# Flat-topped Probability Density Functions for Mixture Models

arXiv: https://arxiv.org/abs/2203.17027 · HTML: https://mlsanity.com/paper/2203.17027/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Inferring Parameters and Structure of Latent Variable Models by Variational Bayes](https://mlsanity.com/paper/1301.6676/) (2013)
- [Mixtures of Multivariate Power Exponential Distributions](https://mlsanity.com/paper/1506.04137/) (2015)

## Abstract (arXiv)

This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the viewpoint of computational tractability, the PDF based on the Fermi-Dirac or logistic function is advantageous in estimating its shape parameters. The most appropriate PDF for n-variate distribution is of the form: pleft(xright)proptoleft[coshleft(left[left(x-mright)^mathsfTboldsymbolSigma-1left(x-mright)right]n/2right)+coshleft(rnright)right]-1 where x,m∈ℝn, boldsymbolSigma is an n× n positive definite matrix, and r>0 is a shape parameter. The flat-topped PDFs can be used as a component of mixture models in machine learning to improve goodness of fit and make a model as simple as possible.