学术报告20250530：Efficient Conformal Prediction in High Dimensional Regression

报告题目：Efficient Conformal Prediction in High Dimensional Regression

报告人：孔令臣

摘 要：In high-dimensional regression, constructing reliable prediction intervals is challenging. While complex machine learning models often overfit, leading to wide intervals, traditional statistical methods, despite their suitability for sparsity, typically yield biased estimators that compromise interval efficiency. To address these limitations, we propose a novel framework that integrates debiased threshold ridge regression (DeCRR) as the base estimator within the conformal prediction. Leveraging threshold ridge regression’s computational efficiency and closed-form solution, our approach explicitly incorporates debiasing corrections into the nonconformity scores, thereby enhancing predictive accuracy while preserving the distribution-free validity inherent in conformal prediction. We theoretically demonstrate that this DeCRR-based conformal prediction rigorously preserves finite-sample marginal coverage and, under specified conditions, achieves asymptotic conditional validity by converging to the oracle prediction band. Numerical experiments show our method’s superior efficiency in delivering tighter prediction intervals compared to conformal prediction based on Lasso, Multi-layer Perceptrons, Random Forests, and the bootstrap method.

报告人简介：孔令臣，教授，博士生导师，中国运筹学会数学规划分会理事长。主要从事对称锥互补问题和最优化、高维数据分析、统计优化与学习、医学成像等方面的研究。在Mathematical Programming、SIAM Journal on Optimization、IEEE Transactions on Pattern Analysis and Machine Intelligence、IEEE Transactions on Signal Processing、Technometrics、Statistica Sinica、Electronic Journal of Statistics等期刊发表论文60余篇。主持国家自然科学基金面上项目4项和专项基金项目4项,参与国家自然科学基金重点项目、重点研发项目以及973课题等。2012年获中国运筹学会青年奖，2022年获教育部自然科学二等奖等。

报告时间：2025年5月30日下午15:00-16:00

报告地点：内蒙古大学玉泉校区西院创新北楼512

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内蒙古大学数学科学学院

2025年5月28日