Graduate Students Seminar

Speaker 1: Nathan Tamiru

Title

Sample-Efficient Black-Box Optimization via Dimensionally Scaled Gaussian Processes

Abstract

Black-box optimization problems arise in many engineering and scientific domains where function evaluations are expensive and gradient information is unavailable. Bayesian Optimization (BO) provides a principled, sample-efficient framework for optimizing such functions by combining surrogate modeling with exploration/exploitation strategies. In this context, Gaussian Processes (GPs) serve as powerful tools within the broader field of Uncertainty Quantification (UQ), allowing the model to represent and propagate uncertainty in function predictions. In this presentation, we explore how GPs, equipped with carefully chosen kernels, can capture relevant structure in high-dimensional functions. Building on recent insights, we discuss how scaling GP length scales with dimensionality preserves correlations and mitigates the curse of dimensionality. Using benchmark problems, we show that even "vanilla" BO can remain effective in high-dimensional settings when GP complexity and uncertainty are properly managed.

Speaker 2: Biswajit Basak

Title

Admissibility and Estimation in Group Testing under Fixed Sampling Designs

Abstract

Group testing refers to procedures in which samples are tested in pools rather than individually, offering substantial efficiency gains when the underlying trait of interest is rare. This seminar begins by introducing the basic principles of group testing, emphasizing when and why it is advantageous. Two key problems are then discussed: (i) estimation of the underlying population parameter under different sampling schemes, and (ii) the optimality of sampling designs for efficient inference. Different sampling plans, such as fixed, inverse, and sequential binomial designs, are compared in terms of their statistical efficiency and practical feasibility. The presentation focuses mainly on fixed sampling plans, where the maximum likelihood estimator (MLE) of the transformed parameter q is examined. Using Johnson [1971]'s framework for admissibility in fixed-sample binomial problems, criteria for establishing the admissibility of the MLE are reviewed and interpreted in the context of group testing.