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This research introduces the aggregated posterior predictive check (APPC), a new diagnostic tool designed to validate sampling strategies in latent variable generative models where standard priors fail to capture data distributions. By establishing theoretical conditions for asymptotic calibration, the study demonstrates that sampling from the fitted aggregated posterior significantly improves generation quality for complex datasets like those with heavy tails or clustering. This work advances the rigorous evaluation of variational autoencoders and similar architectures, addressing a critical gap in ensuring model reliability without relying on overly flexible priors.
Aggregated Posterior Predictive Checks for Generative Modeling
arXiv:2609.20999v1 Announce Type: cross Abstract: Latent variable generative models are commonly fit using simple priors over latent variables, but draws from these priors often fail to produce realistic data. This failure is due to a mismatch between the prior and the aggregated posterior, the distribution of latent variables induced by the fitted model and the data. This mismatch is often viewed as evidence that the prior is misspecified and should be replaced. Alternatively, in modern generative models, a two-stage strategy is increasingly used where first, the model is fit, and second, the aggregated posterior is estimated (van den Oord et al.,2017; Rombach et al., 2022.). Synthetic data are then obtained by sampling from this aggregated posterior instead of the prior. To check such procedures, we introduce the aggregated posterior predictive check (APPC). Theoretically, we establish sufficient conditions under which the APPC is asymptotically calibrated. For probabilistic principal component analysis, we show that the APPC can remain calibrated under a misspecified latent prior when pervasive factors permit recovery of the signal space. Experiments with variational autoencoders show that aggregated posterior sampling improves generation for heavy-tailed and clustered data relative to Gaussian prior sampling while performing comparably to models with more flexible latent priors.
Abstract:Latent variable generative models are commonly fit using simple priors over latent variables, but draws from these priors often fail to produce realistic data. This failure is due to a mismatch between the prior and the aggregated posterior, the distribution of latent variables induced by the fitted model and the data. This mismatch is often viewed as evidence that the prior is misspecified and should be replaced. Alternatively, in modern generative models, a two-stage strategy is increasingly used where first, the model is fit, and second, the aggregated posterior is estimated (van den Oord et al.,2017; Rombach et al., 2022.). Synthetic data are then obtained by sampling from this aggregated posterior instead of the prior. To check such procedures, we introduce the aggregated posterior predictive check (APPC). Theoretically, we establish sufficient conditions under which the APPC is asymptotically calibrated. For probabilistic principal component analysis, we show that the APPC can remain calibrated under a misspecified latent prior when pervasive factors permit recovery of the signal space. Experiments with variational autoencoders show that aggregated posterior sampling improves generation for heavy-tailed and clustered data relative to Gaussian prior sampling while performing comparably to models with more flexible latent priors.
Methodology (stat.ME); Machine Learning (cs.LG); Statistics Theory (math.ST); Machine Learning (stat.ML)
arXiv:2609.20999 [stat.ME]
(or arXiv:2609.20999v1 [stat.ME] for this version)
https://doi.org/10.48550/arXiv.2609.20999 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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