# PMODE: Theoretically Grounded and Modular Mixture Modeling

## TL;DR

PMODE introduces a flexible, modular mixture modeling framework that partitions data for density estimation, achieving near-optimal rates and effective high-dimensional performance, including competitive anomaly detection on CIFAR-10.

## Contribution

It presents PMODE, a novel mixture modeling framework that combines parametric and nonparametric estimators, with a scalable high-dimensional variant called MV-PMODE.

## Key findings

- Achieves near-optimal rates for mixture estimators.
- Valid across different distribution families.
- Performs competitively on CIFAR-10 anomaly detection.

## Abstract

We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate estimators to each subset. It attains near-optimal rates for this estimator class and remains valid even when the mixture components come from different distribution families. As an application, we develop MV-PMODE, which scales a previously theoretical approach to high-dimensional density estimation to settings with thousands of dimensions. Despite its simplicity, it performs competitively against deep baselines on CIFAR-10 anomaly detection.