Date: 2025-11-28

Time: 15:30-16:30 (Montreal time)

Location: In person, Burnside 1104

https://mcgill.zoom.us/j/86339405056

Meeting ID: 863 3940 5056

Passcode: None

Abstract:

Deep neural networks (DNNs) have become a standard tool for tackling complex regression problems, yet identifying an optimal network architecture remains a fundamental challenge. In this work, we connect neuron selection in DNNs with knot placement in basis expansion methods. Building on this connection, we propose a difference-penalty approach that automates knot selection and, in turn, simplifies the process of choosing neurons. We call this method Deep P-Spline (DPS). This approach extends the class of models considered in conventional DNN modeling and forms the basis for a latent-variable modeling framework using the Expectation–Conditional Maximization (ECM) algorithm for efficient network structure tuning with theoretical guarantees. From the perspective of nonparametric regression, DPS alleviates the curse of dimensionality, allowing effective analysis of high-dimensional data where conventional methods often fail. These properties make DPS particularly well suited for applications such as computer experiments and image data analysis, where regression tasks routinely involve a large number of inputs. Numerical studies demonstrate the strong performance of DPS, underscoring its potential as a powerful tool for advanced nonlinear regression problems.

Speaker

Li-Hsiang Lin is an Assistant Professor in the Department of Mathematics and Statistics at Georgia State University. He received his Ph.D. in Industrial Engineering, with a major in Statistics and a minor in Machine Learning, from the Georgia Institute of Technology in 2020. He then served as a Postdoctoral Fellow at the Georgia Institute of Technology and joined Louisiana State University as an Assistant Professor in 2021. He joined Georgia State University in 2023, where he currently holds the position of Assistant Professor. Professor Lin also serves on the editorial boards of Systems and Soft Computing, the Journal of Statistical Computation and Simulation, and Data Science in Science.