Ultra Data-Oriented Parallel Fractional Hot-Deck Imputation With Efficient Linearized Variance Estimation

Abstract

Parallel fractional hot-deck imputation (P-FHDI [1]) is a general-purpose, assumption-free tool for handling item nonresponse in big incomplete data by combining the theory of FHDI and parallel computing. FHDI cures multivariate missing data by filling each missing unit with multiple observed values (thus, hot-deck) without resorting to distributional assumptions. P-FHDI can tackle big incomplete data with millions of instances (big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> ) or 10,000 variables (big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> ). However, handling ultra incomplete data (i.e., concurrently big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> and big- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> ) with tremendous instances and high dimensionality has posed problems to P-FHDI due to excessive memory requirement and execution time. To tackle the aforementioned challenges, we propose the ultra data-oriented P-FHDI (named UP-FHDI) capable of curing ultra incomplete data. In addition to the parallel Jackknife method, this paper enables a computationally efficient ultra data-oriented variance estimation using parallel linearization techniques. Results confirm that UP-FHDI can tackle an ultra dataset with one million instances and 10,000 variables. This paper illustrates the special parallel algorithms of UP-FHDI and confirms its positive impact on the subsequent deep learning performance.