Related papers: Guaranteed Bounds for Posterior Inference in Unive…

In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…

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,…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms…

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…

We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…

The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…

This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these…

In this work, we improve upon the guarantees for sparse random embeddings, as they were recently provided and analyzed by Freksen at al. (NIPS'18) and Jagadeesan (NIPS'19). Specifically, we show that (a) our bounds are explicit as opposed…

A probabilistic program defines a probability measure over its semantic structures. One common goal of probabilistic programming languages (PPLs) is to compute posterior probabilities for arbitrary models and queries, given observed…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…