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Despite their attractiveness, popular perception is that techniques fornonparametric function approximation do not scale to streaming data due to anintractable growth in the amount of storage they require. To solve this problemin a memory-affordable way, we propose an online technique based on functionalstochastic gradient descent in tandem with supervised sparsification based ongreedy function subspace projections. The method, called parsimonious onlinelearning with kernels (POLK), provides a controllable tradeoff? between itssolution accuracy and the amount of memory it requires. We derive conditionsunder which the generated function sequence converges almost surely to theoptimal function, and we establish that the memory requirement remains finite.We evaluate POLK for kernel multi-class logistic regression and kernelhinge-loss classification on three canonical data sets: a synthetic Gaussianmixture model, the MNIST hand-written digits, and the Brodatz texture database.On all three tasks, we observe a favorable tradeoff of objective functionevaluation, classification performance, and complexity of the nonparametricregressor extracted the proposed method.

Parsimonious Online Learning with Kernels via Sparse Projections in Function Space