Statistical Inference for Generative Model Comparison

arXiv:2501.18897v4 Announce Type: replace-cross Abstract: 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.

Abstract: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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2501.18897 [stat.ML]

(or arXiv:2501.18897v4 [stat.ML] for this version)

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Statistical Inference for Generative Model Comparison

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