Graduate Students Seminar

Session Chair:   Mesfin Haileyesus
Discussant:        Dr. Yi Huang 

Speaker 1:  Yuting Liu

Title: Generalized Random Forests

Abstract
Generalized Random Forests (GRF) extend traditional random forests beyond prediction to a flexible framework for statistical estimation and inference. The method interprets random forests as an adaptive nearest-neighbor approach, using forest-based weights to estimate local parameters through moment equations. Unlike traditional random forests, GRF uses a gradient-based splitting criterion designed to identify heterogeneity in the target parameter rather than simply differences in conditional means. The algorithm also incorporates honest sample splitting to reduce bias and support valid inference. Under suitable regularity conditions, the authors establish consistency and asymptotic normality. Through simulations and empirical applications, GRF demonstrates its flexibility in problems such as conditional quantile estimation and heterogeneous treatment effect estimation.

Speaker 2: Alex Sheranko

Title: Efficient Multilevel Methods for Material Properties Inversion in Heat Transfer Problems

Abstract
Inverse problems for partial differential equations arise in many scientific and engineering applications and are often formulated as optimal control problems. This presentation considers the inverse problem of recovering a spatially varying thermal conductivity from the stationary heat equation. We develop a multigrid-based preconditioner to accelerate the Gauss–Newton method used in the optimization process. The governing PDE is discretized using the finite element method, while the multigrid framework exploits a hierarchy of coarser meshes to efficiently approximate the resulting linear systems. Numerical results demonstrate that the proposed preconditioner has good approximation rates  and significantly reduces the number of Conjugate Gradient iterations required at each Gauss–Newton step.