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.

翻译：密度估计作为估计数据分布的重要方法，是概率机器学习的重要分支。以期望最大化算法实现的高斯混合模型（GMM）是密度估计器的一种类型，而另一类密度估计器则是从输入潜变量生成数据的生成模型。掩码自回归流（MAF）作为生成模型的代表，其核心在于运用归一化流与自回归网络技术。本文突破密度估计器通常用于数据分布估计的传统范式，将其应用于分类任务：通过密度估计（具体采用GMM与MAF）对各类数据的似然进行建模。实验表明，相较于仅使用单一高斯分布建模似然的线性判别分析等简单分类器，本文提出的分类器具有更优性能。该研究为发展基于联合密度估计的概率分类器开辟了新思路。