Kernel Ridge Regression Inference

2023-02-13 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

Kernel Ridge Regression (KRR) inference is advanced by a new method for constructing uniform confidence bands, addressing a gap in the inferential theory for this widely used nonparametric regression estimator. KRR is frequently applied to nonstandard data types such as preferences, sequences, and graphs, exemplified by student preferences in school matching mechanisms. The developed procedure yields valid and sharp confidence sets that shrink at nearly the minimax rate, accommodating nonstandard regressors. It incorporates a computationally efficient bootstrap procedure utilizing anti-symmetric multipliers, which also ensures validity even under model mis-specification. This inferential framework is then applied to develop a specific test for "match effects," investigating whether students derive greater benefits from schools they rank highly.

Key takeaway

For research scientists working with Kernel Ridge Regression on nonstandard data like preferences or sequences, this work provides a critical tool for robust inference. You can now construct valid and sharp uniform confidence bands, enabling more reliable hypothesis testing and model validation. This directly addresses the previous lack of comprehensive inferential theory, allowing you to confidently assess effects such as "match effects" in complex systems like school assignments.

Key insights

New uniform confidence bands for Kernel Ridge Regression enable robust inference on nonstandard data types.

Principles

• Confidence sets can shrink at nearly the minimax rate.
• Bootstrap validity is achievable under mis-specification.
• Anti-symmetric multipliers enhance computational efficiency.

Method

A bootstrap procedure employing anti-symmetric multipliers constructs valid and sharp uniform confidence bands for Kernel Ridge Regression, even with nonstandard regressors.

In practice

• Test for match effects in school choice mechanisms.
• Perform inference on preference, sequence, or graph data.

Topics

• Kernel Ridge Regression
• Nonparametric Regression
• Confidence Bands
• Bootstrap Procedures
• Match Effects
• Nonstandard Data

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.