Multi-Source Learning via Completion of Block-Wise Overlapping Noisy Matrices

• Activity Number: 188 - SLDS Student Paper Awards
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Doudou Zhou* and Tianxi Cai and Junwei Lu
• Companies: University of California, Davis and Harvard University and Harvard University
• Keywords: Low-rank matrix; matrix completion; singular value decomposition; transfer learning; PMI matrix; word embedding

Abstract

Matrix completion has attracted attention in many fields. Most of the works focus on the independent sampling models under which the observed entries are sampled independently. Motivated by applications in the integration of knowledge graphs derived from multi-source biomedical data such as those from Electronic Health Records (EHR) and biomedical text, we propose the Block-wise Overlapping Noisy Matrix Integration (BONMI) to treat block-wise missingness of matrices representing relatedness between entity pairs. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption. In the real data analysis, the method is applied to two tasks: (i) the integrating of several point-wise mutual information matrices built by English EHR and Chinese medical text data, and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods.