Statistical Inference for Generative Model Comparison

Generative models have achieved remarkable success across a range of applications, yet their evaluation still lacks principled uncertainty quantification.

In this paper, we develop a method for comparing how close different generative models are to the underlying distribution of test samples.

Particularly, our approach employs the Kullback-Leibler (KL) divergence to measure the distance between a generative model and the unknown test distribution, as KL requires no tuning parameters such as the kernels used by RKHS-based distances, and is the only $f$-divergence that admits a crucial cancellation to enable the uncertainty quantification.

Furthermore, we extend our method to comparing conditional generative models and leverage Edgeworth expansions to address limited-data settings.

On simulated datasets with known ground truth, we show that our approach realizes effective coverage rates, and has higher power compared to kernel-based methods.

When applied to generative models on image and text datasets, our procedure yields conclusions consistent with benchmark metrics but with statistical confidence.