Weak Detection in the Spiked Wigner Model with General Rank

2020/01/16 by Ji Hyung Jung, Jung, Ji Hyung, Hye Won Chung +3
Computer Science · Mathematics · #60B20 #62H15 #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability (math.PR) #Quantum Information and Cryptography #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2001.05676

openalex publication_date 2020/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not depend on the distribution of the signal or the noise. The test is optimal under the Gaussian noise if the signal-to-noise ratio is small, as it minimizes the sum of the Type-I and Type-II errors. Under the non-Gaussian noise, the test can be improved with an entrywise transformation to the data matrix. We also introduce an algorithm that estimates the rank of the signal when it is not known a priori.

Citations

• Optimal hypothesis testing for stochastic block models with growing degrees

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