Aggregated posterior sampling improves data generation realism
Aggregated Posterior Predictive Checks for Generative Modeling
Machine Learning
Summary
Generative models try to create realistic data by learning from examples, but they often use simple assumptions that make the generated data look unrealistic. The authors study a method that samples from a more accurate distribution of hidden factors learned by the model, rather than from the simple initial assumptions. They introduce a way to check if this improved sampling method works well and confirm it behaves as expected under certain conditions. Their tests show this approach makes generated data look better for complex types of data without needing more complicated assumptions beforehand.
What this means in practice
- •For machine learning engineers: Improve generative model outputs by sampling from the aggregated posterior instead of the prior, enhancing realism for complex data patterns.
- •For data scientists in finance: Generate more accurate synthetic financial datasets that capture heavy tails and clusters better by using aggregated posterior samples.
Authors
Shweta Dutta, Gemma E. Moran
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.