Spiked Matrix

Spiked matrix models analyze the recovery of low-rank signals embedded in high-dimensional noise, focusing on understanding the limits of inference and developing efficient algorithms for signal extraction. Current research emphasizes characterizing information-theoretic limits under various noise structures, including structured and non-Gaussian noise, and exploring the performance of algorithms like approximate message passing and spectral methods, often within the context of nonlinear models and deep neural networks. These studies are crucial for advancing our understanding of high-dimensional data analysis and have implications for diverse fields, including signal processing, machine learning, and statistical inference.