Organizer

包承龙

Speaker

Ruiyi Yang（Shanghai Jiao Tong University）

Time

Thursday, 14:00-15:00

Dec. 18, 2025

Venue

C654, Shuangqing Complex Building

Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this talk, we propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. Given an arbitrary density p_0, we construct a multiscale representation of the density and propose data-driven methods for selecting representative models that capture meaningful discrete structure. Our approach uses a nonparametric maximum likelihood estimator to estimate the latent structure at different scales, and we further characterize their asymptotic limits. By carrying out such a multiscale analysis, we obtain coarseto-fine structures inherent in the original distribution, which are integrated via a model selection procedure to yield an interpretable discrete representation of it. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.

About the Speaker

Ruiyi Yang is an incoming Tenure-Track Associate Professor at the Institute of Natural Sciences at Shanghai Jiao Tong University. He obtained his Ph.D. in 2022 at the University of Chicago, followed by a postdoctoral training at Princeton University. His research interests lie in Bayesian computation and nonparametric statistics in non-Euclidean settings, as well as the mathematical foundations of inverse problems and data science.