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Abstract:
We introduce the notion of kernel-alignment, a measure of
similarity between two kernel functions or between a kernel and a
target function. This quantity captures the degree of agreement
between a kernel and a given learning task, and has very natural
interpretations in machine learning, leading also to simple
algorithms for model selection and learning. We analyse its
theoretical properties, proving that it is sharply concentrated
around its expected value, and we discuss its relation with other
standard measures of performance. Finally we describe some of the
algorithms that can be obtained within this framework, giving
experimental results showing that adapting the kernel to improve
alignment on the labelled data significantly increases the
alignment on the test set, giving improved classification
accuracy. Hence, the approach provides a principled method of
performing transduction.
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