Kernel Ridge Regression Inference with Applications to Preference Data

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• Rahul Singh (Harvard University)
• Friday 20 September 2024, 09:00-10:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Qingyuan Zhao.

We provide uniform inference and confidence bands for kernel ridge regression (KRR), a widely-used non-parametric regression estimator for general data types including rankings, images, and graphs. Despite the prevalence of these data—e.g., ranked preference lists in school assignment—the inferential theory of KRR is not fully known, limiting its role in economics and other scientific domains. We construct sharp, uniform confidence sets for KRR , which shrink at nearly the minimax rate, for general regressors. To conduct inference, we develop an efficient bootstrap procedure that uses symmetrization to cancel bias and limit computational overhead. To justify the procedure, we derive finite-sample, uniform Gaussian and bootstrap couplings for partial sums in a reproducing kernel Hilbert space (RKHS). These imply strong approximation for empirical processes indexed by the RKHS unit ball with logarithmic dependence on the covering number. Simulations verify coverage. We use our procedure to construct a novel test for match effects in school assignment, an important question in education economics with consequences for school choice reforms.

This talk is part of the Causal Inference Reading Group series.

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