Density Estimation in the Era of AI

Dear Colleagues,

Probability density estimation has long been a fundamental task in statistics. As the field began moving past the necessity of using simple parametric models, it became important to have reliable nonparametric methods of estimating the distribution of data. Methods such as histograms and kernel estimators therefore became prevalent. However, owing to the “curse of dimensionality,” these methods do not work well for high-dimensional data, which are omnipresent in modern applications. New methods of density estimation, including neural networks, have arisen to deal with complexities in the high-dimensional case.

Neural networks are a key part of machine learning, which in turn informs AI. The main task of neural networks is to learn complex data patterns that are not simply noise. In density estimation, this means discovering a pattern, such as a clustering of high-dimensional data in a manifold, that turns out to be an actual feature of the underlying distribution. This is feasible for large data sets by using the training-validation paradigm.

The purpose of this Special Issue of Entropy is twofold: (1) to familiarize the reader with the challenges of high-dimensional density and conditional density estimation, and (2) to introduce the latest neural network-based methods and explain them in the simplest possible way.

Prof. Dr. Jeffrey D. Hart
Guest Editor

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