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The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Deep neural networks can obtain impressive performance on various tasks under the assumption that their training domain is identical to their target domain. Performance can drop dramatically when this assumption does not hold. One…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
Bayesian Neural Networks (BNNs) offer probability distributions for model parameters, enabling uncertainty quantification in predictions. However, they often underperform compared to deterministic neural networks. Utilizing mutual learning…
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem,…
When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge…
Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…
This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following the manifold hypothesis and adopting a generative modelling…
We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
In this article we consider Bayesian inference associated to deep neural networks (DNNs) and in particular, trace-class neural network (TNN) priors which can be preferable to traditional DNNs as (a) they are identifiable and (b) they…
Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…
Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…