Kernel Ridge Regression
Kernel ridge regression is a regularization-based regression method built on kernel functions. By mapping data into a reproducing kernel Hilbert space (RKHS) and performing linear regression there, it is commonly used for nonlinear regression and classification tasks.
Timeline (last 90 days)
Kernel methods have long faced a computational bottleneck when handling large-scale datasets—the size of the kernel matrix grows quadratically with the number of samples, making direct solution of kernel ridge regression almost infeasible.
A recent research paper systematically analyzes the performance of kernel ridge regression combined with random features (KRR-RF) under general conditions (misspecified models coexisting with heavy-tailed noise).
Standard kernel ridge regression or kernel PCA requires computing an N×N kernel matrix (where N is the number of samples), and when N reaches the million level, both computation and storage are unbearable.
Kernel ridge regression (KRR) is an algorithm with a solid theoretical foundation in nonparametric learning and is often used to study the intrinsic properties of deep learning.
Reducing the number of free parameters in a model controls memory but sacrifices model expressiveness and hurts final accuracy.
The time and memory overhead of exactly solving KRR grows sharply, making it difficult to apply directly to large-scale datasets.
Exact solution of kernel ridge regression requires directly inverting the n×n kernel matrix, with a time complexity of O(n^3).
All Facts (7)
Kernel methods have long faced a computational bottleneck when handling large-scale datasets—the size of the kernel matrix grows quadratically with the number of samples, making direct solution of kernel ridge regression almost infeasible.
70%UnverifiedStandard kernel ridge regression or kernel PCA requires computing an N×N kernel matrix (where N is the number of samples), and when N reaches the million level, both computation and storage are unbearable.
50%UnverifiedExact solution of kernel ridge regression requires directly inverting the n×n kernel matrix, with a time complexity of O(n^3).
50%UnverifiedKernel ridge regression (KRR) is an algorithm with a solid theoretical foundation in nonparametric learning and is often used to study the intrinsic properties of deep learning.
50%UnverifiedReducing the number of free parameters in a model controls memory but sacrifices model expressiveness and hurts final accuracy.
50%UnverifiedThe time and memory overhead of exactly solving KRR grows sharply, making it difficult to apply directly to large-scale datasets.
50%UnverifiedA recent research paper systematically analyzes the performance of kernel ridge regression combined with random features (KRR-RF) under general conditions (misspecified models coexisting with heavy-tailed noise).
50%