Accurate and efficient localization of facial features is a crucial first step in many face-related computer vision tasks. Some of these tasks include, but not limited to: identity recognition, expression recognition, and head-pose estimation. Most effort in the field has been exerted towards developing better ways of modeling prior appearance knowledge and image observations. Modeling prior shape knowledge, on the other hand, has not been explored as much. In this dissertation I primarily focus on the limitations of the existing methods in terms of modeling the prior shape knowledge. I first introduce a new pose-constrained shape model. I describe my shape model as being "highly flexible yet sufficiently strict". Existing pose-constrained shape models are either too strict, and have questionable generalization power, or they are too loose, and have questionable localization accuracies. My model tries to find a good middle-ground by learning which shape constraints are more "informative" and should be kept, and which ones are not-so-important and may be omitted. I build my pose-constrained facial feature localization approach on this new shape model using a probabilistic graphical model framework. Within this framework, observed and unobserved variables are defined as the local image observations, and the feature locations, respectively. Feature localization, or "probabilistic inference", is then achieved by nonparametric belief propagation. I show that this approach outperforms other popular pose-constrained methods through qualitative and quantitative experiments. Next, I expand my pose-constrained localization approach to unconstrained setting using a multi-model strategy. While doing so, once again I identify and address the two key limitations of existing multi-model methods: 1) semantically and manually defining the models or "guiding" their generation, and 2) not having efficient and effective model selection strategies. First, I introduce an approach based on unsupervised clustering where the models are automatically learned from training data. Then, I complement this approach with an efficient and effective model selection strategy, which is based on a multi-class naive Bayesian classifier. This way, my method can have many more models, each with a higher level of expressive power, and consequently, provides a more effective partitioning of the face image space. This approach is validated through extensive experiments and comparisons with state-of-the-art methods on state-of-the-art datasets. In the last part of this dissertation I discuss a particular application of the previously introduced techniques; facial feature localization in unconstrained videos. I improve the frame-by-frame localization results, by estimating the actual head-movement from a sequence of noisy head-pose estimates, and then using this information for detecting and fixing the localization failures. / text

This thesis is concerned with graphical Gaussian models with equality constraints on the concentration or partial correlation matrix introduced by Højsgaard and Lauritzen (2008) as RCON and RCOR models. The models can be represented by vertex and edge coloured graphs G = (V,ε), where parameters associated with equally coloured vertices or edges are restricted to being identical. In the first part of this thesis we study the problem of estimability of a non-zero model mean μ if the covariance structure Σ is restricted to satisfy the constraints of an RCON or RCOR model but is otherwise unknown. Exploiting results in Kruskal (1968), we obtain a characterisation of suitable linear spaces Ω such that if Σ is restricted as above, the maximum likelihood estimator μ(with circumflex) and the least squares estimator μ* of μ coincide for μ ∈ Ω, thus allowing μ and Σ to be estimated independently. For the special case of Ω being specified by equality relations among the entries of μ according to a partition M of the model variables V, our characterisation translates into a necessary and sufficient regularity condition on M and (V,ε). In the second part we address model selection of RCON and RCOR models. Due to the large number of models, we study the structure of four model classes lying strictly within the sets of RCON and RCOR models, each of which is defined by desirable statistical properties corresponding to colouring regularity conditions. Two of these appear in Højsgaard and Lauritzen (2008), while the other two arise from the regularity condition ensuring equality of estimators μ(with circumflex) = μ* we find in the first part. We show each of the colouring classes to form complete lattices, which qualifies the corresponding model spaces for an Edwards-Havránek model selection procedure (Edwards and Havránek, 1987). We develop a coresponding algorithm for one of the model classes and give an algorithm for a systematic search in accordance with the Edwards-Havránek principles for a second class. Both are applied to data sets previously analysed in the literature, with very encouraging performances.

This thesis is concerned with two main areas: approximate inference in discrete graphical models, and random embeddings for dimensionality reduction and approximate inference in kernel methods. Approximate inference is a fundamental problem in machine learning and statistics, with strong connections to other domains such as theoretical computer science. At the same time, there has often been a gap between the success of many algorithms in this area in practice, and what can be explained by theory; thus, an important research effort is to bridge this gap. Random embeddings for dimensionality reduction and approximate inference have led to great improvements in scalability of a wide variety of methods in machine learning. In recent years, there has been much work on how the stochasticity introduced by these approaches can be better controlled, and what further computational improvements can be made. In the first part of this thesis, we study approximate inference algorithms for discrete graphical models. Firstly, we consider linear programming methods for approximate MAP inference, and develop our understanding of conditions for exactness of these approximations. Such guarantees of exactness are typically based on either structural restrictions on the underlying graph corresponding to the model (such as low treewidth), or restrictions on the types of potential functions that may be present in the model (such as log-supermodularity). We contribute two new classes of exactness guarantees: the first of these takes the form of particular hybrid restrictions on a combination of graph structure and potential types, whilst the second is given by excluding particular substructures from the underlying graph, via graph minor theory. We also study a particular family of transformation methods of graphical models, uprooting and rerooting, and their effect on approximate MAP and marginal inference methods. We prove new theoretical results on the behaviour of particular approximate inference methods under these transformations, in particular showing that the triplet relaxation of the marginal polytope is unique in being universally rooted. We also introduce a heuristic which quickly picks a rerooting, and demonstrate benefits empirically on models over several graph topologies. In the second part of this thesis, we study Monte Carlo methods for both linear dimensionality reduction and approximate inference in kernel machines. We prove the statistical benefit of coupling Monte Carlo samples to be almost-surely orthogonal in a variety of contexts, and study fast approximate methods of inducing this coupling. A surprising result is that these approximate methods can simultaneously offer improved statistical benefits, time complexity, and space complexity over i.i.d. Monte Carlo samples. We evaluate our methods on a variety of datasets, directly studying their effects on approximate kernel evaluation, as well as on downstream tasks such as Gaussian process regression.

Orientador: Lucia Galvão de Albuquerque / Resumo: Registros de características quantitativas e informações genotípicas cole- tadas para cada animal são utilizados para identificar regiões do genoma associadas à variação fenotípica. No entanto, essas investigações são, geralmente, realizadas com base em testes estatísticos de correlação ou associação, que não implicam em causalidade. A fim de explorar amplamente essas informações, métodos poderosos de inferência causal foram desenvolvidos para estimar os efeitos causais entre as variáveis estudadas. Apesar do progresso significativo neste campo, inferir os efeitos causais entre variáveis aleatórias contínuas ainda é um desafio e poucos estudos têm explorado as relações causais em genética quantitativa e no melhoramento animal. Neste contexto, dois estudos foram realizados com os seguintes objetivos: 1) Buscar as relações causais entre as características de carcaça e qualidade de carne usando um modelo de equação estrutural (MEE), sob modelo linear misto em bovinos da raça Nelore, e 2) Reconstruir redes de genes-fenótipos e realizar análise de rede causal por meio da integração de dados fenotípicos, genotípicos e transcriptômicos em bovinos da raça Nelore. Para o primeiro estudo, um total de 4.479 animais com informação fenotípica para o peso da carcaça quente (PCQ), área de olho lombo (AOL), espessura de gordura subcutânea (EGS), força de cisalhamento (FC) e marmoreio (MAR) foram usados. Os animais foram genotipados usando os painéis BovineHD Bead- Chip e GeneSeek Genomic Pro... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Quantitative traits and genotypes information have been collected for each animal and used to identify genome regions related to phenotypes variation. However, these investigations are, usually, performed based on correlation or association statistical tests, which do not imply in causation. In order to fully explore these information, powerful causal inference methods have been developed to estimate causal effects among the variables under study. Despite significant progress in this field infer causal effect among random variables remains a challenge and some few studies have explored causal relationships in quantitative genetics and animal breeding. In this context, two studies were performed with the following objectives: 1) Search for the causal relationship among carcass yield and meat quality traits using a structural equation model (SEM), under linear mixed model context in Nelore cattle, and 2) Reconstruct gene-phenotype networks and perform causal network analysis through the integrating of phenotypic, genotypic, and transcriptomic data in Nelore cattle. For the first study, a total of 4,479 animals with phenotypic information for hot carcass weight (HCW), longissimus muscle area (LMA), backfat thickness (BF), Warner-Bratzler shear force (WBSF), and marbling score (MB) traits were used. Animals were genotyped using BovineHD BeadChip and GeneSeek Genomic Profiler Indicus HD - GGP75Ki. For causal inference using SEM a multistep procedure methodology was used as follow:... (Complete abstract click electronic access below) / Doutor

<p>This thesis makes contributions to the statistical research field of causal inference in observational studies. The results obtained are directly applicable in many scientific fields where effects of treatments are investigated and yet controlled experiments are difficult or impossible to implement.</p><p>In the first paper we define a partially specified directed acyclic graph (DAG) describing the independence structure of the variables under study. Using the DAG we show that given that unconfoundedness holds we can use the observed data to select minimal sets of covariates to control for. General covariate selection algorithms are proposed to target the defined minimal subsets.</p><p>The results of the first paper are generalized in Paper II to include the presence of unobserved covariates. Morevoer, the identification assumptions from the first paper are relaxed.</p><p>To implement the covariate selection without parametric assumptions we propose in the third paper the use of a model-free variable selection method from the framework of sufficient dimension reduction. By simulation the performance of the proposed selection methods are investigated. Additionally, we study finite sample properties of treatment effect estimators based on the selected covariate sets.</p><p>In paper IV we investigate misspecifications of parametric models of a scalar summary of the covariates, the propensity score. Motivated by common model specification strategies we describe misspecifications of parametric models for which unbiased estimators of the treatment effect are available. Consequences of the misspecification for the efficiency of treatment effect estimators are also studied.</p>

We present an overview of current research on artificial neural networks, emphasizing a statistical perspective. We view neural networks as parameterized graphs that make probabilistic assumptions about data, and view learning algorithms as methods for finding parameter values that look probable in the light of the data. We discuss basic issues in representation and learning, and treat some of the practical issues that arise in fitting networks to data. We also discuss links between neural networks and the general formalism of graphical models.

Computational vision and image analysis is a multidisciplinary scientific field that aims to make computers "see" in a way that is comparable to human perception. It is currently one of the most challenging research areas in artificial intelligence. In this regard, the extraction of information from the vast amount of visual data that are available today as well as the exploitation of the resulting information space becomes one of the greatest challenges in our days. To address such a challenge, this thesis describes a very general computational framework that can be used for performing efficient inference and learning for visual perception based on very rich and powerful models.

<p>This thesis is about Bayesian approaches for handling multiplicity. It considers three main kinds of multiple-testing scenarios: tests of exchangeable experimental units, tests for variable inclusion in linear regresson models, and tests for conditional independence in jointly normal vectors. Multiplicity adjustment in these three areas will be seen to have many common structural features. Though the modeling approach throughout is Bayesian, frequentist reasoning regarding error rates will often be employed.</p><p>Chapter 1 frames the issues in the context of historical debates about Bayesian multiplicity adjustment. Chapter 2 confronts the problem of large-scale screening of functional data, where control over Type-I error rates is a crucial issue. Chapter 3 develops new theory for comparing Bayes and empirical-Bayes approaches for multiplicity correction in regression variable selection. Chapters 4 and 5 describe new theoretical and computational tools for Gaussian graphical-model selection, where multiplicity arises in performing many simultaneous tests of pairwise conditional independence. Chapter 6 introduces a new approach to sparse-signal modeling based upon local shrinkage rules. Here the focus is not on multiplicity per se, but rather on using ideas from Bayesian multiple-testing models to motivate a new class of multivariate scale-mixture priors. Finally, Chapter 7 describes some directions for future study, many of which are the subjects of my current research agenda.</p> / Dissertation

Probabilistic graphical models (PGMs) provide the capability of evaluating uncertainty and variability of product use in addition to correlating the results with aspects of the usage context. Although energy consumption during use can cause a majority of a product's environmental impact, common practice is to neglect operational variability in life cycle inventories (LCIs). Therefore, the relationship between a product's usage context and its environmental performance is rarely considered in design evaluations. This dissertation demonstrates a method for describing the usage context as a set of factors and representing the usage context through a PGM. The application to LCIs is demonstrated through the use of a lightweight vehicle design example. Although replacing steel vehicle parts with aluminum parts reduces the weight and can increase fuel economy, the energy invested in production of aluminum parts is much larger than that of steel parts. The tradeoff between energy investment and fuel savings is highly dependent upon the vehicle fuel economy and lifetime mileage. The demonstration PGM is constructed from relating factors such as driver behavior, alternative driving schedules, and residential density with local conditional probability distributions derived from publicly available data sources. Unique scenarios are then assembled from sets of conditions on these factors to provide insight for sources of variance. The vehicle example demonstrated that implementation of realistic usage scenarios via a PGM can provide a much higher fidelity investigation of energy savings during use and that distinct scenarios can have significantly different implications for the effectiveness of lightweight vehicle designs. Scenarios with large families, for example, yield high energy savings, especially if the vehicle is used for commuting or stop-and-go traffic conditions. Scenarios of small families and efficient driving schedules yield lower energy savings for lightweight vehicle designs. / text

This work is motivated from error-correcting codes in the brain. To counteract the effect of representation noise, a large number of neurons participate in encoding even low-dimensional variables. In many brain areas, the mean firing rates of neurons as a function of represented variable, called the tuning curve, have unimodal shape centered at different values, defining a unary code. This dissertation focuses on a new type of neural code where neurons have periodic tuning curves, with a diversity of periods. Neurons that exhibit this tuning are grid cells of the entorhinal cortex, which represent self-location in two-dimensional space. First, we investigate mutual information between such multi-scale codes and the coded variable as a function of tuning curve width. For decoding, we consider maximum likelihood (ML) and plausible neural network (NN) based models. For unary neural codes, Fisher information increases with narrower tuning, regardless of the decoding method. By contrast, for the multi-scale neural code, the optimal tuning curve width depends on the decoding method. While narrow tuning is optimal for ML decoding, a finite width, matched to statistics of the noise, is optimal with a NN decoder. This finding may explain why actual neural tuning curves have relatively wide tuning. Next, motivated by the observation that multi-scale codes involve non-trivial decoding, we examine a decoding algorithm based on belief propagation (BP) because BP promises certain gains in decoding efficiency. The decoding problem is first formulated as a subset selection problem on a graph and then approximately solved by BP. Even though the graph has many cycles, BP converges to a fixed point after few iterations. The mean square error of BP approaches to that of ML at high signal-to-noise ratios. Finally, using the multi-scale code, we propose a joint source-channel coding scheme that allows separate senders to transmit complementary information over additive Gaussian noise channels without cooperation. The receiver decodes one sender's codeword using the other as side information and achieves a lower distortion using the same number of transmissions. The proposed scheme offers a new framework to design distributed joint source-channel codes for continuous variables. / text