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…
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…
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 n…