On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights into their operating characteristics, we study here the statistical performance of such approaches within a minimax framework. Focusing on the case of goodness-of-fit tests, our analyses show that a vanilla version of the kernel-embedding based test could be suboptimal, and suggest a simple remedy by moderating the embedding. We prove that the moderated approach provides optimal tests for a wide range of deviations from the null and can also be made adaptive over a large collection of interpolation spaces. Numerical experiments are presented to further demonstrate the merits of our approach.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/07/2019

On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives

Nonparametric tests via kernel embedding of distributions have witnessed...
research
05/12/2023

On the Optimality of Misspecified Kernel Ridge Regression

In the misspecified kernel ridge regression problem, researchers usually...
research
03/27/2023

On the optimality of misspecified spectral algorithms

In the misspecified spectral algorithms problem, researchers usually ass...
research
08/31/2022

A general framework for the analysis of kernel-based tests

Kernel-based tests provide a simple yet effective framework that use the...
research
11/12/2020

Generalized Kernel Two-Sample Tests

Kernel two-sample tests have been widely used for multivariate data in t...
research
08/13/2012

Path Integral Control by Reproducing Kernel Hilbert Space Embedding

We present an embedding of stochastic optimal control problems, of the s...
research
10/10/2021

Adaptive joint distribution learning

We develop a new framework for embedding (joint) probability distributio...

Please sign up or login with your details

Forgot password? Click here to reset