In this paper, we propose a Sparse Random Feature algorithm, which learns a sparse non-linear predictor by minimizing an $\ell_1$-regularized objective function over the Hilbert Space induced from kernel function. By interpreting the algorithm as Randomized Coordinate Descent in the infinite-dimensional space, we show the proposed approach converges to a solution comparable within $\eps$-precision to exact kernel method by drawing $O(1/\eps)$ number of random features, contrasted to the $O(1/\eps^2)$-type convergence achieved by Monte-Carlo analysis in current Random Feature literature. In our experiments, the Sparse Random Feature algorithm obtains sparse solution that requires less memory and prediction time while maintains comparable performance on tasks of regression and classification. In the meantime, as an approximate solver for infinite-dimensional $\ell_1$-regularized problem, the randomized approach converges to better solution than Boosting approach when the greedy step of Boosting cannot be performed exactly.

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.

In this paper, we propose a Sparse Random Feature algorithm, which learns a sparse non-linear predictor by minimizing an \ell_1 -regularized objective function over the Hilbert Space induced from kernel function. By interpreting the algorithm as Randomized Coordinate Descent in the infinite-dimensional space, we show the proposed approach converges to a solution comparable within \eps -precision to exact kernel method by drawing O(1/\eps) number of random features, contrasted to the O(1/\eps 2) -type convergence achieved by Monte-Carlo analysis in current Random Feature literature. In our experiments, the Sparse Random Feature algorithm obtains sparse solution that requires less memory and prediction time while maintains comparable performance on tasks of regression and classification. In the meantime, as an approximate solver for infinite-dimensional \ell_1 -regularized problem, the randomized approach converges to better solution than Boosting approach when the greedy step of Boosting cannot be performed exactly.

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.

In this paper, we propose a Sparse Random Feature algorithm, which learns a sparse non-linear predictor by minimizing an $\ell_1$-regularized objective function over the Hilbert Space induced from kernel function. By interpreting the algorithm as Randomized Coordinate Descent in the infinite-dimensional space, we show the proposed approach converges to a solution comparable within $\eps$-precision to exact kernel method by drawing $O(1/\eps)$ number of random features, contrasted to the $O(1/\eps 2)$-type convergence achieved by Monte-Carlo analysis in current Random Feature literature. In our experiments, the Sparse Random Feature algorithm obtains sparse solution that requires less memory and prediction time while maintains comparable performance on tasks of regression and classification. In the meantime, as an approximate solver for infinite-dimensional $\ell_1$-regularized problem, the randomized approach converges to better solution than Boosting approach when the greedy step of Boosting cannot be performed exactly. Papers published at the Neural Information Processing Systems Conference.

In this paper, we propose a Sparse Random Feature algorithm, which learns a sparse non-linear predictor by minimizing an $\ell_1$-regularized objective function over the Hilbert Space induced from kernel function. By interpreting the algorithm as Randomized Coordinate Descent in the infinite-dimensional space, we show the proposed approach converges to a solution comparable within $\eps$-precision to exact kernel method by drawing $O(1/\eps)$ number of random features, contrasted to the $O(1/\eps^2)$-type convergence achieved by Monte-Carlo analysis in current Random Feature literature. In our experiments, the Sparse Random Feature algorithm obtains sparse solution that requires less memory and prediction time while maintains comparable performance on tasks of regression and classification. In the meantime, as an approximate solver for infinite-dimensional $\ell_1$-regularized problem, the randomized approach converges to better solution than Boosting approach when the greedy step of Boosting cannot be performed exactly.