Related papers: Bayesian Neural Networks for Macroeconomic Analysi…
This work presents a novel ensemble of Bayesian Neural Networks (BNNs) for control of safety-critical systems. Decision making for safety-critical systems is challenging due to performance requirements with significant consequences in the…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…
Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Deep learning approaches require collection of data on many different input features or variables for accurate model training and prediction. Since data collection on input features could be costly, it is crucial to reduce the cost by…
This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification…
Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…
Predicting the economy's short-term dynamics -- a vital input to economic agents' decision-making process -- often uses lagged indicators in linear models. This is typically sufficient during normal times but could prove inadequate during…
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…
Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…
The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global universal approximation theorem based on Barron-type…
Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
Obtaining heteroscedastic predictive uncertainties from a Bayesian Neural Network (BNN) is vital to many applications. Often, heteroscedastic aleatoric uncertainties are learned as outputs of the BNN in addition to the predictive means,…
Bayesian Neural Networks (BNNs) offer a mathematically grounded framework to quantify the uncertainty of model predictions but come with a prohibitive computation cost for both training and inference. In this work, we show a novel network…
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…