相关论文: A new local time-decoupled squared Wasserstein-2 m…

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…

In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are…

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…

This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the…

We perform a mathematical and statistical analysis of the Wasserstein least squares problem, a regression method for vector-valued covariates and distribution-valued responses. Our proposal contrasts with other distributional regression…

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \emph{ambiguity sets} which give a set of possible distributions over parameter sets.…

Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…

We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…

When fine-tuning Deep Neural Networks (DNNs) to new data, DNNs are prone to overwriting network parameters required for task-specific functionality on previously learned tasks, resulting in a loss of performance on those tasks. We propose…

Uncertain differential equations have a wide range of applications. How to obtain estimated values of unknown parameters in uncertain differential equations through observations has always been a subject of concern and research, many…

The increasingly common use of neural network classifiers in industrial and social applications of image analysis has allowed impressive progress these last years. Such methods are however sensitive to algorithmic bias, i.e. to an under- or…

We suggest that the tools of contraction analysis for deterministic systems can be applied towards studying the convergence behavior of stochastic dynamical systems in the Wasserstein metric. In particular, we consider the case of Ito…

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear…