Abstract for the talk on 13.03.2023 (14:00 h)Stochastic Topology and its Applications Seminar
Pei-Chun Su (Duke University)
Optimal shrinkage of singular values under noise with separable covariance & its application to fetal ECG analysis
High dimensional noisy dataset is commonly encountered in many scientific fields, and a critical step in data analysis is denoising. Under the white noise assumption, optimal shrinkage has been well-developed and widely applied to many problems. However, in practice, noise is usually colored and dependent, and the algorithm needs modification. We introduce a novel fully data-driven optimal shrinkage algorithm when the noise satisfies the separable covariance structure. The novelty involves a precise rank estimation and an accurate imputation strategy. In addition to showing theoretical supports under the random matrix framework, we show the performance of our algorithm in simulated datasets and apply the algorithm to extract fetal electrocardiogram from the benchmark trans-abdominal maternal electrocardiogram, which is a special single-channel blind source separation challenge.