Nonparametric Density Estimation using Predictive Recursion

Oregon Convention Center 

We built a novel statistical machine learning framework for nonparametric density estimation, using predictive recursion (PR). In a mixture model, to estimate the unknown mixing density, one can use finite mixture models where there is a need to estimate the number of mixing components or use Dirichlet process where a prior assumption on the form of the mixing density function has to be made. We proposed PR (i) which does not require to estimate the number of components, (ii) which does not need to make assumptions on the form of the mixing density and (iii) which is fast, unlike the MCMC-based methods. PR is capable of capturing spatial characteristics of the data, distinguishing high- and low-density regions. We then extended our approach by integrating deep learning to the conditional nonparametric density estimation setting where we used kernel functions to capture complex and high-dimensional relationships. Finally, we showed the capability of our method in terms of density estimation and predictive performance by comparing its results to state-of-the-art algorithms.

Nonparametric Density Estimation

Machine Learning

Deep Learning

Kernel Functions 

Section on Statistical Learning and Data Science