Deep Generative Imputation Model for Missing Not At Random Data
Jialei Chen Yuanbo Xu Pengyang Wang Yongjian Yang
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.