no code implementations • 19 Apr 2024 • Haobo Zhang, Weihao Lu, Qian Lin
The generalization ability of kernel interpolation in large dimensions (i. e., $n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us understand the 'benign overfitting phenomenon' reported in the neural networks literature.
no code implementations • 2 Jan 2024 • Haobo Zhang, Yicheng Li, Weihao Lu, Qian Lin
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 sample size $n \asymp d^{\gamma}$ for some $\gamma > 0$.
no code implementations • 8 Sep 2023 • Weihao Lu, Haobo Zhang, Yicheng Li, Manyun Xu, Qian Lin
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i. e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ).
no code implementations • 12 May 2023 • Haobo Zhang, Yicheng Li, Weihao Lu, Qian Lin
In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0, 1)$.