The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $250,000 Project Grant to Yale University from September 1, 2023 to August 31, 2026 under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports the development of a new perturbation theory to improve statistical analysis of large data matrices, particularly those with low-rank structure and random noise. Key anticipated outcomes include optimal error bounds for matrix parameters like eigenvalues and eigenvectors, and applying the new theory to enhance algorithms for real-world problems like matrix completion and Gaussian mixture modeling. The project also provides research training opportunities for graduate students.