Practical and Consistent Estimation of f-Divergences
This work addresses a fundamental problem in statistics and machine learning for applications like representation learning and generative modeling, but it is incremental as it builds on existing assumptions to improve estimation.
The paper tackles the problem of estimating f-divergences between probability distributions under stronger structural assumptions common in modern machine learning, such as representation learning and generative modeling, and proposes an estimator that is easy to implement, works well in high dimensions, and achieves faster convergence rates, with empirical verification on synthetic and real data.
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably hard. We consider the case of stronger structural assumptions that are commonly satisfied in modern machine learning, including representation learning and generative modelling with autoencoder architectures. Under these assumptions we propose and study an estimator that can be easily implemented, works well in high dimensions, and enjoys faster rates of convergence. We verify the behavior of our estimator empirically in both synthetic and real-data experiments, and discuss its direct implications for total correlation, entropy, and mutual information estimation.