4 papers
Deflection-Optimal Spectral Design for Diagonal Screening in Sparse Phase Retrieval Initialization
Mengchu Xu, Yonina C. Eldar
Spectral initialization is a critical yet challenging step in sparse phase retrieval. Existing spectral design theory is largely tailored to dense phase retrieval, where the object…
Beyond the Flat-Spike: Adaptive Sparse CCA for Decaying and Unbalanced Signals
Mengchu Xu, Jian Wang, Yonina C. Eldar
Sparse Canonical Correlation Analysis (SCCA) is a fundamental statistical tool for identifying linear relationships in high-dimensional, multi-view data. While minimax theory estab…
Achieving Optimal Sample Complexity for a Broader Class of Signals in Sparse Phase Retrieval
Mengchu Xu, Yuxuan Zhang, Jian Wang
Sparse phase retrieval aims to recover a -sparse signal from phaseless measurements. While the theoretically optimal sample complexity for successful recovery is $Ω(k \log…
Sparse Principal Component Analysis with Energy Profile Dependent Sample Complexity
Mengchu Xu, Jian Wang, Yonina C. Eldar
We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive…