SDS Colloquium, Speaker Jing Lei

Title: Winners with Confidence: Discrete Argmin Inference Using Cross-Validated Exponential Mechanism

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.

Relevant Papers:

• Winners with Confidence: Discrete Argmin Inference with an Application to Model Selection