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Abstract:
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A common way to approach (supervised) nonparametric estimation problems in machine learning is as follows. Bound the empirical risk or minus log likelihood above by a convex functional, L, on a reproducing kernel Hilbert space, H, and (*) minimize over H the sum of L and a penalty proportional to the squared norm on H. (*) is a convex minimization problem. The theory of convex optimization is well developed. However, convex optimization software tends to be specialized and hard to use. We describe an algorithm ("QQMM") designed to solve unconstrained optimization problems of the form (*), particularly when computing L is expensive. QQMM does not require the Hessian matrix of L, but does use (sub)gradients.
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