Matrix completion has attracted a lot of attention in many fields  including statistics, applied mathematics  and electrical engineering. Most of  works focus on the independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in the integration of multiple (point-wise mutual information) PMI matrices , we propose the model {\bf B} lockwise missing {\bf E}mbedding {\bf L}earning {\bf T}ransformer (BELT) to treat row-wise/column-wise missingness. Specifically, our proposed method aims at efficient matrix recovery when every pair of matrices from multiple sources has an overlap. We provide theoretical justification for the proposed BELT method . Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several PMI matrices built by EHR data and Chinese medical text data, which enables us to construct a comprehensive embedding set for CUI and Chinese with high quality .
Matrix completion has attracted attention in many fields , including statistics, applied mathematics , and electrical engineering. 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 multiple Electronic Health Record (EHR) datasets , we propose the method {\bf B} lock-wise missing {\bf E}mbedding {\bf L}earning {\bf T}ransformer (BELT) to treat row-wise/column-wise missingness. Specifically, BELT can recover block-wise missing matrices efficiently when every pair of matrices has an overlap. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices using their overlap, 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 . Simulation studies show that the method performs well under a variety of configurations. 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 .
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a lot of
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,
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,
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the
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individual
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(point-wise mutual information) PMI matrices
Electronic Health Record (EHR) datasets
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model
method
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lockwise
lock-wise
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our proposed method aims at efficient matrix recovery
BELT can recover block-wise missing matrices efficiently
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from multiple sources
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We provide theoretical justification for the proposed BELT method
Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices using their overlap, 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
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in finite sample
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The
In the real data analysis, the
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integrate several PMI
two tasks: (i) the integrating of several point-wise mutual information
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EHR data
English EHR
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which enables us to construct a comprehensive embedding set for CUI and Chinese with high quality
and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods