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.

翻译：数据分析通常面临非随机缺失（MNAR）问题，其中数值缺失的原因未被完全观测。相较于简单化的完全随机缺失（MCAR）问题，MNAR更符合现实场景，但也更为复杂且具有挑战性。现有统计方法通过分解完整数据与缺失掩码的联合分布来建模MNAR机制，然而我们实验发现，直接将此类统计方法融入深度生成模型会得到次优结果。具体而言，在MNAR插补过程中，该方法会忽略重建掩码的置信度，导致信息提取不充分，且插补质量缺乏保障。本文从全新视角重新审视MNAR问题，将完整数据与缺失掩码视为不完整数据的两个对等模态。基于此思路，我们提出一种生成模型专属的联合概率分解方法——共轭模型（Conjunction Model），用于并行表征两个模态的分布，并从完整数据与缺失掩码中充分提取信息。进一步地，我们开发了深度生成式插补模型GNR，在潜在空间中处理真实世界的缺失机制，同时进行不完整数据插补与缺失掩码重建。实验结果表明，我们的GNR模型显著超越当前最优的MNAR基线方法（均方根误差平均提升9.9%至18.8%），并始终实现更优的掩码重建精度，使插补过程更具原理可靠性。