相关论文: General bounds on the quality of Bayesian coresets

The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However,…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

Bayesian coresets approximate a posterior distribution by building a small weighted subset of the data points. Any inference procedure that is too computationally expensive to be run on the full posterior can instead be run inexpensively on…

Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…

The use of Bayesian methods in large-scale data settings is attractive because of the rich hierarchical models, uncertainty quantification, and prior specification they provide. Standard Bayesian inference algorithms are computationally…

Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…

Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…

We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…

In statistical classification/multiple hypothesis testing and machine learning, a model distribution estimated from the training data is usually applied to replace the unknown true distribution in the Bayes decision rule, which introduces a…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

In this paper, we study frequentist coverage errors of Bayesian credible sets for an approximately linear regression model with (moderately) high dimensional regressors, where the dimension of the regressors may increase with but is smaller…

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of…

Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of…