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Missing data are ubiquitous in real world applications and, if not adequatelyhandled, may lead to the loss of information and biased findings in downstreamanalysis. Particularly, high-dimensional incomplete data with a moderate samplesize, 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. Singleimputation methods such as matrix completion methods do not adequately accountfor imputation uncertainty and hence would yield improper statisticalinference. In contrast, multiple imputation (MI) methods allow for properinference but existing methods do not perform well in high-dimensionalsettings. Our work aims to address these significant methodological gaps,leveraging recent advances in neural network Gaussian process (NNGP) from aBayesian viewpoint. We propose two NNGP-based MI methods, namely MI-NNGP, thatcan apply multiple imputations for missing values from a joint (posteriorpredictive) distribution. The MI-NNGP methods are shown to significantlyoutperform existing state-of-the-art methods on synthetic and real datasets, interms of imputation error, statistical inference, robustness to missing rates,and computation costs, under three missing data mechanisms, MCAR, MAR, andMNAR.

Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Data