Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately. Despite the potential of multi-task learning to yield more powerful inference than single-task alternatives, prior work in this area has largely omitted uncertainty quantification. Our focus in this paper is a common multi-task problem in neuroimaging, where the goal is to understand the relationship between multiple cognitive task scores (or other subject-level assessments) and brain connectome data collected from imaging. We propose a framework for selective inference to address this problem, with the flexibility to: (i) jointly identify the relevant covariates for each task through a sparsity-inducing penalty, and (ii) conduct valid inference in a model based on the estimated sparsity structure. Our framework offers a new conditional procedure for inference, based on a refinement of the selection event that yields a tractable selection-adjusted likelihood. This gives an approximate system of estimating equations for maximum likelihood inference, solvable via a single convex optimization problem, and enables us to efficiently form confidence intervals with approximately the correct coverage. Applied to both simulated data and data from the Adolescent Brain Cognitive Development (ABCD) study, our selective inference methods yield tighter confidence intervals than commonly used alternatives, such as data splitting. We also demonstrate through simulations that multi-task learning with selective inference can more accurately recover true signals than single-task methods.

Thesis concerns the study and development of hierarchical representations for spatio-temporal visual attention modeling and understanding in video sequences. More specifically, we propose two computational models for visual attention. First, we present a generative probabilistic model for context-aware visual attention modeling and understanding. Secondly, we develop a deep network architecture for visual attention modeling, which first estimates top-down spatio-temporal visual attention, and ultimately serves for modeling attention in the temporal domain. The first part of the thesis introduces our first proposal: a generative probabilistic framework for spatio-temporal visual attention modeling and understanding.

We address the task of probabilistic anomaly attribution in the black-box regression setting, where the goal is to compute the probability distribution of the attribution score of each input variable, given an observed anomaly. The training dataset is assumed to be unavailable. This task differs from the standard XAI (explainable AI) scenario, since we wish to explain the anomalous deviation from a black-box prediction rather than the black-box model itself. We begin by showing that mainstream model-agnostic explanation methods, such as the Shapley values, are not suitable for this task because of their ``deviation-agnostic property.'' We then propose a novel framework for probabilistic anomaly attribution that allows us to not only compute attribution scores as the predictive mean but also quantify the uncertainty of those scores. This is done by considering a generative process for perturbations that counter-factually bring the observed anomalous observation back to normalcy. We introduce a variational Bayes algorithm for deriving the distributions of per variable attribution scores. To the best of our knowledge, this is the first probabilistic anomaly attribution framework that is free from being deviation-agnostic.

Differential privacy (DP) is by far the most widely accepted framework for mitigating privacy risks in machine learning. However, exactly how small the privacy parameter $\epsilon$ needs to be to protect against certain privacy risks in practice is still not well-understood. In this work, we study data reconstruction attacks for discrete data and analyze it under the framework of multiple hypothesis testing. We utilize different variants of the celebrated Fano's inequality to derive upper bounds on the inferential power of a data reconstruction adversary when the model is trained differentially privately. Importantly, we show that if the underlying private data takes values from a set of size $M$, then the target privacy parameter $\epsilon$ can be $O(\log M)$ before the adversary gains significant inferential power. Our analysis offers theoretical evidence for the empirical effectiveness of DP against data reconstruction attacks even at relatively large values of $\epsilon$.

When performing causal discovery, assumptions have to be made on how the true causal mechanism corresponds to the underlying joint probability distribution. These assumptions are labeled as causal razors in this work. We review numerous causal razors that appeared in the literature, and offer a comprehensive logical comparison of them. In particular, we scrutinize an unpopular causal razor, namely parameter minimality, in multinomial causal models and its logical relations with other well-studied causal razors. Our logical result poses a dilemma in selecting a reasonable scoring criterion for score-based casual search algorithms.

Infectious diseases, either emerging or long-lasting, place numerous people at risk and bring heavy public health burdens worldwide. In the process against infectious diseases, predicting the epidemic risk by modeling the disease transmission plays an essential role in assisting with preventing and controlling disease transmission in a more effective way. In this paper, we systematically describe how machine learning can play an essential role in quantitatively characterizing disease transmission patterns and accurately predicting infectious disease risks. First, we introduce the background and motivation of using machine learning for infectious disease risk prediction. Next, we describe the development and components of various machine learning models for infectious disease risk prediction. Specifically, existing models fall into three categories: Statistical prediction, data-driven machine learning, and epidemiology-inspired machine learning. Subsequently, we discuss challenges encountered when dealing with model inputs, designing task-oriented objectives, and conducting performance evaluation. Finally, we conclude with a discussion of open questions and future directions.

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this work, we study these statistical and computational trade-offs in variational inference via a case study in inferential model selection. Focusing on Gaussian inferential models (or variational approximating families) with diagonal plus low-rank precision matrices, we initiate a theoretical study of the trade-offs in two aspects, Bayesian posterior inference error and frequentist uncertainty quantification error. From the Bayesian posterior inference perspective, we characterize the error of the variational posterior relative to the exact posterior. We prove that, given a fixed computation budget, a lower-rank inferential model produces variational posteriors with a higher statistical approximation error, but a lower computational error; it reduces variance in stochastic optimization and, in turn, accelerates convergence. From the frequentist uncertainty quantification perspective, we consider the precision matrix of the variational posterior as an uncertainty estimate, which involves an additional statistical error originating from the sampling uncertainty of the data. As a consequence, for small datasets, the inferential model need not be full-rank to achieve optimal estimation error (even with unlimited computation budget).

Simulations using machine learning (ML) models and mechanistic models are often run to inform decision-making processes. Uncertainty estimates of simulation results are critical to the decision-making process because simulation results of specific scenarios may have wide, but unspecified, confidence bounds that may impact subsequent analyses and decisions. The objective of this work is to develop a protocol to assess uncertainties in predictions of machine learning and mechanistic simulation models. The protocol will outline an uncertainty quantification workflow that may be used to establish credible bounds of predictability on computed quantities of interest and to assess model sufficiency. The protocol identifies key sources of uncertainties in machine learning and mechanistic modeling, defines applicable methods of uncertainty propagation for these sources, and includes statistically rational estimators for output uncertainties. The work applies the protocol to test cases relevant to the gas distribution industry and presents learnings from its application. The paper concludes with a brief discussion outlining a pathway to the wider adoption of uncertainty quantification within the industry

Context: User intent modeling is a crucial process in Natural Language Processing that aims to identify the underlying purpose behind a user's request, enabling personalized responses. With a vast array of approaches introduced in the literature (over 13,000 papers in the last decade), understanding the related concepts and commonly used models in AI-based systems is essential. Method: We conducted a systematic literature review to gather data on models typically employed in designing conversational recommender systems. From the collected data, we developed a decision model to assist researchers in selecting the most suitable models for their systems. Additionally, we performed two case studies to evaluate the effectiveness of our proposed decision model. Results: Our study analyzed 59 distinct models and identified 74 commonly used features. We provided insights into potential model combinations, trends in model selection, quality concerns, evaluation measures, and frequently used datasets for training and evaluating these models. Contribution: Our study contributes practical insights and a comprehensive understanding of user intent modeling, empowering the development of more effective and personalized conversational recommender systems. With the Conversational Recommender System, researchers can perform a more systematic and efficient assessment of fitting intent modeling frameworks.

We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $\ell_{\alpha}$ norm, with $\alpha \in (0, +\infty)$ to define a penalization on large values of the regression coefficients, which includes the Lasso ($\alpha = 1$) and ridge $(\alpha = 2)$ penalizations as special cases. Full Bayesian inference seamlessly provides joint uncertainty estimates for all model parameters. Although MCMC aproaches are available for bridge regression, it can be slow for large dataset, specially in high dimensions. The ADVI implementation allows the use of small batches of data at each iteration (due to stochastic gradient based algorithms), therefore speeding up computational time in comparison with MCMC. We illustrate the approach on non-parametric regression models with B-splines, although the method works seamlessly for other choices of basis functions. A simulation study shows the main properties of the proposed method.