On the performance of Kernel Density Estimation using Density Matrices

Density estimation methods can be used to solve a variety of statistical and machine learning challenges. They can be used to tackle a variety of problems, including anomaly detection, generative models, semi-supervised learning, compression, and text-to-speech. A popular technique to find density estimates for new samples in a non parametric set up is Kernel Density Estimation, a method which suffers from costly evaluations especially for large data sets and higher dimensions. In this thesis we want to compare the performance of the novel method Kernel Density Estimation using Density Matrices introduced by (Gonzalez et al, 2021) against other state-of-the-art fast procedures for estimating the probability density function indifferent sets of complex synthetic scenarios. Our experimental results show that this novel method is a competitive strategy to calculate density estimates among its competitors and also show advantages when performing on large data sets and high dimensions. The software used for testing the proposed method is available online.