Optimal Kernel Hypothesis Testing by Dr. Antonin Schrab

ABSTRACT
New kernel hypothesis tests are proposed and optimal power guarantees are derived. Various testing frameworks such as the two-sample, independence and goodness-of-fit frameworks are considered. A strong focus is put on the, often ignored, crucial choice of the kernel which strongly impacts the test power. Two methods, namely kernel pooling and aggregation, are proposed to adaptively select the kernels in a parameter-free manner, and are shown to lead to minimax optimal separation rates with respect to the kernel and L2 metrics. Optimal kernel tests are also developed, and their power guarantees theoretically analysed, under various testing constraints such as computation efficiency, differential privacy, and robustness to data corruption.

ABOUT THE SPEAKER
Dr. Antonin Schrab is a postdoctoral researcher at the University of Cambridge. He holds a PhD at University College London, supervised by Benjamin Guedj at the UCL Centre for AI and Inria London, and Arthur Gretton at the Gatsby Computational Neuroscience Unit. His research interests lie on designing optimal kernel-based hypothesis testing for two-sample, independence, and goodness-of-fit problems, with emphasis on both theory (minimax optimality guarantees) and practicality (user-friendly parameter-free implementations).