相关论文: Curved representational Bregman divergences and th…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We introduce squared families, which are families of probability densities obtained by squaring a linear transformation of a statistic. Squared families are singular, however their singularity can easily be handled so that they form regular…
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…
A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…
We propose an extension of a special form of gradient descent -- in the literature known as linearised Bregman iteration -- to a larger class of non-convex functions. We replace the classical (squared) two norm metric in the gradient…
This work uncovers variational principles behind symmetrizing the Bregman divergences induced by generic mirror maps over the cone of positive definite matrices. We show that computing the canonical means for this symmetrization can be…
In this short note, we give the convergence analysis of the policy in the recent famous policy mirror descent (PMD). We mainly consider the unregularized setting following [11] with generalized Bregman divergence. The difference is that we…
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental…
The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statistics and machine learning. We establish fundamental properties…
We investigate adaptive mixture methods that linearly combine outputs of $m$ constituent filters running in parallel to model a desired signal. We use "Bregman divergences" and obtain certain multiplicative updates to train the linear…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
The Bregman divergence have been the subject of several studies. We do not go to do an exhaustive study of its subclasses, but propose a proof that shows that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in this…
We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…
Estimating the Riesz representer is central to debiased machine learning for causal and structural parameter estimation. We propose generalized Riesz regression, a unified framework for estimating the Riesz representer by fitting a…
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…
We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some…
The purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures. Specifically, we focus on the family of Bregman…
The {\em focal curve} of an immersed smooth curve $\gamma:s\mapsto \gamma(s)$, in Euclidean space $\R^{m+1}$, consists of the centres of its osculating hyperspheres. The focal curve may be parametrised in terms of the Frenet frame of…
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…
We introduce an abstract algorithm that aims to find the Bregman projection onto a closed convex set. As an application, the asymptotic behaviour of an iterative method for finding a fixed point of a quasi Bregman nonexpansive mapping with…