Robust and reliable low-rank approximation and dimension reduction with COlumn subset SElection

Objetivo

Modern science and technology generate massive datasets, from genomic profiles to social networks and sensor recordings. To extract knowledge, we need to reduce their dimension without losing interpretability: the Column Subset Selection Problem (CSSP) tackles this problem by choosing a small set of representative columns from a matrix that retain the essential structure of the data. All other columns can be written, approximately, as a linear combination of the few chosen representative columns.

Real data are noisy, incomplete, and subject to external restrictions, be it fairness requirements across sub-populations, physical limits on sensor placement, or computational barriers to accessing the full dataset. While powerful, most current CSSP assume ideal data and unconstrained choices.

The COSE project (Robust and reliable low-rank approximation and dimension reduction with COlumn subset SElection) will tackle this fundamental challenge by developing a unified theoretical and computational framework for fast, robust, and constraint-aware CSSP. The main objectives of COSE are to address (1) robustness to perturbations, noise, and outliers; (2) integration of practical constraints, such as group fairness or limited data access; (3) theoretical guarantees that bridge the gap between heuristic success and rigorous understanding.

COSE will combine insights from numerical linear algebra, randomized algorithms, and optimization to develop provably reliable methods that scale to massive datasets. The outcomes will include new algorithms with theoretical guarantees, open-source software and benchmarks for robust low-rank approximation and dimension reduction, with advances that impact a broad range of fields, from scientific computing to machine learning.