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Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Computation · Statistics 2010-05-04 M. G. B. Blum , O. Francois

Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consists of one outer and one inner integral, separated by the…

Numerical Analysis · Mathematics 2024-11-26 Arved Bartuska , Luis Espath , Raúl Tempone

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Machine Learning · Computer Science 2023-11-09 Vardhan Dongre , Gurpreet Singh Hora

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Machine Learning · Computer Science 2026-03-03 Wenlong Chen

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

Machine Learning · Computer Science 2021-09-28 Mathias Löwe , Per Lunnemann Hansen , Sebastian Risi

Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…

Methodology · Statistics 2020-07-10 Michael A. Chappell , Mark W. Woolrich

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

Machine Learning · Computer Science 2025-03-04 Hyunsu Kim , Giung Nam , Chulhee Yun , Hongseok Yang , Juho Lee

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

Computation · Statistics 2016-05-03 Tiangang Cui , Youssef M. Marzouk , Karen E. Willcox

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…

Numerical Analysis · Mathematics 2021-03-17 Quanhui Zhu , Jiang Yang

Probabilistic neurosymbolic learning seeks to integrate neural networks with symbolic programming. Many state-of-the-art systems rely on a reduction to the Probabilistic Weighted Model Counting Problem (PWMC), which requires computing a…

Artificial Intelligence · Computer Science 2025-01-31 Thomas Jean-Michel Valentin , Luisa Sophie Werner , Pierre Genevès , Nabil Layaïda

Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the…

Machine Learning · Computer Science 2021-06-23 Abhinav Sagar

Recurrent neural networks (RNNs) have shown promising performance for language modeling. However, traditional training of RNNs using back-propagation through time often suffers from overfitting. One reason for this is that stochastic…

Computation and Language · Computer Science 2017-04-25 Zhe Gan , Chunyuan Li , Changyou Chen , Yunchen Pu , Qinliang Su , Lawrence Carin

Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…

Machine Learning · Statistics 2021-10-25 Nicholas Krämer , Nathanael Bosch , Jonathan Schmidt , Philipp Hennig

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

Machine Learning · Computer Science 2024-06-12 Ehsan Saleh , Saba Ghaffari , Timothy Bretl , Luke Olson , Matthew West

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

Machine Learning · Computer Science 2026-01-29 Panayiotis Ioannou , Pietro Liò , Pietro Cicuta

Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…

Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…

Logic in Computer Science · Computer Science 2023-12-12 Claudia Faggian , Daniele Pautasso , Gabriele Vanoni

As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…

Computation · Statistics 2020-04-27 Dimitris Korobilis , Davide Pettenuzzo

Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…

Machine Learning · Statistics 2024-01-02 Tim Z. Xiao , Weiyang Liu , Robert Bamler

While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…

Machine Learning · Statistics 2019-05-10 Ziyu Wang , Tongzheng Ren , Jun Zhu , Bo Zhang