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The phase diagram of kernel interpolation in large dimensions
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.
Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions
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 $\gamma > 0$.
Optimal Rate of Kernel Regression in Large Dimensions
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 $\gamma >0$ ).
On the Optimality of Misspecified Kernel Ridge Regression
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 $s\in (0, 1)$.
