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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 thenaive Missing Completely At Random (MCAR) problem, it is more in line with therealistic scenario whereas more complex and challenging. Existing statisticalmethods model the MNAR mechanism by different decomposition of the jointdistribution of the complete data and the missing mask. But we empirically findthat directly incorporating these statistical methods into deep generativemodels is sub-optimal. Specifically, it would neglect the confidence of thereconstructed mask during the MNAR imputation process, which leads toinsufficient information extraction and less-guaranteed imputation quality. Inthis paper, we revisit the MNAR problem from a novel perspective that thecomplete data and missing mask are two modalities of incomplete data on anequal footing. Along with this line, we put forward a generative-model-specificjoint probability decomposition method, conjunction model, to represent thedistributions of two modalities in parallel and extract sufficient informationfrom both complete data and missing mask. Taking a step further, we exploit adeep generative imputation model, namely GNR, to process the real-world missingmechanism in the latent space and concurrently impute the incomplete data andreconstruct the missing mask. The experimental results show that our GNRsurpasses state-of-the-art MNAR baselines with significant margins (averagelyimproved from 9.9% to 18.8% in RMSE) and always gives a better maskreconstruction accuracy which makes the imputation more principle.

Deep Generative Imputation Model for Missing Not At Random Data