Nonparametric Density Estimation from Markov Chains

TL;DR

This paper introduces a new nonparametric density estimator based on Markov Chains, which generalizes KDE, offers advantages in large samples and high dimensions, and is effective for outlier detection.

Contribution

The paper proposes a novel Markov Chain-inspired density estimator that generalizes KDE and demonstrates its consistency and superior performance in specific scenarios.

Findings

Outperforms KDE in large sample and high-dimensional settings

Proven to be consistent as a density estimator

Effective for local outlier detection in real datasets

Abstract

We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used straightforwardly as a foundation in all density-based algorithms. We prove the consistency of our estimator and we find it typically outperforms KDE in situations of large sample size and high dimensionality. We also employ our density estimator to build a local outlier detector, showing very promising results when applied to some realistic datasets.