Training Normalizing Flows with the Precision-Recall Divergence
This addresses the challenge of capturing distinct failure modes like mode dropping and low sample quality in generative models, offering a more nuanced approach to model evaluation and training, though it is incremental in extending existing precision-recall frameworks.
The paper tackles the problem of evaluating and training generative models by linking precision-recall trade-offs to a family of divergences called PR-divergences, showing that any f-divergence corresponds to a weighted trade-off, and proposes a method to train normalizing flows to minimize these divergences for specified trade-offs.
Generative models can have distinct mode of failures like mode dropping and low quality samples, which cannot be captured by a single scalar metric. To address this, recent works propose evaluating generative models using precision and recall, where precision measures quality of samples and recall measures the coverage of the target distribution. Although a variety of discrepancy measures between the target and estimated distribution are used to train generative models, it is unclear what precision-recall trade-offs are achieved by various choices of the discrepancy measures. In this paper, we show that achieving a specified precision-recall trade-off corresponds to minimising -divergences from a family we call the {\em PR-divergences }. Conversely, any -divergence can be written as a linear combination of PR-divergences and therefore correspond to minimising a weighted precision-recall trade-off. Further, we propose a novel generative model that is able to train a normalizing flow to minimise any -divergence, and in particular, achieve a given precision-recall trade-off.