Optimal recovery of missing values for non-negative matrix factorization: A probabilistic error bound

Rebecca Chen, Lav R. Varshney

Abstract: Missing values imputation is often evaluated on some similarity measure between actual and imputed data. However, it may be more meaningful to evaluate downstream algorithm performance after imputation than the imputation itself. We describe a straightforward unsupervised imputation algorithm, a minimax approach based on optimal recovery, and derive probabilistic error bounds on downstream non-negative matrix factorization (NMF). We also comment on fair imputation.

Keywords: missing values imputation, minimax imputation, probabilistic bound

TL;DR: We describe a straightforward unsupervised minimax imputation and derive probabilistic error bounds on downstream non-negative matrix factorization (NMF).