Abstract
Recently, Balcan and Blum [1] suggested a theory of learning based on general similarity functions, instead of positive semi-definite kernels. We study the gap between the learning guarantees based on kernel-based learning, and those that can be obtained by using the kernel as a similarity function, which was left open by Balcan and Blum. We provide a significantly improved bound on how good a kernel function is when used as a similarity function, and extend the result also to the more practically relevant hinge-loss rather then zero-one-error-rate. Furthermore, we show that this bound is tight, and hence establish that there is in-fact a real gap between the traditional kernel-based notion of margin and the newer similarity-based notion.
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Srebro, N. (2007). How Good Is a Kernel When Used as a Similarity Measure?. In: Bshouty, N.H., Gentile, C. (eds) Learning Theory. COLT 2007. Lecture Notes in Computer Science(), vol 4539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72927-3_24
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DOI: https://doi.org/10.1007/978-3-540-72927-3_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72925-9
Online ISBN: 978-3-540-72927-3
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