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Synthetic data generation has become a key ingredient for training machinelearning procedures, addressing tasks such as data augmentation, analysingprivacy-sensitive data, or visualising representative samples. Assessing thequality of such synthetic data generators hence has to be addressed. As (deep)generative models for synthetic data often do not admit explicit probabilitydistributions, classical statistical procedures for assessing modelgoodness-of-fit may not be applicable. In this paper, we propose a principledprocedure to assess the quality of a synthetic data generator. The procedure isa kernelised Stein discrepancy (KSD)-type test which is based on anon-parametric Stein operator for the synthetic data generator of interest.This operator is estimated from samples which are obtained from the syntheticdata generator and hence can be applied even when the model is only implicit.In contrast to classical testing, the sample size from the synthetic datagenerator can be as large as desired, while the size of the observed data,which the generator aims to emulate is fixed. Experimental results on syntheticdistributions and trained generative models on synthetic and real datasetsillustrate that the method shows improved power performance compared toexisting approaches.

A Kernelised Stein Statistic for Assessing Implicit Generative Models