The last decade's research in artificial intelligence had a significant impact on the advance of autonomous driving. Yet, safety remains a major concern when it comes to deploying such systems in high-risk environments. The objective of this thesis is to develop methodological tools which provide reliable uncertainty estimates for deep neural networks. First, we introduce a new criterion to reliably estimate model confidence: the true class probability (TCP). We show that TCP offers better properties for failure prediction than current uncertainty measures. Since the true class is by essence unknown at test time, we propose to learn TCP criterion from data with an auxiliary model, introducing a specific learning scheme adapted to this context. The relevance of the proposed approach is validated on image classification and semantic segmentation datasets. Then, we extend our learned confidence approach to the task of domain adaptation where it improves the selection of pseudo-labels in self-training methods. Finally, we tackle the challenge of jointly detecting misclassification and out-of-distributions samples by introducing a new uncertainty measure based on evidential models and defined on the simplex.

We present a Bayesian graph neural network (BGNN) that can estimate the weak lensing convergence ($\kappa$) from photometric measurements of galaxies along a given line of sight. The method is of particular interest in strong gravitational time delay cosmography (TDC), where characterizing the "external convergence" ($\kappa_{\rm ext}$) from the lens environment and line of sight is necessary for precise inference of the Hubble constant ($H_0$). Starting from a large-scale simulation with a $\kappa$ resolution of $\sim$1$'$, we introduce fluctuations on galaxy-galaxy lensing scales of $\sim$1$''$ and extract random sightlines to train our BGNN. We then evaluate the model on test sets with varying degrees of overlap with the training distribution. For each test set of 1,000 sightlines, the BGNN infers the individual $\kappa$ posteriors, which we combine in a hierarchical Bayesian model to yield constraints on the hyperparameters governing the population. For a test field well sampled by the training set, the BGNN recovers the population mean of $\kappa$ precisely and without bias, resulting in a contribution to the $H_0$ error budget well under 1\%. In the tails of the training set with sparse samples, the BGNN, which can ingest all available information about each sightline, extracts more $\kappa$ signal compared to a simplified version of the traditional method based on matching galaxy number counts, which is limited by sample variance. Our hierarchical inference pipeline using BGNNs promises to improve the $\kappa_{\rm ext}$ characterization for precision TDC. The implementation of our pipeline is available as a public Python package, Node to Joy.

In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} = \boldsymbol{A}\boldsymbol{x} + \boldsymbol{n}$, where $\boldsymbol{y}, \boldsymbol{n} \in \mathbb{R}^d$, and $\boldsymbol{x} \in \mathbb{R}^p$. By viewing covariance recovery as inference over factor graphs via message passing algorithm, ideas from coding theory, such as \textit{Density Evolution} (DE), are leveraged to construct a framework for the design of the sensing matrix. The proposed framework can handle both (1) regular sensing, i.e., equal importance is given to all entries of the covariance, and (2) preferential sensing, i.e., higher importance is given to a part of the covariance matrix. Through experiments, we show that the sensing matrix designed via density evolution can match the state-of-the-art for covariance recovery in the regular sensing paradigm and attain improved performance in the preferential sensing regime. Additionally, we study the feasibility of causal graph structure recovery using the estimated covariance matrix obtained from the compressed measurements.

Nowadays, many people worldwide suffer from brain disorders, and their health is in danger. So far, numerous methods have been proposed for the diagnosis of Schizophrenia (SZ) and attention deficit hyperactivity disorder (ADHD), among which functional magnetic resonance imaging (fMRI) modalities are known as a popular method among physicians. This paper presents an SZ and ADHD intelligent detection method of resting-state fMRI (rs-fMRI) modality using a new deep learning method. The University of California Los Angeles dataset, which contains the rs-fMRI modalities of SZ and ADHD patients, has been used for experiments. The FMRIB software library toolbox first performed preprocessing on rs-fMRI data. Then, a convolutional Autoencoder model with the proposed number of layers is used to extract features from rs-fMRI data. In the classification step, a new fuzzy method called interval type-2 fuzzy regression (IT2FR) is introduced and then optimized by genetic algorithm, particle swarm optimization, and gray wolf optimization (GWO) techniques. Also, the results of IT2FR methods are compared with multilayer perceptron, k-nearest neighbors, support vector machine, random forest, and decision tree, and adaptive neuro-fuzzy inference system methods. The experiment results show that the IT2FR method with the GWO optimization algorithm has achieved satisfactory results compared to other classifier methods. Finally, the proposed classification technique was able to provide 72.71% accuracy.

Entity matching (EM) refers to the problem of identifying pairs of data records in one or more relational tables that refer to the same entity in the real world. Supervised machine learning (ML) models currently achieve state-of-the-art matching performance; however, they require many labeled examples, which are often expensive or infeasible to obtain. This has inspired us to approach data labeling for EM using weak supervision. In particular, we use the labeling function abstraction popularized by Snorkel, where each labeling function (LF) is a user-provided program that can generate many noisy match/non-match labels quickly and cheaply. Given a set of user-written LFs, the quality of data labeling depends on a labeling model to accurately infer the ground-truth labels. In this work, we first propose a simple but powerful labeling model for general weak supervision tasks. Then, we tailor the labeling model specifically to the task of entity matching by considering the EM-specific transitivity property. The general form of our labeling model is simple while substantially outperforming the best existing method across ten general weak supervision datasets. To tailor the labeling model for EM, we formulate an approach to ensure that the final predictions of the labeling model satisfy the transitivity property required in EM, utilizing an exact solution where possible and an ML-based approximation in remaining cases. On two single-table and nine two-table real-world EM datasets, we show that our labeling model results in a 9% higher F1 score on average than the best existing method. We also show that a deep learning EM end model (DeepMatcher) trained on labels generated from our weak supervision approach is comparable to an end model trained using tens of thousands of ground-truth labels, demonstrating that our approach can significantly reduce the labeling efforts required in EM.

Sum-product networks (SPNs) have recently emerged as a novel deep learning architecture enabling highly efficient probabilistic inference. Since their introduction, SPNs have been applied to a wide range of data modalities and extended to time-sequence data. In this paper, we propose a general framework for modelling sequential treatment decision-making behaviour and treatment response using recurrent sum-product networks (RSPNs). Models developed using our framework benefit from the full range of RSPN capabilities, including the abilities to model the full distribution of the data, to seamlessly handle latent variables, missing values and categorical data, and to efficiently perform marginal and conditional inference. Our methodology is complemented by a novel variant of the expectation-maximization algorithm for RSPNs, enabling efficient training of our models. We evaluate our approach on a synthetic dataset as well as real-world data from the MIMIC-IV intensive care unit medical database. Our evaluation demonstrates that our approach can closely match the ground-truth data generation process on synthetic data and achieve results close to neural and probabilistic baselines while using a tractable and interpretable model.

Conditional Independence (CI) graphs are a type of probabilistic graphical models that are primarily used to gain insights about feature relationships. Each edge represents the partial correlation between the connected features which gives information about their direct dependence. In this survey, we list out different methods and study the advances in techniques developed to recover CI graphs. We cover traditional optimization methods as well as recently developed deep learning architectures along with their recommended implementations. To facilitate wider adoption, we include preliminaries that consolidate associated operations, for example techniques to obtain covariance matrix for mixed datatypes. It is often beneficial to know which features are directly correlated to which other features. This can help us understand the input data better by giving a feature inter-dependence overview and also assist in taking system design decisions.

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate when data comes from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) tensor-variate distributions and derive its characterizations, moments, marginal and conditional distributions, and the EC Wishart distribution. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, where we extend Tyler's robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop tensor-variate classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and tensor-variate analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age and ethnic origin than the usual TVN-based TANOVA in the celebrated Labeled Faces of the Wild dataset.

Characterizing the differential excision of mRNA is critical for understanding the functional complexity of a cell or tissue, from normal developmental processes to disease pathogenesis. Most transcript reconstruction methods infer full-length transcripts from high-throughput sequencing data. However, this is a challenging task due to incomplete annotations and the differential expression of transcripts across cell-types, tissues, and experimental conditions. Several recent methods circumvent these difficulties by considering local splicing events, but these methods lose transcript-level splicing information and may conflate transcripts. We develop the first probabilistic model that reconciles the transcript and local splicing perspectives. First, we formalize the sequence of mRNA excisions (SME) reconstruction problem, which aims to assemble variable-length sequences of mRNA excisions from RNA-sequencing data. We then present a novel hierarchical Bayesian admixture model for the Reconstruction of Excised mRNA (BREM). BREM interpolates between local splicing events and full-length transcripts and thus focuses only on SMEs that have high posterior probability. We develop posterior inference algorithms based on Gibbs sampling and local search of independent sets and characterize differential SME usage using generalized linear models based on converged BREM model parameters. We show that BREM achieves higher F1 score for reconstruction tasks and improved accuracy and sensitivity in differential splicing when compared with four state-of-the-art transcript and local splicing methods on simulated data. Lastly, we evaluate BREM on both bulk and scRNA sequencing data based on transcript reconstruction, novelty of transcripts produced, model sensitivity to hyperparameters, and a functional analysis of differentially expressed SMEs, demonstrating that BREM captures relevant biological signal.

This abstracts the core ideas beyond logic programming as such to encompass frameworks from probabilistic databases, probabilistic finite model theory and discrete lifted Bayesian networks. To demonstrate the usefulness of such a general approach, we completely characterise the projective families of distributions representable in the generalised distribution semantics and we demonstrate both that large classes of interesting projective families cannot be represented in a generalised distribution semantics and that already a very limited fragment of logic programming (acyclic determinate logic programs) in the determinsitic part suffices to represent all those projective families that are representable in the generalised distribution semantics at all.