Project Grant 2606337

The National Science Foundation Division of Mathematical Sciences awarded the University of Southern California $100,864 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop theoretical and computational methods for incomplete tensors in data-driven applications.

The project addresses the practical challenge of reasoning and computing with incomplete, noisy, or partially observable datasets that constrain performance and reliability in real-world machine learning and data analytics systems. The research develops a toolkit spanning three complementary approaches: analyzing the sample complexity required to recover low-rank tensors, developing numerical methods for tensor completion under structured missingness patterns, and creating completion-free alternatives when tensor completion is infeasible. The project introduces a randomized sampling paradigm demonstrating that carefully designed sampling schemes enable polynomial-time recovery with nearly linear sample complexity. Graduate student training in these theoretical and algorithmic techniques is integrated into the research activities.

The award funds work performed at USC's Los Angeles, California campus through August 31, 2029. The funding mechanism is a project grant.