StreamedIRLS: Streaming Relearning and Unlearning in Matrix Completion

StreamedIRLS: Streaming Relearning and Unlearning in Matrix Completion StreamedIRLS is a rank-agnostic computational framework for streaming matrix completion under dynamic row and column additions and deletions. It supports the incorporation of new users or items and the removal of existing users or items without repeatedly solving the entire matrix completion problem from scratch. The framework employs iteratively reweighted least squares (IRLS) for convex, smoothed nuclear-norm regularized matrix completion. Its computational design combines warm-started conjugate-gradient corrections, blockwise optimization, and incremental rank-one singular value decomposition (SVD) updates to maintain and refine the completed matrix efficiently as its dimensions change. The software supports four streaming operations: row addition, row deletion, column addition, and column deletion. It does not require prior knowledge of the underlying matrix rank. Unlearning refers to removing rows or columns and updating the completion over the retained matrix, rather than certified machine unlearning. The repository includes the StreamedIRLS implementation, ADMiRA and R1MP comparison algorithms, synthetic rank-ablation experiments, and real-data evaluation workflows using MovieLens 100K, 1M, and 10M. Reproducibility scripts, experimental configurations, numerical results, visualization utilities, and validation tests are provided. The framework is intended for research and experimentation in dynamic low-rank matrix recovery, collaborative filtering, recommender systems, incremental optimization, and streaming matrix completion.