Related papers: The Exact Equivalence of Distance and Kernel Metho…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

We introduce a powerful scan statistic and the corresponding test for detecting the presence and pinpointing the location of a change point within the distribution of a data sequence with the data elements residing in a separable metric…

The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…

Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…

Computing a consensus object from a set of given objects is a core problem in machine learning and pattern recognition. One popular approach is to formulate it as an optimization problem using the generalized median. Previous methods like…

Kernel change-point detection (KCPD) has become a widely used tool for identifying structural changes in complex data. While existing theory establishes consistency under independence assumptions, real-world sequential data such as text…

We study the fundamental question of how to define and measure the distance from calibration for probabilistic predictors. While the notion of perfect calibration is well-understood, there is no consensus on how to quantify the distance…

The consistency of a learning method is usually established under the assumption that the observations are a realization of an independent and identically distributed (i.i.d.) or mixing process. Yet, kernel methods such as support vector…

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…

We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…

Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…

This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

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…

In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…

Pairwise learning or dyadic prediction concerns the prediction of properties for pairs of objects. It can be seen as an umbrella covering various machine learning problems such as matrix completion, collaborative filtering, multi-task…