In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

In this dissertation, I explored relational learning via latent variable models. Traditional machine learning algorithms cannot handle many learning problems where there is a need for modeling both relations and noise. Statistical relational learning approaches emerged to handle these applications by incorporating both relations and uncertainties in these problems. Latent variable models are one of the successful approaches for statistical relational learning. These models assume a latent variable for each entity and then the probability distribution over relationships between entities is modeled via a function over latent variables. One important example of relational learning via latent variables is text data modeling. In text data modeling, we are interested in modeling the relationship between words and documents. Latent variable models learn this data by assuming a latent variable for each word and document. The co-occurrence value is defined as a function of these random variables. For modeling co-occurrence data in general (and text data in particular), we proposed latent logistic allocation (LLA). LLA outperforms the-state-of-the-art model --- latent Dirichlet allocation --- in text data modeling, document categorization and information retrieval. We also proposed query-based visualization which embeds documents relevant to a query in a 2-dimensional space. Additionally, I used latent variable models for other single-relational problems such as collaborative filtering and educational data mining. To move towards multi-relational learning via latent variable models, we propose latent feature networks (LFN). Multi-relational learning approaches model multiple relationships simultaneously. LFN assumes a component for each relationship. Each component is a latent variable model where a latent variable is defined for each entity and the relationship is a function of latent variables. However, if an entity participates in more than one relationship, then it will have a separate random variable for each relationship. We used LFN for modeling two different problems: microarray classification and social network analysis with a side network. In the first application, LFN outperforms support vector machines --- the best propositional model for that application. In the second application, using the side information via LFN can drastically improve the link prediction task in a social network.

There has been a significant increase in private vehicle ownership in the last decade leading to substantial increase in air pollution, depleting fuel reserves, etc. One of the alternatives known as battery operated electric vehicles (BEVs) has the potential to reduce carbon footprints due to lesser or no emissions and thus the focus on shifting people from gasoline operated vehicles (GVs) to BEVs has increased considerably recently. However, BEVs have a limited ‘range’ and takes considerable time to completely recharge its battery. In addition, charging stations are not as pervasive as gasoline stations. As a result a new fear of getting stranded is observed in BEV drivers, known as range anxiety. Range anxiety has the potential to substantially affect the route choice of a BEV user. It has also been a major cause of lower market shares of BEVs. Range anxiety is a latent feeling which cannot be measured directly. It is not homogenous either and varies among different socio-economic groups. Thus, a better understanding of BEV users’ behavior may shed light on some potential solutions that can then be used to improve their market shares and help in developing new network models which can realistically capture effects of varying EV adoptions. Thus, in this study, we analyze the factors that may impact BEV users’ range anxiety in addition to their route choice behavior using the integrated choice latent variable model (ICLV) proposed by Bhat and Dubey (2014). Our results indicate that an individual’s range anxiety is significantly affected by their age, gender, income, awareness of charging stations, BEV ownership and other category vehicle ownership. Further, it also highlights the importance of including disutility caused by distance while considering network flow models with combined GV and BEV assignment. Finally, a more concentrated effort can be directed towards increasing the awareness of charging station locations in the neighborhood to help reduce the psychological barrier associated with range anxiety. Overcoming this barrier may help increase consumer confidence, resulting in increased BEV adoption and ultimately will lead towards a potentially pollution-free environment. / text

The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.

The phrase "opportunities to learn" (OTL) is most commonly interpreted in institutional, or inter-individual, terms but it can also be viewed as a cognitive, or intra-individual, phenomenon. How student learning heterogeneity (LH) - learning differences manifested when children's understanding is later assessed - is understood varies by OTL interpretation. In this study, I argue that the cognitive underpinning of learning disability, learning difficulty, typical achievement, and gifted achievement in mathematics is not well understood in part because of the ambiguity of LH assumptions in previous studies. Data from 104,315 Ontario students who had responded to provincially-mandated mathematics tests in grades 3, 6, and 9 dataset were analyzed using latent trait analysis (LTM) and latent class analysis (LCA). The tests were constructed to distinguish four achievement levels per grade and, either five curriculum strands (grades 3 and 6), three strands (grade 9 applied) or four strands (grade 9 academic). Best-fitting LTM models reflected 3- or 4-factors (grade 9 applied and grades 3, 6, 9 academic, respectively). Best-fitting LCA solutions reflected 4- or 5-classes (grade 3, 6 and grade 9 applied, academic, respectively). There were differences in relative proportions of students who were distributed across levels and classes. Moreover, grade 9 models were more complex than the reported four achievement levels. To explore intrinsic modeled results further, latent factors were plotted against latent classes. Implications of institutional versus cognitive interpretations are discussed.

Correlated ordinal data typically arises from multiple measurements on a collection of subjects. Motivated by an application in credit risk, where multiple credit rating agencies assess the creditworthiness of a firm on an ordinal scale, we consider multivariate ordinal regression models with a latent variable specification and correlated error terms. Two different link functions are employed, by assuming a multivariate normal and a multivariate logistic distribution for the latent variables underlying the ordinal outcomes. Composite likelihood methods, more specifically the pairwise and tripletwise likelihood approach, are applied for estimating the model parameters. Using simulated data sets with varying number of subjects, we investigate the performance of the pairwise likelihood estimates and find them to be robust for both link functions and reasonable sample size. The empirical application consists of an analysis of corporate credit ratings from the big three credit rating agencies (Standard & Poor's, Moody's and Fitch). Firm-level and stock price data for publicly traded US firms as well as an unbalanced panel of issuer credit ratings are collected and analyzed to illustrate the proposed framework.

We propose a statistical model for weighted temporal networks capable of measuring the level of heterogeneity in a financial system. Our model focuses on the level of diversification of financial institutions; that is, whether they are more inclined to distribute their assets equally among partners, or if they rather concentrate their commitment towards a limited number of institutions. Crucially, a Markov property is introduced to capture time dependencies and to make our measures comparable across time. We apply the model on an original dataset of Austrian interbank exposures. The temporal span encompasses the onset and development of the financial crisis in 2008 as well as the beginnings of European sovereign debt crisis in 2011. Our analysis highlights an overall increasing trend for network homogeneity, whereby core banks have a tendency to distribute their market exposures more equally across their partners.

Correlated ordinal data typically arise from multiple measurements on a collection of subjects. Motivated by an application in credit risk, where multiple credit rating agencies assess the creditworthiness of a firm on an ordinal scale, we consider multivariate ordinal models with a latent variable specification and correlated error terms. Two different link functions are employed, by assuming a multivariate normal and a multivariate logistic distribution for the latent variables underlying the ordinal outcomes. Composite likelihood methods, more specifically the pairwise and tripletwise likelihood approach, are applied for estimating the model parameters. We investigate how sensitive the pairwise likelihood estimates are to the number of subjects and to the presence of observations missing completely at random, and find that these estimates are robust for both link functions and reasonable sample size. The empirical application consists of an analysis of corporate credit ratings from the big three credit rating agencies (Standard & Poor's, Moody's and Fitch). Firm-level and stock price data for publicly traded US companies as well as an incomplete panel of issuer credit ratings are collected and analyzed to illustrate the proposed framework. / Series: Research Report Series / Department of Statistics and Mathematics

This work discusses the detection of latent variables, which create indices of economic freedom. Firstly, we present the most well-known indices of economic freedom (IEF, EFW). Secondly, this work discusses multivariate statistical method - factor analysis, which we use to detect latent variables. We show different methods of estimates in factor analysis and we focus on principal factor method. Furthermore, we compare already defined methods by analysing the structure of EFW index. According to estimated models, we interpret detected latent variables. We use statistical software SPSS and R for factor analysis of EFW index.

In this thesis we present novel methods for constructing and fitting 2d models of shape and appearance which are used for analysing human faces. The first contribution builds on previous work on discriminative fitting strategies for active appearance models (AAMs) in which regression models are trained to predict the location of shapes based on texture samples. In particular, we investigate non-parametric regression methods including random forests and Gaussian processes which are used together with gradient-like features for shape model fitting. We then develop two training algorithms which combine such models into sequences, and systematically compare their performance to existing linear generative AAM algorithms. Inspired by the performance of the Gaussian process-based regression methods, we investigate a group of non-linear latent variable models known as Gaussian process latent variable models (GPLVM). We discuss how such models may be used to develop a generative active appearance model algorithm whose texture model component is non-linear, and show how this leads to lower-dimensional models which are capable of generating more natural-looking images of faces when compared to equivalent linear models. We conclude by describing a novel supervised non-linear latent variable model based on Gaussian processes which we apply to the problem of recognising emotions from facial expressions.