Ling, Y; Liu, Z; Xue, J; (2022) Dimension reduction for data with heterogeneous missingness. In: Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence (UAI 2021). (pp. pp. 1310-1320). MLResearchPress

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Abstract

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, obser- vations with missing values present serious difficul- ties in directly applying standard dimension reduc- tion techniques. As a large number of dimension reduction approaches are based on the Gram ma- trix, we first investigate the effects of missingness on dimension reduction by studying the statisti- cal properties of the Gram matrix with or without missingness, and then we present a bias-corrected Gram matrix with nice statistical properties under heterogeneous missingness. Extensive empirical re- sults, on both simulated and publicly available real datasets, show that the proposed unbiased Gram matrix can significantly improve a broad spectrum of representative dimension reduction approaches.

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