aiqbench takeMachine Learning

This research advances the inferential theory of Kernel Ridge Regression by constructing valid confidence bands for nonstandard data structures like graphs and sequences. The proposed anti-symmetric bootstrap procedure offers computational efficiency while maintaining validity under model mis-specification, addressing a critical gap in statistical learning applications.

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Kernel Ridge Regression Inference

arXivJuly 23, 20261 min read

arXiv:2302.06578v4 Announce Type: replace-cross Abstract: We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student preferences in school matching mechanisms--the inferential theory of KRR is not fully known. We construct valid and sharp confidence sets that shrink at nearly the minimax rate, allowing nonstandard regressors. Our bootstrap procedure uses anti-symmetric multipliers for computational efficiency and for validity under mis-specification. We use the procedure to develop a test for match effects, i.e. whether students benefit more from the schools they rank highly.

Abstract:We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student preferences in school matching mechanisms--the inferential theory of KRR is not fully known. We construct valid and sharp confidence sets that shrink at nearly the minimax rate, allowing nonstandard regressors. Our bootstrap procedure uses anti-symmetric multipliers for computational efficiency and for validity under mis-specification. We use the procedure to develop a test for match effects, i.e. whether students benefit more from the schools they rank highly.

Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2302.06578 [math.ST]

(or arXiv:2302.06578v4 [math.ST] for this version)

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