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SUMMARY:Kernel Ridge Regression Inference with Applications to Preference 
 Data - Rahul Singh (Harvard University)
DTSTART:20240920T080000Z
DTEND:20240920T090000Z
UID:TALK220900@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:We provide uniform inference and confidence bands for kernel r
 idge regression (KRR)\, a widely-used non-parametric regression estimator 
 for general data types including rankings\, images\, and graphs. Despite t
 he prevalence of these data -- e.g.\, ranked preference lists in school as
 signment -- the inferential theory of KRR is not fully known\, limiting it
 s role in economics and other scientific domains. We construct sharp\, uni
 form confidence sets for KRR\, which shrink at nearly the minimax rate\, f
 or general regressors. To conduct inference\, we develop an efficient boot
 strap procedure that uses symmetrization to cancel bias and limit computat
 ional overhead. To justify the procedure\, we derive finite-sample\, unifo
 rm Gaussian and bootstrap couplings for partial sums in a reproducing kern
 el Hilbert space (RKHS). These imply strong approximation for empirical pr
 ocesses indexed by the RKHS unit ball with logarithmic dependence on the c
 overing number. Simulations verify coverage. We use our procedure to const
 ruct a novel test for match effects in school assignment\, an important qu
 estion in education economics with consequences for school choice reforms.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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