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.
翻译:缺少的数据在现实世界应用中是普遍存在的,如果处理不当,可能导致下游分析中的信息丢失和有偏差的结果。特别是,具有中等样本规模的高维不完整数据,如多组群集数据分析,具有巨大的挑战。光化可以说是处理缺失数据最流行的方法,尽管现有的估算方法存在一些局限性。矩阵完成方法等单一估算方法不能充分说明估算不确定性,因此会产生不适当的统计推断。相比之下,多重估算方法(MI)允许正确推断,但现有方法在高维环境中效果不佳。我们的工作旨在解决这些重大的方法差距,从巴伊西亚的角度利用神经网络Gausian进程(NNGPP)的最新进展。我们建议采用两种基于NGPM方法,即MI-NGP方法,这种方法可以对联合(预测性)分布的缺失值进行多次估算。 MI-NGP方法显示,在高维度环境中,在合成数据率和错误差的三个数据机制中,MI-NGP方法大大超出现有状态,在合成数据率和误差的MAR机制下,在合成和误差误差数据机制中,MUMFER。