We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this problem rely on the so-called maximum-likelihood estimation (MLE) with relaxed regularization, which neither results in ideal statistical properties nor scale to the dimensions encountered in realistic settings. In this paper, we address these challenges by departing from the MLE paradigm and resorting to a new class of constrained optimization problems with exact, discrete regularization to promote sparsity in the estimated parameters. Despite the nonconvex and discrete nature of our formulation, we show that it can be solved efficiently and parametrically for all sparsity levels. More specifically, we show that the entire solution path of the time-varying MRF for all sparsity levels can be obtained in $\mathcal{O}(pT^3)$, where $T$ is the number of time steps and $p$ is the number of unknown parameters at any given time. The efficient and parametric characterization of the solution path renders our approach highly suitable for cross-validation, where parameter estimation is required for varying regularization values. Despite its simplicity and efficiency, we show that our proposed approach achieves provably small estimation error for different classes of time-varying MRFs, namely Gaussian and discrete MRFs, with as few as one sample per time. Utilizing our algorithm, we can recover the complete solution path for instances of time-varying MRFs featuring over 30 million variables in less than 12 minutes on a standard laptop computer. Our code is available at \url{https://sites.google.com/usc.edu/gomez/data}.

Federated learning has gained popularity for distributed learning without aggregating sensitive data from clients. But meanwhile, the distributed and isolated nature of data isolation may be complicated by data quality, making it more vulnerable to noisy labels. Many efforts exist to defend against the negative impacts of noisy labels in centralized or federated settings. However, there is a lack of a benchmark that comprehensively considers the impact of noisy labels in a wide variety of typical FL settings. In this work, we serve the first standardized benchmark that can help researchers fully explore potential federated noisy settings. Also, we conduct comprehensive experiments to explore the characteristics of these data settings and unravel challenging scenarios on the federated noisy label learning, which may guide method development in the future. We highlight the 20 basic settings for more than 5 datasets proposed in our benchmark and standardized simulation pipeline for federated noisy label learning. We hope this benchmark can facilitate idea verification in federated learning with noisy labels. \texttt{FedNoisy} is available at \codeword{https://github.com/SMILELab-FL/FedNoisy}.

Despite their importance for assessing reliability of predictions, uncertainty quantification (UQ) measures for machine learning models have only recently begun to be rigorously characterized. One prominent issue is the curse of dimensionality: it is commonly believed that the marginal likelihood should be reminiscent of cross-validation metrics and that both should deteriorate with larger input dimensions. We prove that by tuning hyperparameters to maximize marginal likelihood (the empirical Bayes procedure), the performance, as measured by the marginal likelihood, improves monotonically} with the input dimension. On the other hand, we prove that cross-validation metrics exhibit qualitatively different behavior that is characteristic of double descent. Cold posteriors, which have recently attracted interest due to their improved performance in certain settings, appear to exacerbate these phenomena. We verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

This thesis work falls within the framework of question answering (QA) in the biomedical domain where several specific challenges are addressed, such as specialized lexicons and terminologies, the types of treated questions, and the characteristics of targeted documents. We are particularly interested in studying and improving methods that aim at finding accurate and short answers to biomedical natural language questions from a large scale of biomedical textual documents in English. QA aims at providing inquirers with direct, short and precise answers to their natural language questions. In this Ph.D. thesis, we propose four contributions to improve the performance of QA in the biomedical domain. In our first contribution, we propose a machine learning-based method for question type classification to determine the types of given questions which enable to a biomedical QA system to use the appropriate answer extraction method. We also propose an another machine learning-based method to assign one or more topics (e.g., pharmacological, test, treatment, etc.) to given questions in order to determine the semantic types of the expected answers which are very useful in generating specific answer retrieval strategies. In the second contribution, we first propose a document retrieval method to retrieve a set of relevant documents that are likely to contain the answers to biomedical questions from the MEDLINE database. We then present a passage retrieval method to retrieve a set of relevant passages to questions. In the third contribution, we propose specific answer extraction methods to generate both exact and ideal answers. Finally, in the fourth contribution, we develop a fully automated semantic biomedical QA system called SemBioNLQA which is able to deal with a variety of natural language questions and to generate appropriate answers by providing both exact and ideal answers.

Prevalent in many real-world settings such as healthcare, irregular time series are challenging to formulate predictions from. It is difficult to infer the value of a feature at any given time when observations are sporadic, as it could take on a range of values depending on when it was last observed. To characterize this uncertainty we present EDICT, a strategy that learns an evidential distribution over irregular time series in continuous time. This distribution enables well-calibrated and flexible inference of partially observed features at any time of interest, while expanding uncertainty temporally for sparse, irregular observations. We demonstrate that EDICT attains competitive performance on challenging time series classification tasks and enabling uncertainty-guided inference when encountering noisy data.

The emergence of artificial emotional intelligence technology is revolutionizing the fields of computers and robotics, allowing for a new level of communication and understanding of human behavior that was once thought impossible. While recent advancements in deep learning have transformed the field of computer vision, automated understanding of evoked or expressed emotions in visual media remains in its infancy. This foundering stems from the absence of a universally accepted definition of "emotion", coupled with the inherently subjective nature of emotions and their intricate nuances. In this article, we provide a comprehensive, multidisciplinary overview of the field of emotion analysis in visual media, drawing on insights from psychology, engineering, and the arts. We begin by exploring the psychological foundations of emotion and the computational principles that underpin the understanding of emotions from images and videos. We then review the latest research and systems within the field, accentuating the most promising approaches. We also discuss the current technological challenges and limitations of emotion analysis, underscoring the necessity for continued investigation and innovation. We contend that this represents a "Holy Grail" research problem in computing and delineate pivotal directions for future inquiry. Finally, we examine the ethical ramifications of emotion-understanding technologies and contemplate their potential societal impacts. Overall, this article endeavors to equip readers with a deeper understanding of the domain of emotion analysis in visual media and to inspire further research and development in this captivating and rapidly evolving field.

The availability of both structured and unstructured databases, such as electronic health data, social media data, patent data, and surveys that are often updated in real time, among others, has grown rapidly over the past decade. With this expansion, the statistical and methodological questions around data integration, or rather merging multiple data sources, has also grown. Specifically, the science of the "data cleaning pipeline" contains four stages that allow an analyst to perform downstream tasks, predictive analyses, or statistical analyses on "cleaned data." This article provides a review of this emerging field, introducing technical terminology and commonly used methods. Statement of Significance: The article reviews the data cleaning pipeline, introducing technical terminology and commonly used methods.

We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of Principal Variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum likelihood estimation within a certain semi-parametric model. Using these connections, we show how to efficiently (1) perform CSS using only summary statistics from the original dataset; (2) perform CSS in the presence of missing and/or censored data; and (3) select the subset size for CSS in a hypothesis testing framework.

We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices. The estimator is positive definite by construction, and the Mahalanobis distance minimized to obtain it possesses properties which enable practical computation. We show that our manifold regression multifidelity (MRMF) covariance estimator is a maximum likelihood estimator under a certain error model on manifold tangent space. More broadly, we show that our Riemannian regression framework encompasses existing multifidelity covariance estimators constructed from control variates. We demonstrate via numerical examples that our estimator can provide significant decreases, up to one order of magnitude, in squared estimation error relative to both single-fidelity and other multifidelity covariance estimators. Furthermore, preservation of positive definiteness ensures that our estimator is compatible with downstream tasks, such as data assimilation and metric learning, in which this property is essential.

We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed model, whereas a nonlinear classifier with a memorization capacity can. This confirms that for long-tailed distributions, rare training examples must be considered for optimal generalization to new data. Finally, we show that the performance gap between linear and nonlinear models can be lessened as the tail becomes shorter in the subpopulation frequency distribution, as confirmed by experiments on synthetic and real data.