Estimating conditional density of missing values using deep Gaussian mixture model

TL;DR

This paper introduces a deep neural network-based method for estimating the conditional distribution of missing data, combining neural flexibility with Gaussian mixture models to improve likelihood and imputation quality.

Contribution

It presents a novel approach that integrates deep neural networks with Gaussian mixture models for conditional density estimation of missing values.

Findings

Our model achieves higher log-likelihood than traditional conditional GMMs.

Imputed missing values are visually plausible and effective.

The method demonstrates improved performance in handling incomplete data.

Abstract

We consider the problem of estimating the conditional probability distribution of missing values given the observed ones. We propose an approach, which combines the flexibility of deep neural networks with the simplicity of Gaussian mixture models (GMMs). Given an incomplete data point, our neural network returns the parameters of Gaussian distribution (in the form of Factor Analyzers model) representing the corresponding conditional density. We experimentally verify that our model provides better log-likelihood than conditional GMM trained in a typical way. Moreover, imputation obtained by replacing missing values using the mean vector of our model looks visually plausible.