arXiv Machine Learning
Oct 9

Conditional Kernel Stein Discrepancy

The paper introduces a Conditional Kernel Stein Discrepancy (CKSD) that extends traditional Kernel Stein Discrepancies to evaluate goodness‑of‑fit for conditional distributions. By employing an operator‑valued kernel on the covariate space, the authors lift unconditional KSDs to settings where only a conditional target model and joint samples are available, covering both smooth manifolds and discrete spaces. They prove that the CKSD statistic vanishes exactly when the conditional model matches the true conditional distribution for almost all covariates, and demonstrate its practical effectiveness through experiments on level, power, and runtime.

By Federico Matteucci, Florian Kalinke
arXiv Machine Learning
Aug 6

Nonparametric Goodness-of-fit Testing under Covariate Shift

arXiv:2608. 04860v1 Announce Type: cross Abstract: This paper develops procedures for nonparametric goodness-of-fit testing under covariate shift, where labelled data are drawn from a source population but goodness-of-fit is evaluated for a target population.

By Zhen Hou, Dong Xia
arXiv Machine Learning
6d ago

Measuring Differences between Conditional Distributions using Kernel Embeddings

The paper introduces a unified framework for measuring divergences between conditional distributions using kernel embeddings, termed conditional maximum mean discrepancy (CMMD). It defines a family of CMMD metrics—CMMD_0, CMMD_1, and CMMD_2—each based on different RKHS embeddings, and generalizes them to a level‑s CMMD with clear assumptions and operator‑based smoothing connections. Additionally, the authors present a novel doubly robust estimator for CMMD and demonstrate through experiments that the metric captures complex conditional dependencies for statistical testing.

By Peter Moskvichev, Siu Lun Chau, Dino Sejdinovic