  Entropy estimation is of practical importance in information theory and
statistical science. Many existing entropy estimators suffer from fast growing
estimation bias with respect to dimensionality, rendering them unsuitable for
high-dimensional problems. In this work we propose a transform-based method for
high-dimensional entropy estimation, which consists of the following two main
ingredients. First by modifying the k-NN based entropy estimator, we propose a
new estimator which enjoys small estimation bias for samples that are close to
a uniform distribution. Second we design a normalizing flow based mapping that
pushes samples toward a uniform distribution, and the relation between the
entropy of the original samples and the transformed ones is also derived. As a
result the entropy of a given set of samples is estimated by first transforming
them toward a uniform distribution and then applying the proposed estimator to
the transformed samples. The performance of the proposed method is compared
against several existing entropy estimators, with both mathematical examples
and real-world applications.
