Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  propose a Sparse Random Features algorithm, which learns a sparse non-linear predictor by minimizing an l1-regularized objective function over the Hilbert Space induced from a kernel function. By interpreting the algorithm as Randomized Coordinate Descent in an infinite-dimensional space,  show the proposed approach converges to a solution within ∊-precision of that using an exact kernel method, by drawing O(1/∊) random features, in contrast to the O(1/∊2) convergence achieved by current Monte-Carlo analyses of Random Features. In our experiments, the Sparse Random Feature algorithm obtains a sparse solution that requires less memory and prediction time, while maintaining comparable performance on regression and classification tasks. Moreover, as an approximate solver for the infinite-dimensional l1-regularized problem, the randomized approach also enjoys better convergence guarantees than a Boosting approach in the setting where the greedy Boosting step cannot be performed exactly.
['En-Hsu Yen', 'Ting-Wei Lin', 'Shou-De Lin', 'Pradeep Ravikumar', 'Inderjit S. Dhillon']
I am writing a research paper on a idea Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space
[{"from": "human", "value": "I am writing a research paper on a idea Sparse Random Feature Algorithm as Coordinate Descent in Hilbert Space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  propose a Sparse Random Features algorithm, which learns a sparse non-linear predictor by minimizing an l1-regularized objective function over the Hilbert Space induced from a kernel function. By interpreting the algorithm as Randomized Coordinate Descent in an infinite-dimensional space,  show the proposed approach converges to a solution within \u220a-precision of that using an exact kernel method, by drawing O(1/\u220a) random features, in contrast to the O(1/\u220a2) convergence achieved by current Monte-Carlo analyses of Random Features. In our experiments, the Sparse Random Feature algorithm obtains a sparse solution that requires less memory and prediction time, while maintaining comparable performance on regression and classification tasks. Moreover, as an approximate solver for the infinite-dimensional l1-regularized problem, the randomized approach also enjoys better convergence guarantees than a Boosting approach in the setting where the greedy Boosting step cannot be performed exactly."}]