# Estimating Kullback-Leibler Divergence Using Kernel Machines

## TL;DR

This paper introduces a new kernel-based estimator for Kullback-Leibler divergence that is consistent and more reliable on small datasets compared to neural network-based methods like MINE.

## Contribution

The paper proposes a kernel space estimator for KL divergence that guarantees consistency, improving reliability especially with small datasets.

## Key findings

- Kernel-based estimator is consistent.
- Performs better than MINE on small datasets.
- Comparable to MINE on large datasets.

## Abstract

Recently, a method called the Mutual Information Neural Estimator (MINE) that uses neural networks has been proposed to estimate mutual information and more generally the Kullback-Leibler (KL) divergence between two distributions. The method uses the Donsker-Varadhan representation to arrive at the estimate of the KL divergence and is better than the existing estimators in terms of scalability and flexibility. The output of MINE algorithm is not guaranteed to be a consistent estimator. We propose a new estimator that instead of searching among functions characterized by neural networks searches the functions in a Reproducing Kernel Hilbert Space. We prove that the proposed estimator is consistent. We carry out simulations and show that when the datasets are small the proposed estimator is more reliable than the MINE estimator and when the datasets are large the performance of the two methods are close.