相关论文: Hilbert space embeddings of independence tests of …

In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We…

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams…

Recent works investigated the generalization properties in deep neural networks (DNNs) by studying the Information Bottleneck in DNNs. However, the mea- surement of the mutual information (MI) is often inaccurate due to the density…

Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…

Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…

We propose a greedy strategy to spectrally train a deep network for multi-class classification. Each layer is defined as a composition of linear weights with the feature map of a Gaussian kernel acting as the activation function. At each…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$\chi^2$ null limits force a permutation calibration that multiplies the…

The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…

We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…

Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed…

There exists a plethora of parametric models for positive definite kernels, and their use is ubiquitous in disciplines as diverse as statistics, machine learning, numerical analysis, and approximation theory. Usually, the kernel parameters…

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…

Since persistence diagrams do not admit an inner product structure, a map into a Hilbert space is needed in order to use kernel methods. It is natural to ask if such maps necessarily distort the metric on persistence diagrams. We show that…

The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…