Discrete Argmin Inference Using Cross-Validated Exponential Mechanism
Speaker: Jing Lei
Abstract: We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. By integrating concepts and tools from cross-validation and differential privacy, we develop a test statistic that is asymptotically normal even in high-dimensional settings, and allows for arbitrarily many ties in the population mean vector. The key technical ingredient is a central limit theorem for globally dependent data characterized by stability. We also propose a practical method for selecting the tuning parameter that adapts to the signal landscape.