A note on the statistical view of matrix completion
This work addresses a foundational limitation in matrix completion theory for researchers and practitioners, though it appears incremental as it builds on known missing data analysis results.
The paper tackles the matrix completion problem by introducing a statistical interpretation that validates the procedure even without the missing completely at random (MCAR) assumption, which is commonly required in existing theoretical studies.
A very simple interpretation of matrix completion problem is introduced based on statistical models. Combined with the well-known results from missing data analysis, such interpretation indicates that matrix completion is still a valid and principled estimation procedure even without the missing completely at random (MCAR) assumption, which almost all of the current theoretical studies of matrix completion assume.