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In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

We propose an Gaussian Mixture Model (GMM) learning algorithm, based on our previous work of GMM expansion idea. The new algorithm brings more robustness and simplicity than classic Expectation Maximization (EM) algorithm. It also improves…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks.…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…

We extend Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariates, that take…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples…

Causal discovery and inference from observational data is an essential problem in statistics posing both modeling and computational challenges. These are typically addressed by imposing strict assumptions on the joint distribution such as…

Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses,…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…