Random Kitchen Sinks
Features are those pesky data attributes on which all machine learning algorithms are trained. While there are many possibilities out there for engineering high-quality features, a particularly simple trick is to just grab a bunch of features at random. Due to some happy coincidences in functional analysis, this lazy technique still provides excellent accurary. Random features thus provide a simple path to generate accurate learning algorithms that run extremely fast and are very easy to implement.
As an illustrative example, training a Random Feature learner that approximates the Gaussian kernel takes the following three lines of MATLAB code.
w = randn(D, size(X,1)); Z = exp(i*w*X); alpha = (eye(size(X,1))*lambda+Z*Z')\(Z*y(:));
Evaluating the resulting predictor takes one line of MATLAB code.
ztest = alpha(:)'*exp(i*w*xtest(:));
Relevant papers and reports
Weighted Sums of Random Kitchen Sinks: Replacing minimization with randomization in Learning. Ali Rahimi and Benjamin Recht. In Advances in Neural Information Processing Systems, 2008.
Uniform Approximation of Functions with Random Bases. Ali Rahimi and Benjamin Recht. In Proceedings of the 46th Annual Allerton Conference on Communication, Control, and Computing, 2008.
Random Features for Large-Scale Kernel Machines. Ali Rahimi and Benjamin Recht. In Advances in Neural Information Processing Systems, 2007.
Dimensionality reduction: beyond the Johnson-Lindenstrauss bound. Yair Bartal, Benjamin Recht, and Leonard Schulman. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2011.