Talk Title
A Spectral Embedding Test for Signal Structure in the Matrix Denoising Model
Abstract
In matrix denoising, it is common to either make assumptions or utilize the results of exploratory clustering regarding the block structure of the signal matrix. To evaluate the appropriateness of these assumptions or exploratory results, we introduce a spectral embedding-based testing procedure which assesses the goodness-of-fit of the block structure of the signal matrix in the Gaussian matrix denoising setting. We formulate a test statistic based on an adjusted two-to-infinity norm subspace distance, and study its asymptotic distributional properties. Under suitable assumptions, the Type I error probability of our test can be precisely controlled, and for a certain class of null and alternative hypotheses, we show that the power of our test tends to one. We illustrate the performance of our test on a series of simulated datasets.