Related papers: The Representation Jensen-Shannon Divergence
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…
Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these…
This paper focuses on generalization performance analysis for distributed algorithms in the framework of learning theory. Taking distributed kernel ridge regression (DKRR) for example, we succeed in deriving its optimal learning rates in…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…
This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these…
This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…
Neural networks with randomly generated hidden weights (RaNNs) have been extensively studied, both as a standalone learning method and as an initialization for fully trainable deep learning methods. In this work, we study RaNN expressivity…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…
Species distribution modeling (SDM) plays a crucial role in investigating habitat suitability and addressing various ecological issues. While likelihood analysis is commonly used to draw ecological conclusions, it has been observed that its…
Semi-Supervised Learning (SSL) has become a preferred paradigm in many deep learning tasks, which reduces the need for human labor. Previous studies primarily focus on effectively utilising the labelled and unlabeled data to improve…
Unsupervised representation learning, particularly sequential disentanglement, aims to separate static and dynamic factors of variation in data without relying on labels. This remains a challenging problem, as existing approaches based on…
A new probability distribution to study lifetime data in reliability is introduced in this paper. This one is a first approach to a non-homogeneous phase-type distribution. It is built by considering one cut-point in the non-negative…
The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…