  Missing data are ubiquitous in real world applications and, if not adequately
handled, may lead to the loss of information and biased findings in downstream
analysis. Particularly, high-dimensional incomplete data with a moderate sample
size, such as analysis of multi-omics data, present daunting challenges.
Imputation is arguably the most popular method for handling missing data,
though existing imputation methods have a number of limitations. Single
imputation methods such as matrix completion methods do not adequately account
for imputation uncertainty and hence would yield improper statistical
inference. In contrast, multiple imputation (MI) methods allow for proper
inference but existing methods do not perform well in high-dimensional
settings. Our work aims to address these significant methodological gaps,
leveraging recent advances in neural network Gaussian process (NNGP) from a
Bayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, that
can apply multiple imputations for missing values from a joint (posterior
predictive) distribution. The MI-NNGP methods are shown to significantly
outperform existing state-of-the-art methods on synthetic and real datasets, in
terms of imputation error, statistical inference, robustness to missing rates,
and computation costs, under three missing data mechanisms, MCAR, MAR, and
MNAR.
