Optimal Non-Parametric Detection of the Number of Signals

Determining the number of signals (sources / components) in a factor model is a fundamental model selection problem in many scientific fields, including signal processing and analytical chemistry. The most common methods in signal processing are based on information theoretic criteria, such as minimum description length (MDL). In this talk we'll present a statistical analysis of this problem, derive the information limit of detection, analyze the advantages but also limitations of the MDL estimator, and describe a novel non-parametric estimation method based on a sequence of hypothesis tests. The proposed method uses the eigenvalues of the sample covariance matrix, and combines a matrix perturbation approach with recent results from random matrix theory regarding the behavior of noise eigenvalues. We'll present the theoretical derivation of the method, analysis of its consistency and its limit of detection. As we'll show in simulations, under a wide range of conditions our estimator compares favorably with other competing methods, and is in fact almost optimal (near the limit of detection).
Joint work with Shira Kritchman (Weizmann).

Boaz Nadler is a senior scientist at the department of computer science and applied mathematics at Weizmann Institute of Science in Israel. He holds a PhD in applied mathematics from Tel-Aviv University, and prior to joining Weizmann he spent 3 years as an assistant professor at Yale University. His research interests are in mathematical statistics, high dimensional data analysis and signal processing.