Download Advances in Large-Margin Classifiers by Alexander J. Smola, Peter Bartlett, Bernhard Schölkopf, Dale PDF

By Alexander J. Smola, Peter Bartlett, Bernhard Schölkopf, Dale Schuurmans

The concept that of enormous margins is a unifying precept for the research of many various techniques to the type of knowledge from examples, together with boosting, mathematical programming, neural networks, and aid vector machines. the truth that it's the margin, or self assurance point, of a classification--that is, a scale parameter--rather than a uncooked education errors that issues has develop into a key software for facing classifiers. This e-book indicates how this concept applies to either the theoretical research and the layout of algorithms.The ebook presents an summary of contemporary advancements in huge margin classifiers, examines connections with different tools (e.g., Bayesian inference), and identifies strengths and weaknesses of the tactic, in addition to instructions for destiny learn. one of the participants are Manfred Opper, Vladimir Vapnik, and beauty Wahba.

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See [Williams, 1998] for more details on this subject. 4 A Bound on the Leave- One-Out Estimate Besides the bounds directly involving large margins, which are useful for stating uniform convergence results, one may also try to estimate R(f) by using leave­ one-out estimates. Denote by Ii the estimate obtained from X\{ Xi}, Y \ { Yi } . , [Vapnik, 1979]) that the latter is an unbiased estimator of R(f) . Unfortunately, Rout (f) is hard to compute and thus rarely used. In the case of Support Vector classification, however, an upper bound on Rout (f) is not too difficult to obtain.

With an efficient sparse representation, the dot-product of two sparse vectors can be computed in a time proportional to the total number of non­ zero elements in the two vectors. A kernel implemented as a sparse dot-product is a natural method of applying linear methods to sequences. Examples of such sparse-vector mappings are: • mapping a text to the set of words it contains • mapping a text to the set of pairs of words that are in the same sentence • mapping a symbol sequence to the set of all subsections of some fixed length m 42 Dynamic Alignment Kernels "Sparse-vector kernels" are an important extension of the range of applicability of linear methods.

4 Boosting Freund and Schapire [ 1997] proposed the AdaBoost algorithm for combining classi­ fiers produced by other learning algorithms. AdaBoost has been very successful in practical applications (see Section 1 . 5) . It turns out that it is also a large margin technique. Table 1 . 2 gives the pseudocode for the algorithm. It returns a convex combination of classifiers from a class G, by using a learning algorithm L that takes as input a training sample X, Y and a distribution D on X (not to be confused with the true distribution p), and returns a classifier from G.

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