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Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

Selection of an architectural prior well suited to a task (e.g. convolutions for image data) is crucial to the success of deep neural networks (NNs). Conversely, the weight priors within these architectures are typically left vague,…

Bayesian Networks (BN) provide robust probabilistic methods of reasoning under uncertainty, but despite their formal grounds are strictly based on the notion of conditional dependence, not much attention has been paid so far to their use in…

Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to…

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…

Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…

Incorporation of external information into high-dimensional modeling for gene expression data has been shown, both theoretically and empirically, to substantially enhance performance. Such external information, sometimes referred to as…

We show that regularizing Bayesian predictive regressions provides a framework for prior sensitivity analysis. We develop a procedure that jointly regularizes expectations and variance-covariance matrices using a pair of shrinkage priors.…

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…

Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability…

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…

Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…

Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…

Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first…