Abstract:
Controlling the False Discovery Rate (FDR) in transformation selection is critical for conducting multiple comparison hypothesis tests and has applications in diverse fields such as aligning large language models with human feedback, neuroimaging studies of Alzheimer’s Disease, and trend filtering in economics. In this talk, we introduce the Split Knockoff method---a data-adaptive approach to FDR control with a finite-sample guarantee tailored for transformational selection. Our method leverages both variable splitting and data splitting: the linear transformation constraint is relaxed to its Euclidean proximity in a lifted parameter space, yielding an orthogonal design that enhances statistical power and facilitates the creation of orthogonal Split Knockoff copies. To overcome the challenge posed by the failure of exchangeability---stemming from heterogeneous noise introduced by the transformation---we develop novel inverse supermartingale structures that ensure provable FDR control even when directional effects are present. We also discuss a generalization to the Model-X framework, which achieves robust FDR control with nonlinear models provided that the marginal distribution of the random design can be accurately estimated. Finally, we demonstrate the effectiveness of our approach with applications to an Alzheimer's Disease study and the assessment of large language models.
This is a joint work with Yang Cao (Yale), Hangyu Lin (HKUST), and Xinwei Sun (Fudan).
About the Speaker:
YAO, Yuan is currently Professor of Mathematics and by courtesy of Computer Science & Engineering in the Hong Kong University of Science and Technology. Dr. Yao received his PhD in Mathematics from UC Berkeley with Prof. Steve Smale and worked in Stanford University and Peking University before joining HKUST in 2016. His main research interests lie in mathematics of data science and machine learning, with applications in computational biology and information technology.
Homepage: https://yao-lab.github.io/
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