Probabilistic Classification by Density Estimation Using Gaussian
  Mixture Model and Masked Autoregressive Flow
Benyamin Ghojogh Milad Amir Toutounchian
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.