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Kernel method has been developed as one of the standard approaches fornonlinear learning, which however, does not scale to large data set due to itsquadratic complexity in the number of samples. A number of kernel approximationmethods have thus been proposed in the recent years, among which the randomfeatures method gains much popularity due to its simplicity and directreduction of nonlinear problem to a linear one. The Random Binning (RB)feature, proposed in the first random-feature paper \cite{rahimi2007random},has drawn much less attention than the Random Fourier (RF) feature. In thiswork, we observe that the RB features, with right choice of optimizationsolver, could be orders-of-magnitude more efficient than other random featuresand kernel approximation methods under the same requirement of accuracy. Wethus propose the first analysis of RB from the perspective of optimization,which by interpreting RB as a Randomized Block Coordinate Descent in theinfinite-dimensional space, gives a faster convergence rate compared to that ofother random features. In particular, we show that by drawing $R$ random gridswith at least $\kappa$ number of non-empty bins per grid in expectation, RBmethod achieves a convergence rate of $O(1/(\kappa R))$, which not onlysharpens its $O(1/\sqrt{R})$ rate from Monte Carlo analysis, but also shows a$\kappa$ times speedup over other random features under the same analysisframework. In addition, we demonstrate another advantage of RB in theL1-regularized setting, where unlike other random features, a RB-basedCoordinate Descent solver can be parallelized with guaranteed speedupproportional to $\kappa$. Our extensive experiments demonstrate the superiorperformance of the RB features over other random features and kernelapproximation methods. Our code and data is available at {\url{https://github.com/teddylfwu/RB_GEN}}.

Revisiting Random Binning Features: Fast Convergence and Strong Parallelizability