# From Adaptive Kernel Density Estimation to Sparse Mixture Models

## TL;DR

This paper presents a semi-parametric method that transitions from adaptive kernel density estimation to sparse Gaussian mixture models, enabling low-complexity models that adaptively reduce components with increased smoothing.

## Contribution

It introduces a balloon estimator within a generalized EM framework for automatic parameter estimation, bridging non-parametric KDE and parametric mixture models.

## Key findings

- Sparse models retain detail of adaptive KDE
- Model complexity decreases with higher smoothing
- Method effectively estimates mixture parameters from limited data

## Abstract

We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this regularization strategy yields low-complexity sparse models where the number of effective mixture components reduces with an increase of a smoothing probability parameter $\mathbf{P>0}$. This semi-parametric method bridges from non-parametric adaptive kernel density estimation (KDE) to parametric ordinary least-squares when $\mathbf{P=1}$. Experiments show that simpler sparse mixture models retain the level of details present in the adaptive KDE solution.