A Witness Two-Sample Test

Mär 28, 2022



The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a weighted sum of kernel evaluations on a set of basis points. Typically the kernel is optimized on a training set, and hypothesis testing is performed on a separate test set to avoid overfitting (i.e., control type-I error). That is, the test set is used to simultaneously estimate the expectations and define the basis points, while the training set only serves to select the kernel and is discarded. In this work, we propose to use the training data to also define the weights and the basis points for better data efficiency. We show that 1) the new test is consistent and has a well-controlled type-I error; 2) the optimal witness function is given by a precision-weighted mean in the reproducing kernel Hilbert space associated with the kernel; and 3) the test power of the proposed test is comparable or exceeds that of the MMD and other modern tests, as verified empirically on challenging synthetic and real problems (e.g., Higgs data).


Über AISTATS 2022

AISTATS is an interdisciplinary gathering of researchers at the intersection of computer science, artificial intelligence, machine learning, statistics, and related areas. Since its inception in 1985, the primary goal of AISTATS has been to broaden research in these fields by promoting the exchange of ideas among them. We encourage the submission of all papers which are in keeping with this objective at AISTATS.

Präsentation speichern

Soll diese Präsentation für 1000 Jahre gespeichert werden?

Wie speichern wir Präsentationen?

Ewigspeicher-Fortschrittswert: 0 = 0.0%


Empfohlene Videos

Präsentationen, deren Thema, Kategorie oder Sprecher:in ähnlich sind

Interessiert an Vorträgen wie diesem? AISTATS 2022 folgen