Related papers: Variational Inference with Normalizing Flows

We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is…

Variational inference often struggles with the posterior geometry exhibited by complex hierarchical Bayesian models. Recent advances in flow-based variational families and Variationally Inferred Parameters (VIP) each address aspects of this…

Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of…

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…

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a…

Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to…

Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…

We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained…

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend…

Stochastic planning can be reduced to probabilistic inference in large discrete graphical models, but hardness of inference requires approximation schemes to be used. In this paper we argue that such applications can be disentangled along…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is…

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability. We tackle this challenge by introducing a novel…