Related papers: A Unified View of Optimal Kernel Hypothesis Testin…
We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…
Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors,…
The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
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…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Our main result shows that if a lower-semicontinuous kernel K satisfies some mild additional hypotheses, then asympotitically polarization optimal configurations are precisely those that are asymptotically distributed according to the…
Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as the sample size grows. Despite this,…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
We study kernel methods in machine learning from the perspective of feature subspace. We establish a one-to-one correspondence between feature subspaces and kernels and propose an information-theoretic measure for kernels. In particular, we…
In nonparametric independence testing, we observe i.i.d.\ data $\{(X_i,Y_i)\}_{i=1}^n$, where $X \in \mathcal{X}, Y \in \mathcal{Y}$ lie in any general spaces, and we wish to test the null that $X$ is independent of $Y$. Modern test…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…