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September 7 Math Colloquium

Martin Jones, CofC

Reproducing Kernel Hilbert Spaces and Statistical Learning

Typical problems in statistical learning involve building models from a set of training data that can be used to predict future values of the response variable. The challenge is to have a rich class of approximating functions to fit to the data so that future predictions will be accurate, but at the same time keeping the class “manageable” enough so that the approximating functions can be computed in real time using matrix manipulations. How can we possibly hope to win this statistical tug-of-war? The answer lies in constructing the right type of function space, namely a Reproducing Kernel Hilbert Space. In this talk, we will see how good predictive models can be constructed even when our space of functions is infinite dimensional.

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