allowing to design algorithms which are both fast and generic. Two main contributions are proposed here. The first one is a method for simplification of kernel density estimators. This simplification is made with clustering algorithms, first with the Bregman divergence and next, for speed reason, with the Fisher-Rao distance and model centroids. The second contribution is a generalization of the k-MLE algorithm which allows to deal with mixtures where all the components do not belong to the same family: this method is applied to mixtures of generalized Gaussians and of Gamma laws and is faster than existing methods. The description of this two algorithms comes with a complete software implementation and their efficiency is evaluated through applications in bio-informatics and texture classification
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Julien, Charbel. "Image statistical learning using mixture models." Lyon 2, 2008. http://theses.univ-lyon2.fr/documents/lyon2/2008/julien_c.
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This thesis addresses the problem of modeling the low level visual content (Color, Texture, etc…). Modeling the low level visual content is the first step in any content based image retrieval system. In this thesis we have chosen to model low-level visual content by using a discrete distribution (signature) or a discrete mixture model (GMM) as alternatives, instead of using a multi-dimensional feature vector. Learning a model by signature or by a GMM employing user constraints was presented also. In the literature many relevant works prove the better performance of this kind of image representation instead of the classical fixed-size feature vector. A prototype of image database browsing as well as a semi-automatic image organizing tool that exploits user feedbacks was proposed. Canonical distances such as Euclidian distance, L-2 distance, etc. Can’t be used in the case of signatures. Instead, distances like “Mallows distance” and “Earth Mover’s distance EMD” based on linear optimization are to be considered in the case of signatures. We use an iterative algorithm to compute a model that represents image-sets using user constraints. This optimization problem can be considered as an expectation maximization process. For the expectation step, a soft clustering, with a partial weight, is done with every component's distribution associated with a component of the mixture model we seek to compute. The expectation step is worked out by solving a linear optimization problem. Later, using these partial weights we recompute new components and new component-weights of the centroid, i. E. The maximization step<br>Les travaux de la thèse ont porté essentiellement sur la modélisation du contenu visuel de bas niveau des images (Couleur, Texture, etc…). La modélisation de contenu visuel est la première étape à considérer dans tout système automatique de recherche d'image par contenu, y compris les approches d'apprentissage supervisé, non-supervisé, et semi-supervisé. Dans cette thèse nous avons choisi de modéliser le contenu visuel de bas niveau, par une signature « discret distribution » ou par un modèle du mélange « GMM » au lieu des simples modèles statistiques largement utilisés dans la littérature. En utilisant ces deux types de représentation, un prototype de clustering des bases d'images a été implémenté. Ce prototype est capable d'extraire les signatures et les GMM qui représentent les images, elles sont sauvegardées pour des traitements ultérieurs y compris le clustering des images. Dans ce type de représentation les distances classiques comme la distance Euclidienne, L-2 distance, etc. Ne seront plus applicables. Des distances qui nécessitent une optimisation linéaire peuvent être utilisées pour mesurer la distance entre signatures ou GMMs, exemple : « Mallows distance » et « Earth Mover’s distance EMD ». Calculer un vecteur moyen dans le cas où on utilise des vecteurs multidimensionnels, de longueur fixe, pour représenter les images peut être relativement facile. Par contre, dans notre cas un algorithme itératif qui nécessite de nouveau une optimisation linéaire a été proposé pour apprendre un modèle, signature ou GMM, et cela en exploitant les contraintes fixées par les utilisateurs
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Julien, Charbel Zighed Djamel Abdelkader Saitta Lorenza. "Image statistical learning using mixture models." Lyon : Université Lumière Lyon 2, 2008. http://theses.univ-lyon2.fr/sdx/theses/lyon2/2008/julien_c.
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Reproduction de : Thèse de doctorat : Informatique : Lyon 2 : 2008. Reproduction de : Thèse de doctorat : Informatique : Università di Torino : 2008.<br>Thèse soutenue en co-tutelle. Titre provenant de l'écran-titre. Bibliogr.
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WADE, SARA KATHRYN. "Bayesian nonparametric regression through mixture models." Doctoral thesis, Università Bocconi, 2013. https://hdl.handle.net/11565/4054326.
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Kutal, Durga Hari. "Various Approaches on Parameter Estimation in Mixture and Non-mixture Cure Models." Thesis, Florida Atlantic University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10929031.
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<p> Analyzing life-time data with long-term survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or long-term survivors. In order to include the proportion of cure subjects, mixture and non-mixture cure models are considered. In this dissertation, we utilize both maximum likelihood and Bayesian methods to estimate model parameters. Simulation studies are carried out to verify the finite sample performance of the estimation methods. Real data analyses are reported to illustrate the goodness-of-fit via Fréchet, Weibull and Exponentiated Exponential susceptible distributions. Among the three parametric susceptible distributions, Fréchet is the most promising. </p><p> Next, we extend the non-mixture cure model to include a change point in a covariate for right censored data. The smoothed likelihood approach is used to address the problem of a log-likelihood function which is not differentiable with respect to the change point. The simulation study is based on the non-mixture change point cure model with an exponential distribution for the susceptible subjects. The simulation results revealed a convincing performance of the proposed method of estimation.</p><p>
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Frühwirth-Schnatter, Sylvia. "Model Likelihoods and Bayes Factors for Switching and Mixture Models." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2002. http://epub.wu.ac.at/474/1/document.pdf.
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In the present paper we discuss the problem of estimating model likelihoods from the MCMC output for a general mixture and switching model. Estimation is based on the method of bridge sampling (Meng and Wong, 1996), where the MCMC sample is combined with an iid sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC output using a mixture of complete data posteriors. Whereas the importance sampling estimator as well as the reciprocal importance sampling estimator are sensitive to the tail behaviour of the importance density, we demonstrate that the bridge sampling estimator is far more robust in this concern. Our case studies range from computing marginal likelihoods for a mixture of multivariate normal distributions, testing for the inhomogeneity of a discrete time Poisson process, to testing for the presence of Markov switching and order selection in the MSAR model. (author's abstract)<br>Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Frühwirth-Schnatter, Sylvia. "Model Likelihoods and Bayes Factors for Switching and Mixture Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/1146/1/document.pdf.
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In the present paper we explore various approaches of computing model likelihoods from the MCMC output for mixture and switching models, among them the candidate's formula, importance sampling, reciprocal importance sampling and bridge sampling. We demonstrate that the candidate's formula is sensitive to label switching. It turns out that the best method to estimate the model likelihood is the bridge sampling technique, where the MCMC sample is combined with an iid sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC output using a mixture of complete data posteriors. Whereas the importance sampling estimator as well as the reciprocal importance sampling estimator are sensitive to the tail behaviour of the importance density, we demonstrate that the bridge sampling estimator is far more robust in this concern. Our case studies range from from selecting the number of classes in a mixture of multivariate normal distributions, testing for the inhomogeneity of a discrete time Poisson process, to testing for the presence of Markov switching and order selection in the MSAR model. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
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Haas, Markus. "Dynamic mixture models for financial time series /." Berlin : Pro Business, 2004. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=012999049&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Gundersen, Terje. "Voice Transformation based on Gaussian mixture models." Thesis, Norwegian University of Science and Technology, Department of Electronics and Telecommunications, 2010. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-10878.
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<p>In this thesis, a probabilistic model for transforming a voice to sound like another specific voice is tested. The model is fully automatic and only requires some 100 training sentences from both speakers with the same acoustic content. The classical source-filter decomposition allows prosodic and spectral transformation to be performed independently. The transformations are based on a Gaussian mixture model and a transformation function suggested by Y. Stylianou. Feature vectors of the same content from the source and target speaker, aligned in time by dynamic time warping, are fitted to a GMM. The short time spectra, represented as cepstral coefficients and derived from LPC, and the pitch periods, represented as fundamental frequency estimated from the RAPT algorithm, are transformed with the same probabilistic transformation function. Several techniques of spectrum and pitch transformation were assessed in addition to some novel smoothing techniques of the fundamental frequency contour. The pitch transform was implemented on the excitation signal from the inverse LP filtering by time domain PSOLA. The transformed spectrum parameters were used in the synthesis filter with the transformed excitation as input to yield the transformed voice. A listening test was performed with the best setup from objective tests and the results indicate that it is possible to recognise the transformed voice as the target speaker with a 72 % probability. However, the synthesised voice was affected by a muffling effect due to incorrect frequency transformation and the prosody sounded somewhat robotic.</p>
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Saba, Laura M. "Latent pattern mixture models for binary outcomes /." Connect to full text via ProQuest. Limited to UCD Anschutz Medical Campus, 2007.
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Thesis (Ph.D. in Biostatistics) -- University of Colorado Denver, 2007.<br>Typescript. Includes bibliographical references (leaves 70-71). Free to UCD affiliates. Online version available via ProQuest Digital Dissertations;
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Liu, Zhao, and 劉釗. "On mixture double autoregressive time series models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/196465.
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Conditional heteroscedastic models are one important type of time series models which have been widely investigated and brought out continuously by scholars in time series analysis. Those models play an important role in depicting the characteristics of the real world phenomenon, e.g. the behaviour of _nancial market. This thesis proposes a mixture double autoregressive model by adopting the exibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed by Ling (2004). Probabilistic properties including strict stationarity and higher order moments are derived for this new model and, to make it more exible, a logistic mixture double autoregressive model is further introduced to take into account the time varying mixing proportions. Inference tools including the maximum likelihood estimation, an EM algorithm for searching the estimator and an information criterion for model selection are carefully studied for the logistic mixture double autoregressive model. We notice that the shape changing characteristics of the multimodal conditional distributions is an important feature of this new type of model. The conditional heteroscedasticity of time series is also well depicted. Monte Carlo experiments give further support to these two new models, and the analysis of an empirical example based on our new models as well as other mainstream ones is also reported.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Master<br>Master of Philosophy
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Fahey, Michael Thomas. "Finite mixture models for dietary pattern identification." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611505.
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Wei, Yan. "Robust mixture regression models using t-distribution." Kansas State University, 2012. http://hdl.handle.net/2097/14110.
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Master of Science<br>Department of Statistics<br>Weixin Yao<br>In this report, we propose a robust mixture of regression based on t-distribution by
extending the mixture of t-distributions proposed by Peel and McLachlan (2000) to the
regression setting. This new mixture of regression model is robust to outliers in y direction but not robust to the outliers with high leverage points. In order to combat this, we also propose a modified version of the proposed method, which fits the mixture of regression based on t-distribution to the data after adaptively trimming the high leverage points. We
further propose to adaptively choose the degree of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degree of freedom. We demonstrate the effectiveness of the proposed new method and compare it with some of the existing methods through simulation study.
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Morfopoulou, S. "Bayesian mixture models for metagenomic community profiling." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1473450/.
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Metagenomics can be defined as the study of DNA sequences from environmental or community samples. This is a rapidly progressing field and application ideas that seemed outlandish a few years ago are now routine and familiar. Metagenomics’ scope is broad and includes the analysis of a diverse set of samples such as environmental or clinical samples. Human tissues are in essence metagenomic samples due to the presence of microorganisms, such as bacteria, viruses and fungi in both healthy and diseased individuals. Deep sequencing of clinical samples is now an established tool for pathogen detection, with direct medical applications. The large amount of data generated produces an opportunity to detect species even at very low levels, provided that computational tools can effectively profile the relevant metagenomic communities. Data interpretation is complicated by the fact that short sequencing reads can match multiple organisms and by the lack of completeness of existing databases, particularly for viruses. The research presented in this thesis focuses on using Bayesian Mixture Model techniques to produce taxonomic profiles for metagenomic data. A novel Bayesian mixture model framework for resolving complex metagenomic mixtures is introduced, called metaMix. The use of parallel Monte Carlo Markov chains (MCMC) for the exploration of the species space enables the identification of the set of species most likely to contribute to the mixture. The improved accuracy of metaMix compared to relevant methods is demonstrated, particularly for profiling complex communities consisting of several related species. metaMix was designed specifically for the analysis of deep transcriptome sequencing datasets, with a focus on viral pathogen detection. However, the principles are generally applicable to all types of metagenomic mixtures. metaMix is implemented as a user friendly R package, freely available on CRAN: http://cran.r-project.org/web/packages/metaMix.
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Zhang, Xiuyun. "Efficient Algorithms for Fitting Bayesian Mixture Models." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1243990513.
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He, Ruofei. "Bayesian mixture models for frequent itemset mining." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/bayesian-mixture-models-for-frequent-itemset-mining(6d88d0d1-3066-4545-8565-56d651eeadc4).html.
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In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely used in the development of probability models in machine learning in recent years and these methods have many advantages, including their abilities to avoid overfitting. In this thesis, we develop two Bayesian mixture models with the Dirichlet distribution prior and the Dirichlet process (DP) prior to improve the previous non-Bayesian mixture model developed for transaction dataset mining. First, we develop a finite Bayesian mixture model by introducing conjugate priors to the model. Then, we extend this model to an infinite Bayesian mixture using a Dirichlet process prior. The Dirichlet process mixture model is a nonparametric Bayesian model which allows for the automatic determination of an appropriate number of mixture components. We implement the inference of both mixture models using two methods: a collapsed Gibbs sampling scheme and a variational approximation algorithm. Experiments in several benchmark problems have shown that both mixture models achieve better performance than a non-Bayesian mixture model. The variational algorithm is the faster of the two approaches while the Gibbs sampling method achieves a more accurate result. The Dirichlet process mixture model can automatically grow to a proper complexity for a better approximation. However, these approaches also show that mixture models underestimate the probabilities of frequent itemsets. Consequently, these models have a higher sensitivity but a lower specificity.
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Subramaniam, Anand D. "Gaussian mixture models in compression and communication /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3112847.
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Kang, An. "Online Bayesian nonparametric mixture models via regression." Thesis, University of Kent, 2018. https://kar.kent.ac.uk/66306/.
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Sensors are widely used in modern industrial systems as well as consumer devices, such as food production, energy transportation and nuclear power plant. The sensors of interest in this project from an engineering company are associated with industrial control systems, where high precision is the dominant concern. Due to manufacturing variation, sensors manufactured from the same production line are non-identical. Therefore, each sensor needs to be characterised via parameter estimation to achieve a high precision or accuracy before sending to the end users. The classical linear regression model has been adopted in current industry procedure, which requires a certain number of measurements per device to achieve the required level of accuracy. The aim of the project is, under guarantee of the required level of accuracy, to use the available information and advanced statistical models to reduce the number of measurements needed per sensor, and hence reduce both costs and time for the characterisation process. To achieve this, a Bayesian linear model with Dirichlet process mixture prior (BL-DPMP) is proposed, where the Bayesian linear regression presents the relationship between the response variable and the covariates demonstrated to be appropriate by the company, and the regression coefficients are modelled by a Dirichlet process mixture (DPM) model. The idea here is to apply the DPM model to the historical information from similar sensors to provide adequate prior information to the linear regression model in order to compensate the current characterising sensor with block missing measurements, at the same time to maintain the required level of accuracy. The slice sampling scheme based on the full conditional posteriors of hyperparameters is used to update the parameters in the DPM model. Also, a generalised Dirichlet process mixture regression model is proposed with a data-driven prediction procedure to deal with the considered situation. By reducing the number of measurements required per sensor, we could drastically reduce the characterisation period. However, two proposed approaches are quite computationally intensive, which counteract the time saved from collecting a fewer number of measurements. Hence, there is a clearly pressing need for dramatically faster alternatives. A hybrid Variational Bayes (HVB) procedure following a greedy searching scheme is proposed, which can dramatically reduce the computational time, at the same time provide highly accurate approximations of the exact posterior distributions. The ultimate goal of this project is to implement the proposed advanced statistical model in the production line, where the model can be executed within seconds (online). An optimal permutation sequential (OPS) algorithm for the DPM model is proposed, which differs from MCMC algorithms. The idea is to draw approximate independent and identically distributed samples from the posterior distribution of the latent allocations, and to draw samples from the weights and locations conditional on the allocations. Hence, independent draws are taken from the posterior distribution, which allow us to take independent samples from the predictive distribution. The OPS algorithm requires only a single run which the computational costs of a few seconds. We present examples to show model performance on simulated and real datasets. It is worth noting that the proposed Bayesian linear model with Dirichlet process mixture prior together with the OPS algorithm is under the testing stage of being implemented in our industrial partner's production line. This research acts as the underpinning work and contributes to a potential impact case for the Research Excellence Framework (REF) 2021.
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Yu, Chun. "Robust mixture modeling." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18153.
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Doctor of Philosophy<br>Department of Statistics<br>Weixin Yao and Kun Chen<br>Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual
values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters.
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Cilliers, Francois Dirk. "Tree-based Gaussian mixture models for speaker verification." Thesis, Link to the online version, 2005. http://hdl.handle.net/10019.1/1639.
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Chang, Ilsung. "Bayesian inference on mixture models and their applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3990.
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Mixture models are useful in describing a wide variety of random phenomena because
of their flexibility in modeling. They have continued to receive increasing attention
over the years from both a practical and theoretical point of view. In their applications,
estimating the number of mixture components is often the main research
objective or the first step toward it. Estimation of the number of mixture components
heavily depends on the underlying distribution. As an extension of normal
mixture models, we introduce a skew-normal mixture model and adapt the reversible
jump Markov chain Monte Carlo algorithm to estimate the number of components
with some applications to biological data.
The reversible jump algorithm is also applied to the Cox proportional hazard
model with frailty. We consider a regression model for the variance components in
the proportional hazards frailty model. We propose a Bayesian model averaging procedure
with a reversible jump Markov chain Monte Carlo step which selects the model
automatically. The resulting regression coefficient estimates ignore the model uncertainty
from the frailty distribution. Finally, the proposed model and the estimation
procedure are illustrated with simulated example and real data.
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Yen, Ming-Fang. "Frailty and mixture models in cancer screening evaluation." Thesis, University College London (University of London), 2004. http://discovery.ucl.ac.uk/1446761/.
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The prevalence of screen-detected premalignancies is too large for it to be feasible that all can progress to carcinoma at the same average rate, unless that rate is very low indeed. There are likely to be frailties in the rates of progression. Failure to take heterogeneity into account will lead to biased estimates and could result in inappropriate screening policy. Approaches to investigation of heterogeneity in the propensity for screen-detected disease to progress comprise the main objectives of this project. We used Markov models with constant hazard rates in sequence throughout the process of disease natural history within subjects, with heterogeneity terms by means of (1) frailty models for continuous heterogeneity, (2) mover-stayer models for dichotomous heterogeneity (in both cases for progression between sequential homogeneous models), and (3) latent variables and states to estimate the parameters of progressive disease natural history in the presence of unobserved factors. Approaches had to be developed to address problems of tractability and estimation. For example, in the presence of frailty, solution of the Kolmogorov equations by routine matrix algebra is no longer possible. Heterogeneous models, both discrete and continuous, were found to be tractable, and estimation was possible for a variety of designs and data structures. Such models illuminated various issues in real screening applications. Quantifying heterogeneity of potential progress of disease is of potential importance to the screening process. There are trade-offs between model complexity, identifiability and data availability, but there are clear examples, such as that of cervical screening, where a heterogeneous model improves model fit and gives more realistic estimates than a homogenous.
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Zhang, Xuekui. "Mixture models for analysing high throughput sequencing data." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/35982.
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The goal of my thesis is to develop methods and software for analysing high-throughput sequencing data, emphasizing sonicated ChIP-seq. For this goal, we developed a few variants of mixture models for genome-wide profiling of transcription factor binding sites and nucleosome positions. Our methods have been implemented into Bioconductor packages, which are freely available to other researchers.
For profiling transcription factor binding sites, we developed a method, PICS, and implemented it into a Bioconductor package. We used a simulation study to confirm that PICS compares favourably to rival methods, such as MACS, QuEST, CisGenome, and USeq. Using published GABP and FOXA1 data from human cell lines, we then show that PICS predicted binding sites were more consistent with computationally predicted binding motifs than the alternative methods.
For motif discovery using transcription binding sites, we combined PICS with two other existing packages to create the first complete set of Bioconductor tools for peak-calling and binding motif analysis of ChIP-Seq and ChIP-chip data. We demonstrate the effectiveness of our pipeline on published human ChIP-Seq datasets for FOXA1, ER, CTCF and STAT1, detecting co-occurring motifs that were consistent with the literature but not detected by other methods.
For nucleosome positioning, we modified PICS into a method called PING. PING can handle MNase-Seq and MNase- or sonicated-ChIP-Seq data. It compares favourably to NPS and TemplateFilter in scalability, accuracy and robustness to low read density. To demonstrate that PING predictions from sonicated data can have sufficient spatial resolution to be biologically meaningful, we use H3K4me1 data to detect nucleosome shifts, discriminate functional and non-functional transcription factor binding sites, and confirm that Foxa2 associates with the accessible major groove of nucleosomal DNA.
All of the above uses single-end sequencing data. At the end of the thesis, we briefly discuss the issue of processing paired-end data, which we are currently investigating.
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Lu, Liang. "Subspace Gaussian mixture models for automatic speech recognition." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8065.
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In most of state-of-the-art speech recognition systems, Gaussian mixture models (GMMs) are used to model the density of the emitting states in the hidden Markov models (HMMs). In a conventional system, the model parameters of each GMM are estimated directly and independently given the alignment. This results a large number of model parameters to be estimated, and consequently, a large amount of training data is required to fit the model. In addition, different sources of acoustic variability that impact the accuracy of a recogniser such as pronunciation variation, accent, speaker factor and environmental noise are only weakly modelled and factorized by adaptation techniques such as maximum likelihood linear regression (MLLR), maximum a posteriori adaptation (MAP) and vocal tract length normalisation (VTLN). In this thesis, we will discuss an alternative acoustic modelling approach — the subspace Gaussian mixture model (SGMM), which is expected to deal with these two issues better. In an SGMM, the model parameters are derived from low-dimensional model and speaker subspaces that can capture phonetic and speaker correlations. Given these subspaces, only a small number of state-dependent parameters are required to derive the corresponding GMMs. Hence, the total number of model parameters can be reduced, which allows acoustic modelling with a limited amount of training data. In addition, the SGMM-based acoustic model factorizes the phonetic and speaker factors and within this framework, other source of acoustic variability may also be explored. In this thesis, we propose a regularised model estimation for SGMMs, which avoids overtraining in case that the training data is sparse. We will also take advantage of the structure of SGMMs to explore cross-lingual acoustic modelling for low-resource speech recognition. Here, the model subspace is estimated from out-domain data and ported to the target language system. In this case, only the state-dependent parameters need to be estimated which relaxes the requirement of the amount of training data. To improve the robustness of SGMMs against environmental noise, we propose to apply the joint uncertainty decoding (JUD) technique that is shown to be efficient and effective. We will report experimental results on the Wall Street Journal (WSJ) database and GlobalPhone corpora to evaluate the regularisation and cross-lingual modelling of SGMMs. Noise compensation using JUD for SGMM acoustic models is evaluated on the Aurora 4 database.
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Hernandez-Vela, Carlos Erwin Rodriguez. "Contributions to the Bayesian analysis of mixture models." Thesis, University of Kent, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.594272.
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Mixture models can be used to approximate irregular densities or to model heterogeneity. ·When a density estimate is needed, then we can approximate any distribution on the real line using an infinite number of normals (Ferguson (1983)). On the other hand, when a mLxture model is used to model heterogeneity, there is a proper interpretation for each element of the modeL If the distributional assumptions about the components are met and the number of underlying clusters within the data is known, then in a Bayesian setting, to perform classification analysis and in general component specific inference, methods to undo the label switching and recover the interpretation of the components need to be applied. If latent allocations for the design of the Markov chain Monte Carlo (MCMC) strategy are included, and the sampler has converged, then labels assigned to each component may change from iteration to iteration. However, observations being allocated together must remain similar, and we use this fundamental fact to derive an easy and efficient solution to the label switching problem. We compare our strategy with other relabeling algorithms on univariate and multivariate data examples and demonstrate improvements over alternative strategies. When there is no further information about the shape of components and the number of clusters within the data, then a common theme is the use of the normal distribution as the "benchmark" components distribution. However, if a cluster is skewed or heavy tailed, then the normal distribution will be inefficient and many may be needed to model a single cluster. In this thesis, we present an attempt to solve this problem. We define a cluster to be a group of data which can be modeled by a unimodal density function. Hence, our intention is to use a family of univariate distribution funct ions, to replace the normal, for which the only constraint is unimodality. With this aim, we devise a new family of nonparametric unimodal distributions, which has large support over the space of univariate unimoda1 distributions. The difficult aspect of the Bayesian model is to construct a suitable MCMC algorithm to sample from the correct posterior distribution. The key will be the introduction of strategic latent variables and the use of the product space (Godsill (2001») view of reversible jump (Green (1995») methodology. We illustrate and compare our methodology against the classic mixture of normals using simulated and real data sets. To solve the label switching problem we use the new relabeling algorithm.
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Al, Hakmani Rahab. "Bayesian Estimation of Mixture IRT Models using NUTS." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1641.
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The No-U-Turn Sampler (NUTS) is a relatively new Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior that common MCMC algorithms such as Gibbs sampling or Metropolis Hastings usually exhibit. Given the fact that NUTS can efficiently explore the entire space of the target distribution, the sampler converges to high-dimensional target distributions more quickly than other MCMC algorithms and is hence less computational expensive. The focus of this study is on applying NUTS to one of the complex IRT models, specifically the two-parameter mixture IRT (Mix2PL) model, and further to examine its performance in estimating model parameters when sample size, test length, and number of latent classes are manipulated. The results indicate that overall, NUTS performs well in recovering model parameters. However, the recovery of the class membership of individual persons is not satisfactory for the three-class conditions. Also, the results indicate that WAIC performs better than LOO in recovering the number of latent classes, in terms of the proportion of the time the correct model was selected as the best fitting model. However, when the effective number of parameters was also considered in selecting the best fitting model, both fully Bayesian fit indices perform equally well. In addition, the results suggest that when multiple latent classes exist, using either fully Bayesian fit indices (WAIC or LOO) would not select the conventional IRT model. On the other hand, when all examinees came from a single unified population, fitting MixIRT models using NUTS causes problems in convergence.
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Qarmalah, Najla Mohammed A. "Finite mixture models : visualisation, localised regression, and prediction." Thesis, Durham University, 2018. http://etheses.dur.ac.uk/12486/.
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Initially, this thesis introduces a new graphical tool, that can be used to summarise data possessing a mixture structure. Computation of the required summary statistics makes use of posterior probabilities of class membership obtained from a fitted mixture model. In this context, both real and simulated data are used to highlight the usefulness of the tool for the visualisation of mixture data in comparison to the use of a traditional boxplot. This thesis uses localised mixture models to produce predictions from time series data. Estimation method used in these models is achieved using a kernel-weighted version of an EM-algorithm: exponential kernels with different bandwidths are used as weight functions. By modelling a mixture of local regressions at a target time point, but using different bandwidths, an informative estimated mixture probabilities can be gained relating to the amount of information available in the data set. This information is given a scale of resolution, that corresponds to each bandwidth. Nadaraya-Watson and local linear estimators are used to carry out localised estimation. For prediction at a future time point, a new methodology of bandwidth selection and adequate methods are proposed for each local method, and then compared to competing forecasting routines. A simulation study is executed to assess the performance of this model for prediction. Finally, double-localised mixture models are presented, that can be used to improve predictions for a variable time series using additional information provided by other time series. Estimation for these models is achieved using a double-kernel-weighted version of the EM-algorithm, employing exponential kernels with different horizontal bandwidths and normal kernels with different vertical bandwidths, that are focused around a target observation at a given time point. Nadaraya-Watson and local linear estimators are used to carry out the double-localised estimation. For prediction at a future time point, different approaches are considered for each local method, and are compared to competing forecasting routines. Real data is used to investigate the performance of the localised and double-localised mixture models for prediction. The data used predominately in this thesis is taken from the International Energy Agency (IEA).
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Meddings, D. P. "Statistical inference in mixture models with random effects." Thesis, University College London (University of London), 2014. http://discovery.ucl.ac.uk/1455733/.
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There is currently no existing asymptotic theory for statistical inference on the maximum likelihood estimators of the parameters in a mixture of linear mixed models (MLMMs). Despite this many researchers assume the estimators are asymptotically normally distributed with covariance matrix given by the inverse of the information matrix. Mixture models create new identifability problems that are not inherited from the underlying linear mixed model (LMM), and this subject has not been investigated for these models. Since identifability is a prerequisite for the existence of a consistent estimator of the model parameters, then this is an important area of research that has been neglected. MLMMs are mixture models with random effects, and they are typically used in medical and genetics settings where random heterogeneity in repeated measures data are observed between measurement units (people, genes), but where it is assumed the units belong to one and only one of a finite number of sub-populations or components. This is expressed probabalistically by using a sub-population specific probability distribution function which are often called the component distribution functions. This thesis is motivated by the belief that the use of MLMMs in applied settings such as these is being held back by the lack of development of the statistical inference framework. Specifically this thesis has the following primary objectives; i To investigate the quality of statistical inference provided by different information matrix based methods of confidence interval construction. ii To investigate the impact of component distribution function separation on the quality of statistical inference, and to propose a new method to quantify this separation. iii To determine sufficient conditions for identifiability of MLMMs.
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Pinto, Rafael Coimbra. "Continuous reinforcement learning with incremental Gaussian mixture models." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/157591.
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A contribução original desta tese é um novo algoritmo que integra um aproximador de funções com alta eficiência amostral com aprendizagem por reforço em espaços de estados contínuos. A pesquisa completa inclui o desenvolvimento de um algoritmo online e incremental capaz de aprender por meio de uma única passada sobre os dados. Este algoritmo, chamado de Fast Incremental Gaussian Mixture Network (FIGMN) foi empregado como um aproximador de funções eficiente para o espaço de estados de tarefas contínuas de aprendizagem por reforço, que, combinado com Q-learning linear, resulta em performance competitiva. Então, este mesmo aproximador de funções foi empregado para modelar o espaço conjunto de estados e valores Q, todos em uma única FIGMN, resultando em um algoritmo conciso e com alta eficiência amostral, i.e., um algoritmo de aprendizagem por reforço capaz de aprender por meio de pouquíssimas interações com o ambiente. Um único episódio é suficiente para aprender as tarefas investigadas na maioria dos experimentos. Os resultados são analisados a fim de explicar as propriedades do algoritmo obtido, e é observado que o uso da FIGMN como aproximador de funções oferece algumas importantes vantagens para aprendizagem por reforço em relação a redes neurais convencionais.<br>This thesis’ original contribution is a novel algorithm which integrates a data-efficient function approximator with reinforcement learning in continuous state spaces. The complete research includes the development of a scalable online and incremental algorithm capable of learning from a single pass through data. This algorithm, called Fast Incremental Gaussian Mixture Network (FIGMN), was employed as a sample-efficient function approximator for the state space of continuous reinforcement learning tasks, which, combined with linear Q-learning, results in competitive performance. Then, this same function approximator was employed to model the joint state and Q-values space, all in a single FIGMN, resulting in a concise and data-efficient algorithm, i.e., a reinforcement learning algorithm that learns from very few interactions with the environment. A single episode is enough to learn the investigated tasks in most trials. Results are analysed in order to explain the properties of the obtained algorithm, and it is observed that the use of the FIGMN function approximator brings some important advantages to reinforcement learning in relation to conventional neural networks.
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Jayaram, Vikram. "Reduced dimensionality hyperspectral classification using finite mixture models." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Desai, Manisha. "Mixture models for genetic changes in cancer cells /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/9566.
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Yu, Chen. "The use of mixture models in capture-recapture." Thesis, University of Kent, 2015. https://kar.kent.ac.uk/50775/.
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Mixture models have been widely used to model heterogeneity. In this thesis, we focus on the use of mixture models in capture--recapture, for both closed populations and open populations. We provide both practical and theoretical investigations. A new model is proposed for closed populations and the practical difficulties of model fitting for mixture models are demonstrated for open populations. As the number of model parameters can increase with the number of mixture components, whether we can estimate all of the parameters using the method of maximum likelihood is an important issue. We explore this using formal methods and develop general rules to ensure that all parameters are estimable.
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Paganin, Sally. "Prior-driven cluster allocation in bayesian mixture models." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3426831.
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There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations of such prior in terms of an Exchangeable Partition Probability Function (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. Our motivation is drawn from an epidemiological application, in which we wish to cluster birth defects into groups and we have a prior knowledge of an initial clustering provided by experts. The underlying assumption is that birth defects in the same group may have similar coefficients in logistic regression analysis relating different exposures to risk of developing the defect. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies a base EPPF to favor partitions in a convenient distance neighborhood of the initial clustering. This thesis focus on providing characterization of such new class, along with properties and general algorithms for posterior computation. We illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
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Kremer, Laura. "Assessment of a Credit Value atRisk for Corporate Credits." Thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-124146.
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In this thesis I describe the essential steps of developing a credit rating system. This comprises the credit scoring process that assigns a credit score to each credit, the forming of rating classes by the k-means algorithm and the assignment of a probability of default (PD) for the rating classes. The main focus is on the PD estimation for which two approaches are presented. The first and simple approach in form of a calibration curve assumes independence of the defaults of different corporate credits. The second approach with mixture models is more realistic as it takes default dependence into account. With these models we can use an estimate of a country’s GDP to calculate an estimate for the Value-at-Risk of some credit portfolio.
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He, Xiaojun Velu Rajabather Palani. "Two essays on applications of mixture models in finance." Related Electronic Resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2003. http://wwwlib.umi.com/cr/syr/main.
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