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Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
We introduce overdispersed black-box variational inference, a method to reduce the variance of the Monte Carlo estimator of the gradient in black-box variational inference. Instead of taking samples from the variational distribution, we use…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
Deep neural network training spends most of the computation on examples that are properly handled, and could be ignored. We propose to mitigate this phenomenon with a principled importance sampling scheme that focuses computation on…
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…