3 citations · 13 across the 25 of their papers we have counts for
25 papers
Risk Equivalence between RKHS Regression and Sequence Models for Lipschitz Spectral Algorithms
Yicheng Li, Yuqian Cheng, Zhuo Chen +1
Kernel spectral algorithms are often summarized by convergence rates, which hide how their risk depends jointly on regularization, noise, the population spectrum, target coefficien…
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…
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…
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…
Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators
Weiye Gan, Yicheng Li, Qian Lin +1
Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep ne…
On the Saturation Effects of Spectral Algorithms in Large Dimensions
Weihao Lu, Haobo Zhang, Yicheng Li +1
The saturation effects, which originally refer to the fact that kernel ridge regression (KRR) fails to achieve the information-theoretical lower bound when the regression function…
Diagonal Over-parameterization in Reproducing Kernel Hilbert Spaces as an Adaptive Feature Model: Generalization and Adaptivity
Yicheng Li, Qian Lin
This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel method…
Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories
Yicheng Li, Haobo Zhang, Jianfa Lai +2
A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamic…
Improving Adaptivity via Over-Parameterization in Sequence Models
Yicheng Li, Qian Lin
It is well known that eigenfunctions of a kernel play a crucial role in kernel regression. Through several examples, we demonstrate that even with the same set of eigenfunctions, t…
On the Impacts of the Random Initialization in the Neural Tangent Kernel Theory
Guhan Chen, Yicheng Li, Qian Lin
This paper aims to discuss the impact of random initialization of neural networks in the neural tangent kernel (NTK) theory, which is ignored by most recent works in the NTK theory…
On the Pinsker bound of inner product kernel regression in large dimensions
Weihao Lu, Jialin Ding, Haobo Zhang +1
Building on recent studies of large-dimensional kernel regression, particularly those involving inner product kernels on the sphere , we investigate the Pinsker bou…
On the Saturation Effect of Kernel Ridge Regression
Yicheng Li, Haobo Zhang, Qian Lin
The saturation effect refers to the phenomenon that the kernel ridge regression (KRR) fails to achieve the information theoretical lower bound when the smoothness of the undergroun…
The phase diagram of kernel interpolation in large dimensions
Haobo Zhang, Weihao Lu, Qian Lin
The generalization ability of kernel interpolation in large dimensions (i.e., for some ) might be one of the most interesting problems in the recent renaissance…
The Optimality of Kernel Classifiers in Sobolev Space
Jianfa Lai, Zhifan Li, Dongming Huang +1
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper…
Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions
Haobo Zhang, Yicheng Li, Weihao Lu +1
Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the…
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…
On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay
Yicheng Li, Haobo Zhang, Qian Lin
The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theo…
Optimal Rate of Kernel Regression in Large Dimensions
Weihao Lu, Haobo Zhang, Yicheng Li +2
We perform a study on kernel regression for large-dimensional data (where the sample size is polynomially depending on the dimension of the samples, i.e., for…
Generalization Ability of Wide Residual Networks
Jianfa Lai, Zixiong Yu, Songtao Tian +1
In this paper, we study the generalization ability of the wide residual network on with the ReLU activation function. We first show that as the width $m\rightarr…
On the Optimality of Misspecified Kernel Ridge Regression
Haobo Zhang, Yicheng Li, Weihao Lu +1
In the misspecified kernel ridge regression problem, researchers usually assume the underground true function , a less-smooth interpolation space of…
On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains
Yicheng Li, Zixiong Yu, Guhan Chen +1
In this paper, we provide a strategy to determine the eigenvalue decay rate (EDR) of a large class of kernel functions defined on a general domain rather than . This…
Kernel interpolation generalizes poorly
Yicheng Li, Haobo Zhang, Qian Lin
One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help…