12 papers
Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay
Yicheng Li, Weiye Gan, Zuoqiang Shi +1
The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice…
Large Dimensional Kernel Ridge Regression: Extending to Product Kernels
Yang Zhou, Yicheng Li, Yuqian Cheng +1
Recent studies have reported and in large dimensional kernel ridge regression (KRR). However, these findings are…
Alignment-Sensitive Minimax Rates for Spectral Algorithms with Learned Kernels
Dongming Huang, Zhifan Li, Yicheng Li +1
We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that dep…
Optimal Confidence Band for Kernel Gradient Flow Estimator
Yuqian Cheng, Zhuo Chen, Qian Lin
In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows.…
Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
Weihao Lu, Qian Lin, Yingcun Xia +1
Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored.…
Supporting Evidence for the Adaptive Feature Program across Diverse Models
Yicheng Li, Qian Lin
Theoretically exploring the advantages of neural networks might be one of the most challenging problems in the AI era. An adaptive feature program has recently been proposed to ana…