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Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…

In this paper we propose a dimension-reduction strategy in order to improve the performance of importance sampling in high dimension. The idea is to estimate variance terms in a small number of suitably chosen directions. We first prove…

In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…

We quantify the performance of approximations to stochastic filtering by the Kullback-Leibler divergence to the optimal Bayesian filter. Using a two-state Markov process that drives a Brownian measurement process as prototypical test case,…

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…

This paper investigates the accuracy of generative models and the impact of knowledge transfer on their generation precision. Specifically, we examine a generative model for a target task, fine-tuned using a pre-trained model from a source…

Online machine learning (OML) algorithms do not need any training phase and can be deployed directly in an unknown environment. OML includes multi-armed bandit (MAB) algorithms that can identify the best arm among several arms by achieving…

A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…

At the heart of reinforcement learning are actions -- decisions made in response to observations of the environment. Actions are equally fundamental in the modeling of stochastic processes, as they trigger discontinuous state transitions…

The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…

Multimodal learning with deep Boltzmann machines (DBMs) is an generative approach to fuse multimodal inputs, and can learn the shared representation via Contrastive Divergence (CD) for classification and information retrieval tasks.…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…

The Indexed Minimum Empirical Divergence (IMED) algorithm is a highly effective approach that offers a stronger theoretical guarantee of the asymptotic optimality compared to the Kullback--Leibler Upper Confidence Bound (KL-UCB) algorithm…

This paper studies the problem of interacting multiple model (IMM) estimation for jump Markov linear systems with unknown measurement noise covariance. The system state and the unknown covariance are jointly estimated in the framework of…

Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…

We study the problem of collaborative best-arm identification in stochastic linear bandits under a fixed-budget scenario. In our learning model, we first consider multiple agents connected through a star network, interacting with a linear…

In this work we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate…

The automated and intelligent processing of massive remote sensing (RS) datasets is critical in Earth observation (EO). Existing automated systems are normally task-specific, lacking a unified framework to manage diverse, end-to-end…