Related papers: Batch learning equals online learning in Bayesian …

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the…

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…

The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several…

Prompt learning has emerged as an effective technique for fine-tuning large-scale foundation models for downstream tasks. However, conventional prompt learning methods are prone to overfitting and can struggle with out-of-distribution…

Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an…

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational…

A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…

Machine Learning often involves various imprecise labels, leading to diverse weakly supervised settings. While recent methods aim for universal handling, they usually suffer from complex manual pre-work, ignore the relationships between…

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Domain generalization is challenging due to the domain shift and the uncertainty caused by the inaccessibility of target domain data. In this paper, we address both challenges with a probabilistic framework based on variational Bayesian…

Recent methods for deep metric learning have been focusing on designing different contrastive loss functions between positive and negative pairs of samples so that the learned feature embedding is able to pull positive samples of the same…

Contrastive learning is among the most popular and powerful approaches for self-supervised representation learning, where the goal is to map semantically similar samples close together while separating dissimilar ones in the latent space.…

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node…