Training Normalizing Flows with the Precision-Recall Divergence

TL;DR

This paper introduces PR-divergences to evaluate and train generative models, enabling control over precision-recall trade-offs, and proposes a novel method for training normalizing flows to minimize any divergence, including specific precision-recall balances.

Contribution

It establishes a theoretical link between precision-recall trade-offs and PR-divergences, and proposes a new training method for normalizing flows to optimize any divergence, including desired precision-recall characteristics.

Findings

PR-divergences characterize precision-recall trade-offs in generative models.

Any divergence can be expressed as a combination of PR-divergences.

The proposed method can train normalizing flows to minimize specific divergences and control precision-recall balance.

Abstract

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.