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Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work…

We introduce a reproducible, bias-resistant machine learning framework that integrates domain-informed feature engineering, nested cross-validation, and calibrated decision-threshold optimization for small-sample neuroimaging data.…

Bayesian inference is on the rise, partly because it allows researchers to quantify parameter uncertainty, evaluate evidence for competing hypotheses, incorporate model ambiguity, and seamlessly update knowledge as information accumulates.…

Task functional magnetic resonance imaging (fMRI) is a type of neuroimaging data used to identify areas of the brain that activate during specific tasks or stimuli. These data are conventionally modeled using a massive univariate approach…

Meta-analysis is a statistical method used in evidence synthesis for combining, analyzing and summarizing studies that have the same target endpoint and aims to derive a pooled quantitative estimate using fixed and random effects models or…

Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…

In this paper, we propose a general framework for combining evidence of varying quality to estimate underlying binary latent variables in the presence of restrictions imposed to respect the scientific context. The resulting algorithms…

Machine learning provides a valuable tool for analyzing high-dimensional functional neuroimaging data, and is proving effective in predicting various neurological conditions, psychiatric disorders, and cognitive patterns. In functional…

Random effects meta-analysis is widely used for synthesizing studies under the assumption that underlying effects come from a normal distribution. However, under certain conditions the use of alternative distributions might be more…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

Meta-analysis aims to generalize results from multiple related statistical analyses through a combined analysis. While the natural outcome of a Bayesian study is a posterior distribution, traditional Bayesian meta-analyses proceed by…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

Subtle alterations in brain network topology often evade detection by traditional statistical methods. To address this limitation, we introduce a Bayesian inference framework for topological comparison of brain networks that…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…