Deep Generative Imputation Model for Missing Not At Random Data

TL;DR

This paper introduces a novel deep generative model, GNR, for imputing missing data under MNAR conditions by treating data and missing masks as equal modalities, leading to improved accuracy over existing methods.

Contribution

It proposes a joint probability decomposition method and a deep generative model that simultaneously imputes data and reconstructs missing masks under MNAR, addressing limitations of previous statistical approaches.

Findings

GNR outperforms state-of-the-art MNAR imputation methods with 9.9% to 18.8% RMSE improvement.

The model achieves higher mask reconstruction accuracy, enhancing imputation quality.

Experimental results validate the effectiveness of the joint modality approach in real-world scenarios.

Abstract

Data analysis usually suffers from the Missing Not At Random (MNAR) problem, where the cause of the value missing is not fully observed. Compared to the naive Missing Completely At Random (MCAR) problem, it is more in line with the realistic scenario whereas more complex and challenging. Existing statistical methods model the MNAR mechanism by different decomposition of the joint distribution of the complete data and the missing mask. But we empirically find that directly incorporating these statistical methods into deep generative models is sub-optimal. Specifically, it would neglect the confidence of the reconstructed mask during the MNAR imputation process, which leads to insufficient information extraction and less-guaranteed imputation quality. In this paper, we revisit the MNAR problem from a novel perspective that the complete data and missing mask are two modalities of incomplete data on an equal footing. Along with this line, we put forward a generative-model-specific joint probability decomposition method, conjunction model, to represent the distributions of two modalities in parallel and extract sufficient information from both complete data and missing mask. Taking a step further, we exploit a deep generative imputation model, namely GNR, to process the real-world missing mechanism in the latent space and concurrently impute the incomplete data and reconstruct the missing mask. The experimental results show that our GNR surpasses state-of-the-art MNAR baselines with significant margins (averagely improved from 9.9% to 18.8% in RMSE) and always gives a better mask reconstruction accuracy which makes the imputation more principle.