  Missing values widely exist in many real-world datasets, which hinders the
performing of advanced data analytics. Properly filling these missing values is
crucial but challenging, especially when the missing rate is high. Many
approaches have been proposed for missing value imputation (MVI), but they are
mostly heuristics-based, lacking a principled foundation and do not perform
satisfactorily in practice. In this paper, we propose a probabilistic framework
based on deep generative models for MVI. Under this framework, imputing the
missing entries amounts to seeking a fixed-point solution between two
conditional distributions defined on the missing entries and latent variables
respectively. These distributions are parameterized by deep neural networks
(DNNs) which possess high approximation power and can capture the nonlinear
relationships between missing entries and the observed values. The learning of
weight parameters of DNNs is performed by maximizing an approximation of the
log-likelihood of observed values. We conducted extensive evaluation on 13
datasets and compared with 11 baselines methods, where our methods largely
outperforms the baselines.
