Related papers: Stochastic variance-reduced Gaussian variational i…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…
Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…
Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…
We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in…
For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of…
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial…
The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction…
The Importance-Weighted Evidence Lower Bound (IW-ELBO) has emerged as an effective objective for variational inference (VI), tightening the standard ELBO and mitigating the mode-seeking behaviour. However, optimizing the IW-ELBO in…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…
Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…
We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler…
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the…
We develop a new primitive for stochastic optimization: a low-bias, low-cost estimator of the minimizer $x_\star$ of any Lipschitz strongly-convex function. In particular, we use a multilevel Monte-Carlo approach due to Blanchet and Glynn…
Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…