Related papers: Forward Amortized Inference for Likelihood-Free Va…

We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors,…

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 study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…

Assume that we would like to estimate the expected value of a function $F$ with respect to an intractable density $\pi$, which is specified up to some unknown normalising constant. We prove that if $\pi$ is close enough under KL divergence…

We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…

The use of latent variable models has shown to be a powerful tool for modeling probability distributions over sequences. In this paper, we introduce a new variational model that extends the recurrent network in two ways for the task of…

Learning disentangled representations, where distinct factors of variation are captured by independent latent variables, is a central goal in machine learning. The dominant approach has been the Variational Autoencoder (VAE) framework,…

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving…

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear…

Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…

Beta coefficients for linear regression models represent the ideal form of an interpretable feature effect. However, for non-linear models and especially generalized linear models, the estimated coefficients cannot be interpreted as a…

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized…

Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence…