Nonparametric Density Estimation for High-Dimensional Data - Algorithms and Applications

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization, and machine learning. Density Estimation is widely adopted in the domain of unsupervised learning especially for the application of clustering. As big data become pervasive in almost every area of data sciences, analyzing high-dimensional data that have many features and variables appears to be a major focus in both academia and industry. High-dimensional data pose challenges not only from the theoretical aspects of statistical inference, but also from the algorithmic/computational considerations of machine learning and data analytics. This paper reviews a collection of selected nonparametric density estimation algorithms for high-dimensional data, some of them are recently published and provide interesting mathematical insights. The important application domain of nonparametric density estimation, such as { modal clustering}, are also included in this paper. Several research directions related to density estimation and high-dimensional data analysis are suggested by the authors.