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The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem.…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and…

We present two sampling algorithms for probabilistic confidence inference in Bayesian networks. These two algorithms (we call them AIS-BN-mu and AIS-BN-sigma algorithms) guarantee that estimates of posterior probabilities are with a given…

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

Graphical models have found widespread applications in many areas of modern statistics and machine learning. Iterative Proportional Fitting (IPF) and its variants have become the default method for undirected graphical model estimation, and…

We can perform inference in Bayesian belief networks by enumerating instantiations with high probability thus approximating the marginals. In this paper, we present a method for determining the fraction of instantiations that has to be…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…

This paper focuses on variational inference with intractable likelihood functions that can be unbiasedly estimated. A flexible variational approximation based on Gaussian mixtures is developed, by adopting the mixture population Monte Carlo…

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…

Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…

Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…

We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…

A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic…

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…