I am interested in applied probability and high-dimensional statistics in general. Recently, I have been working on High-dimensional Bayesian Variational Inference and Adaptive Experimental Design.
Publications and Preprints
- Qiu, J. and Sen, S. (2022+). The TAP Free Energy for High-Dimensional Linear Regression, Submitted. [PDF] [arXiv]
- We derived a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression with a uniform spher- ical prior and an i.i.d. Gaussian design. We work under the “proportional" asymptotic regime, where the number of observations and the number of fea- tures grow at a proportional rate. This rigorously establishes the Thouless- Anderson-Palmer (TAP) approximation arising from spin glass theory, and proves a conjecture of [Krzakala et al., 2014] in the special case of the spherical prior.
- Ham, D.* and Qiu, J.*. (2022+). Hypothesis Testing in Sequentially Sampled Data: AdapRT to Maximize Power Beyond iid Sampling, [PDF] [arXiv]
- Testing whether a variable of interest affects the outcome is one of the most fundamental problems in statistics. To tackle this problem, the conditional randomization test (CRT) is a design-based method that is widely used to test the independence of a variable of interest (X) with an outcome (Y) holding some controls (Z) fixed. The CRT relies solely on the random iid sampling of (X,Z) to produce exact finite-sample p-values that are constructed using any test statistic. We propose a new method, the adaptive randomization test (AdapRT), that similarly tackles the independence problem but allows the data to be sequentially sampled. Like the CRT, the AdapRT relies solely on knowing the (adaptive) sampling distribution of (X,Z). In this paper, we additionally show the significant power increase by adaptively sampling in two illustrative settings.