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This paper establishes a rigorous theoretical framework for assessing the generalization performance of generative models, distinguishing between metrics like Integral Probability Metrics (IPMs) and those such as Rényi divergences that cannot be reliably estimated from finite samples. By analyzing how rare events impact divergence calculations and evaluating perplexity limitations, the work provides essential guidance on selecting robust evaluation methods for open-ended AI systems.
A Theoretical Framework for Statistical Evaluability of Generative Models
arXiv:2604.05324v3 Announce Type: replace Abstract: Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and R\'enyi divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, R\'enyi and KL divergences are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.
Abstract:Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and Rényi divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, Rényi and KL divergences are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.
Machine Learning (cs.LG); Information Theory (cs.IT)
arXiv:2604.05324 [cs.LG]
(or arXiv:2604.05324v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.05324 Focus to learn more arXiv-issued DOI via DataCite
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