# Probabilistic Classification by Density Estimation Using Gaussian Mixture Model and Masked Autoregressive Flow

arXiv: https://arxiv.org/abs/2310.10843 · HTML: https://mlsanity.com/paper/2310.10843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [An Alternative to EM for Gaussian Mixture Models: Batch and Stochastic Riemannian Optimization](https://mlsanity.com/paper/1706.03267/) (2017)
- [Linear and Quadratic Discriminant Analysis: Tutorial](https://mlsanity.com/paper/1906.02590/) (2019)
- [Fitting A Mixture Distribution to Data: Tutorial](https://mlsanity.com/paper/1901.06708/) (2019)
- [A Triangular Network For Density Estimation](https://mlsanity.com/paper/2004.14593/) (2020)

## Abstract (arXiv)

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization. Another family of density estimators is the generative models which generate data from input latent variables. One of the generative models is the Masked Autoregressive Flow (MAF) which makes use of normalizing flows and autoregressive networks. In this paper, we use the density estimators for classification, although they are often used for estimating the distribution of data. We model the likelihood of classes of data by density estimation, specifically using GMM and MAF. The proposed classifiers outperform simpler classifiers such as linear discriminant analysis which model the likelihood using only a single Gaussian distribution. This work opens the research door for proposing other probabilistic classifiers based on joint density estimation.