Made available in DSpace on 2016-06-02T20:06:51Z (GMT). No. of bitstreams: 1 6609.pdf: 3049383 bytes, checksum: 33c7f1618f776ca50cf4694aaba80ea5 (MD5) Previous issue date: 2015-03-09 / In this work we propose a Bayesian nonparametric approach for modeling extreme value data. We treat the location parameter _ of the generalized extreme value distribution as a random function following a Gaussian process model (Rasmussem & Williams 2006). This configuration leads to no closed-form expressions for the highdimensional posterior distribution. To tackle this problem we use the Riemannian Manifold Hamiltonian Monte Carlo algorithm which allows samples from the posterior distribution with complex form and non-usual correlation structure (Calderhead & Girolami 2011). Moreover, we propose an autoregressive time series model assuming the generalized extreme value distribution for the noise and obtained its Fisher information matrix. Throughout this work we employ some computational simulation studies to assess the performance of the algorithm in its variants and show many examples with simulated and real data-sets. / Neste trabalho propomos uma abordagem Bayesiana não-paramétrica para a modelagem de dados com comportamento extremo. Tratamos o parâmetro de locação _ da distribuição generalizada de valor extremo como uma função aleatória e assumimos um processo Gaussiano para tal função (Rasmussem & Williams 2006). Esta situação leva à intratabilidade analítica da distribuição a posteriori de alta dimensão. Para lidar com este problema fazemos uso do método Hamiltoniano de Monte Carlo em variedade Riemanniana que permite a simulação de valores da distribuição a posteriori com forma complexa e estrutura de correlação incomum (Calderhead & Girolami 2011). Além disso, propomos um modelo de série temporal autoregressivo de ordem p, assumindo a distribuição generalizada de valor extremo para o ruído e determinamos a respectiva matriz de informação de Fisher. No decorrer de todo o trabalho, estudamos a qualidade do algoritmo em suas variantes através de simulações computacionais e apresentamos vários exemplos com dados reais e simulados.

In recent times there has been an explosion of online user-generated video content. This has generated significant research interest in video analytics. Human users understand videos based on high-level semantic concepts. However, most of the current research in video analytics are driven by low-level features and descriptors, which often lack semantic interpretation. Existing attempts in semantic video analytics are specialized and require additional resources like movie scripts, which are not available for most user-generated videos. There are no general purpose approaches to understanding videos through semantic concepts. In this thesis we attempt to bridge this gap. We view videos as collections of entities which are semantic visual concepts like the persons in a movie, or cars in a F1 race video. We focus on two fundamental tasks in Video Understanding, namely summarization and scene- discovery. Entity-driven Video Summarization and Entity-driven Scene discovery are important open problems. They are challenging due to the spatio-temporal nature of videos, and also due to lack of apriori information about entities. We use Bayesian nonparametric methods to solve these problems. In the absence of external resources like scripts we utilize fundamental structural properties like temporal coherence in videos- which means that adjacent frames should contain the same set of entities and have similar visual features. There have been no focussed attempts to model this important property. This thesis makes several contributions in Computer Vision and Bayesian nonparametrics by addressing Entity-driven Video Understanding through temporal coherence modeling. Temporal Coherence in videos is observed across its frames at the level of features/descriptors, as also at semantic level. We start with an attempt to model TC at the level of features/descriptors. A tracklet is a spatio-temporal fragment of a video- a set of spatial regions in a short sequence (5-20) of consecutive frames, each of which enclose a particular entity. We attempt to find a representation of tracklets to aid tracking of entities. We explore region descriptors like Covari- ance Matrices of spatial features in individual frames. Due to temporal coherence, such matrices from corresponding spatial regions in successive frames have nearly identical eigenvectors. We utilize this property to model a tracklet using a covariance matrix, and use it for region-based entity tracking. We propose a new method to estimate such a matrix. Our method is found to be much more efficient and effective than alternative covariance-based methods for entity tracking. Next, we move to modeling temporal coherence at a semantic level, with special emphasis on videos of movies and TV-series episodes. Each tracklet is associated with an entity (say a particular person). Spatio-temporally close but non-overlapping tracklets are likely to belong to the same entity, while tracklets that overlap in time can never belong to the same entity. Our aim is to cluster the tracklets based on the entities associated with them, with the goal of discovering the entities in a video along with all their occurrences. We argue that Bayesian Nonparametrics is the most convenient way for this task. We propose a temporally coherent version of Chinese Restaurant Process (TC-CRP) that can encode such constraints easily, and results in discovery of pure clusters of tracklets, and also filter out tracklets resulting from false detections. TC-CRP shows excellent performance on person discovery from TV-series videos. We also discuss semantic video summarization, based on entity discovery. Next, we consider entity-driven temporal segmentation of a video into scenes, where each scene is characterized by the entities present in it. This is a novel application, as existing work on temporal segmentation have focussed on low-level features of frames, rather than entities. We propose EntScene: a generative model for videos based on entities and scenes, and propose an inference algorithm based on Blocked Gibbs Sampling, for simultaneous entity discovery and scene discovery. We compare it to alternative inference algorithms, and show significant improvements in terms of segmentatio and scene discovery. Video representation by low-rank matrix has gained popularity recently, and has been used for various tasks in Computer Vision. In such a representation, each column corresponds to a frame or a single detection. Such matrices are likely to have contiguous sets of identical columns due to temporal coherence, and hence they should be low-rank. However, we discover that none of the existing low-rank matrix recovery algorithms are able to preserve such structures. We study regularizers to encourage these structures for low-rank matrix recovery through convex optimization, but note that TC-CRP-like Bayesian modeling is better for enforcing them. We then focus our attention on modeling temporal coherence in hierarchically grouped sequential data, such as word-tokens grouped into sentences, paragraphs, documents etc in a text corpus. We attempt Bayesian modeling for such data, with application to multi-layer segmentation. We first make a detailed study of existing models for such data. We present a taxonomy for such models called Degree-of-Sharing (DoS), based on how various mixture components are shared by the groups of data in these models. We come up with Layered Dirichlet Process which generalizes Hierarchical Dirichlet Process to multiple layers, and can also handle sequential information easily through Markovian approach. This is applied to hierarchical co-segmentation of a set of news transcripts- into broad categories (like politics, sports etc) and individual stories. We also propose a explicit-duration (semi-Markov) approach for this purpose, and provide an efficient inference algorithm for this. We also discuss generative processes for distribution matrices, where each column is a probability distribution. For this we discuss an application: to infer the correct answers to questions on online answering forums from opinions provided by different users.

<p dir="ltr">In this thesis, we delve into the exploration of several nonparametric and semiparametric econometric models within the Bayesian framework, highlighting their applicability across a broad spectrum of microeconomic and macroeconomic issues. Positioned in the big data era, where data collection and storage expand at an unprecedented rate, the complexity of economic questions we aim to address is similarly escalating. This dual challenge ne- cessitates leveraging increasingly large datasets, thereby underscoring the critical need for designing flexible Bayesian priors and developing scalable, efficient algorithms tailored for high-dimensional datasets.</p><p dir="ltr">The initial two chapters, Chapter 2 and 3, are dedicated to crafting Bayesian priors suited for environments laden with a vast array of variables. These priors, alongside their corresponding algorithms, are optimized for computational efficiency, scalability to extensive datasets, and, ideally, distributability. We aim for these priors to accommodate varying levels of dataset sparsity. Chapter 2 assesses nonparametric additive models, employing a smoothing prior alongside a band matrix for each additive component. Utilizing the Bayesian backfitting algorithm significantly alleviates the computational load. In Chapter 3, we address multiple linear regression settings by adopting a flexible scale mixture of normal priors for coefficient parameters, thus allowing data-driven determination of the necessary amount of shrinkage. The use of a conjugate prior enables a closed-form solution for the posterior, markedly enhancing computational speed.</p><p dir="ltr">The subsequent chapters, Chapter 4 and 5, pivot towards time series dataset model- ing and Bayesian algorithms. A semiparametric modeling approach dissects the stochastic volatility in macro time series into persistent and transitory components, the latter addi- tional component addressing outliers. Utilizing a Dirichlet process mixture prior for the transitory part and a collapsed Gibbs sampling algorithm, we devise a method capable of efficiently processing over 10,000 observations and 200 variables. Chapter 4 introduces a simple univariate model, while Chapter 5 presents comprehensive Bayesian VARs. Our al- gorithms, more efficient and effective in managing outliers than existing ones, are adept at handling extensive macro datasets with hundreds of variables.</p>

<p dir="ltr">This dissertation advances the field of causal inference by developing methodologies in the face of assumption violations. Traditional causal inference methodologies hinge on a core set of assumptions, which are often violated in the complex landscape of modern experiments and observational studies. This dissertation proposes novel methodologies designed to address the challenges posed by single or multiple assumption violations. By applying these innovative approaches to real-world datasets, this research uncovers valuable insights that were previously inaccessible with existing methods. </p><p><br></p><p dir="ltr">First, three significant sources of complications in causal inference that are increasingly of interest are interference among individuals, nonadherence of individuals to their assigned treatments, and unintended missing outcomes. Interference exists if the outcome of an individual depends not only on its assigned treatment, but also on the assigned treatments for other units. It commonly arises when limited controls are placed on the interactions of individuals with one another during the course of an experiment. Treatment nonadherence frequently occurs in human subject experiments, as it can be unethical to force an individual to take their assigned treatment. Clinical trials, in particular, typically have subjects that do not adhere to their assigned treatments due to adverse side effects or intercurrent events. Missing values also commonly occur in clinical studies. For example, some patients may drop out of the study due to the side effects of the treatment. Failing to account for these considerations will generally yield unstable and biased inferences on treatment effects even in randomized experiments, but existing methodologies lack the ability to address all these challenges simultaneously. We propose a novel Bayesian methodology to fill this gap. </p><p><br></p><p dir="ltr">My subsequent research further addresses one of the limitations of the first project: a set of assumptions about interference structures that may be too restrictive in some practical settings. We introduce a concept of the ``degree of interference" (DoI), a latent variable capturing the interference structure. This concept allows for handling arbitrary, unknown interference structures to facilitate inference on causal estimands. </p><p><br></p><p dir="ltr">While randomized experiments offer a solid foundation for valid causal analysis, people are also interested in conducting causal inference using observational data due to the cost and difficulty of randomized experiments and the wide availability of observational data. Nonetheless, using observational data to infer causality requires us to rely on additional assumptions. A central assumption is that of \emph{ignorability}, which posits that the treatment is randomly assigned based on the variables (covariates) included in the dataset. While crucial, this assumption is often debatable, especially when treatments are assigned sequentially to optimize future outcomes. For instance, marketers typically adjust subsequent promotions based on responses to earlier ones and speculate on how customers might have reacted to alternative past promotions. This speculative behavior introduces latent confounders, which must be carefully addressed to prevent biased conclusions. </p><p dir="ltr">In the third project, we investigate these issues by studying sequences of promotional emails sent by a US retailer. We develop a novel Bayesian approach for causal inference from longitudinal observational data that accommodates noncompliance and latent sequential confounding. </p><p><br></p><p dir="ltr">Finally, we formulate the causal inference problem for the privatized data. In the era of digital expansion, the secure handling of sensitive data poses an intricate challenge that significantly influences research, policy-making, and technological innovation. As the collection of sensitive data becomes more widespread across academic, governmental, and corporate sectors, addressing the complex balance between making data accessible and safeguarding private information requires the development of sophisticated methods for analysis and reporting, which must include stringent privacy protections. Currently, the gold standard for maintaining this balance is Differential privacy. </p><p dir="ltr">Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in additional bias and variance in their analyses. Thus, it is of great importance for analysts to incorporate the privacy noise into valid inference.</p><p dir="ltr">In this final project, we develop methodologies to infer causal effects from locally privatized data under randomized experiments. We present frequentist and Bayesian approaches and discuss the statistical properties of the estimators, such as consistency and optimality under various privacy scenarios.</p>

Cette thèse étudie deux modèles paramétriques et non paramétriques pour le changement de représentation. L'objectif des deux modèles diffère. Le premier cherche une représentation en plus grande dimension pour gagner en robustesse. L'objectif est de répartir uniformément l’information d’un signal sur toutes les composantes de sa représentation en plus grande dimension. La recherche d'un tel code s'exprime comme un problème inverse impliquant une régularisation de type norme infinie. Nous proposons une formulation bayésienne du problème impliquant une nouvelle loi de probabilité baptisée démocratique, qui pénalise les fortes amplitudes. Deux algorithmes MCMC proximaux sont présentés pour approcher des estimateurs bayésiens. La méthode non supervisée présentée est appelée BAC-1. Des expériences numériques illustrent les performances de l’approche pour la réduction de facteur de crête. Le second modèle identifie un sous-espace pertinent de dimension réduite à des fins de modélisation. Mais les méthodes probabilistes proposées nécessitent généralement de fixer à l'avance la dimension du sous-espace. Ce travail introduit BNP-PCA, une version bayésienne non paramétrique de l'analyse en composantes principales. La méthode couple une loi uniforme sur les bases orthonormales à un a priori non paramétrique de type buffet indien pour favoriser une utilisation parcimonieuse des composantes principales et aucun réglage n'est nécessaire. L'inférence est réalisée à l'aide des méthodes MCMC. L'estimation de la dimension du sous-espace et le comportement numérique de BNP-PCA sont étudiés. Nous montrons la flexibilité de BNP-PCA sur deux applications / This thesis proposes Bayesian parametric and nonparametric models for signal representation. The first model infers a higher dimensional representation of a signal for sake of robustness by enforcing the information to be spread uniformly. These so called anti-sparse representations are obtained by solving a linear inverse problem with an infinite-norm penalty. We propose in this thesis a Bayesian formulation of anti-sparse coding involving a new probability distribution, referred to as the democratic prior. A Gibbs and two proximal samplers are proposed to approximate Bayesian estimators. The algorithm is called BAC-1. Simulations on synthetic data illustrate the performances of the two proposed samplers and the results are compared with state-of-the art methods. The second model identifies a lower dimensional representation of a signal for modelisation and model selection. Principal component analysis is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Few works have proposed a probabilistic approach to infer the number of significant components. We propose a Bayesian nonparametric principal component analysis called BNP-PCA. The proposed model involves an Indian buffet process to promote a parsimonious use of principal components, which is assigned a prior distribution defined on the manifold of orthonormal basis. Inference is done using MCMC methods. The estimators of the latent dimension are theoretically and empirically studied. The relevance of the approach is assessed on two applications

Nous proposons deux nouvelles approches pour les systèmes de recommandation et les réseaux. Dans la première partie, nous donnons d’abord un aperçu sur les systèmes de recommandation avant de nous concentrer sur les approches de rang faible pour la complétion de matrice. En nous appuyant sur une approche probabiliste, nous proposons de nouvelles fonctions de pénalité sur les valeurs singulières de la matrice de rang faible. En exploitant une représentation de modèle de mélange de cette pénalité, nous montrons qu’un ensemble de variables latentes convenablement choisi permet de développer un algorithme espérance-maximisation afin d’obtenir un maximum a posteriori de la matrice de rang faible complétée. L’algorithme résultant est un algorithme à seuillage doux itératif qui adapte de manière itérative les coefficients de réduction associés aux valeurs singulières. L’algorithme est simple à mettre en œuvre et peut s’adapter à de grandes matrices. Nous fournissons des comparaisons numériques entre notre approche et de récentes alternatives montrant l’intérêt de l’approche proposée pour la complétion de matrice à rang faible. Dans la deuxième partie, nous présentons d’abord quelques prérequis sur l’approche bayésienne non paramétrique et en particulier sur les mesures complètement aléatoires et leur extension multivariée, les mesures complètement aléatoires composées. Nous proposons ensuite un nouveau modèle statistique pour les réseaux creux qui se structurent en communautés avec chevauchement. Le modèle est basé sur la représentation du graphe comme un processus ponctuel échangeable, et généralise naturellement des modèles probabilistes existants à structure en blocs avec chevauchement au régime creux. Notre construction s’appuie sur des vecteurs de mesures complètement aléatoires, et possède des paramètres interprétables, chaque nœud étant associé un vecteur représentant son niveau d’affiliation à certaines communautés latentes. Nous développons des méthodes pour simuler cette classe de graphes aléatoires, ainsi que pour effectuer l’inférence a posteriori. Nous montrons que l’approche proposée peut récupérer une structure interprétable à partir de deux réseaux du monde réel et peut gérer des graphes avec des milliers de nœuds et des dizaines de milliers de connections. / We propose two novel approaches for recommender systems and networks. In the first part, we first give an overview of recommender systems and concentrate on the low-rank approaches for matrix completion. Building on a probabilistic approach, we propose novel penalty functions on the singular values of the low-rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an expectation-maximization algorithm to obtain a maximum a posteriori estimate of the completed low-rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low-rank matrix completion. In the second part, we first introduce some background on Bayesian nonparametrics and in particular on completely random measures (CRMs) and their multivariate extension, the compound CRMs. We then propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with overlapping block-structure to the sparse regime. Our construction builds on vectors of CRMs, and has interpretable parameters, each node being assigned a vector representing its level of affiliation to some latent communities. We develop methods for simulating this class of random graphs, as well as to perform posterior inference. We show that the proposed approach can recover interpretable structure from two real-world networks and can handle graphs with thousands of nodes and tens of thousands of edges.