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The computational complexity of kernel methods has often been a major barrierfor applying them to large-scale learning problems. We argue that this barriercan be effectively overcome. In particular, we develop methods to scale upkernel models to successfully tackle large-scale learning problems that are sofar only approachable by deep learning architectures. Based on the seminal workby Rahimi and Recht on approximating kernel functions with features derivedfrom random projections, we advance the state-of-the-art by proposing methodsthat can efficiently train models with hundreds of millions of parameters, andlearn optimal representations from multiple kernels. We conduct extensiveempirical studies on problems from image recognition and automatic speechrecognition, and show that the performance of our kernel models matches that ofwell-engineered deep neural nets (DNNs). To the best of our knowledge, this isthe first time that a direct comparison between these two methods onlarge-scale problems is reported. Our kernel methods have several appealingproperties: training with convex optimization, cost for training a single modelcomparable to DNNs, and significantly reduced total cost due to fewerhyperparameters to tune for model selection. Our contrastive study betweenthese two very different but equally competitive models sheds light onfundamental questions such as how to learn good representations.

How to Scale Up Kernel Methods to Be As Good As Deep Neural Nets