Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n 3 ) and O(n 2 ) respectively, and so is prohibitive in many cases.  propose approximations of KRR based on m-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension m can be chosen while still preserving minimax optimality of the approximate KRR estimate. For various classes of randomized sketches, including those based on Gaussian and randomized Hadamard matrices,  prove that it suffices to choosethe sketch dimension m proportional to the statistical dimension (modulo logarithmic factors). Thus,  obtain fast and minimax optimal approximations to the KRR estimate for non-parametric regression.
['Yun Yang', 'Mert Pilanci', 'Martin J. Wainwright']
I am writing a research paper on a idea Randomized sketches for kernels: Fast and optimal non-parametric regression
[{"from": "human", "value": "I am writing a research paper on a idea Randomized sketches for kernels: Fast and optimal non-parametric regression"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n 3 ) and O(n 2 ) respectively, and so is prohibitive in many cases.  propose approximations of KRR based on m-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension m can be chosen while still preserving minimax optimality of the approximate KRR estimate. For various classes of randomized sketches, including those based on Gaussian and randomized Hadamard matrices,  prove that it suffices to choosethe sketch dimension m proportional to the statistical dimension (modulo logarithmic factors). Thus,  obtain fast and minimax optimal approximations to the KRR estimate for non-parametric regression."}]