Related papers: Variational Inference for Nonlinear Inverse Proble…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…
Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused…
Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by…
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…