Matrix Completion

Matrix completion aims to recover missing entries in a data matrix, often assuming the underlying data possesses a low-rank structure. Current research emphasizes developing efficient algorithms, such as those based on matrix factorization, alternating least squares, and proximal gradient descent, to handle various data types (e.g., count data, ordinal ratings) and sampling patterns (including non-uniform and block-wise missingness). These advancements are crucial for numerous applications, including recommender systems, image inpainting, and causal inference, where incomplete data is a common challenge. The field is also actively exploring the theoretical underpinnings of implicit regularization and the impact of data connectivity on algorithm performance.