Estimating Kullback-Leibler Divergence Using Kernel Machines
This provides a more reliable estimator for KL divergence, particularly beneficial for small datasets in statistical and machine learning applications, though it is incremental over MINE.
The paper tackles the problem of estimating Kullback-Leibler divergence by proposing a new estimator based on Reproducing Kernel Hilbert Spaces, proving it is consistent and showing it is more reliable than the neural network-based MINE estimator on small datasets, with performance close on large datasets.
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.