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We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of…
We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…
Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used…
We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…
This paper introduces a Bayesian inference framework for incomplete structural models, termed distribution-matching posterior inference (DMPI). Extending the minimal econometric interpretation (MEI), DMPI constructs a divergence-based…
Variational Bayes (VB) is a popular estimation method for Bayesian inference. However, most existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many important situations. Tran et…
The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along…
Bayesian inference for exponential family random graph models (ERGMs) is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as…
Given observed data and a probabilistic generative model, Bayesian inference searches for the distribution of the model's parameters that could have yielded the data. Inference is challenging for large population studies where millions of…
Sparse deep neural networks have proven to be efficient for predictive model building in large-scale studies. Although several works have studied theoretical and numerical properties of sparse neural architectures, they have primarily…
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…