How might a kernel a that ignores them completely

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Suppose that the p predictors X arise from sampling relatively smooth analog curves at p uniformly spaced abscissa values. Denote by Cov(X|Y ) = Σ the conditional covariance matrix of the predictors, and assume this does not change much with Y . Discuss the nature of Mahalanobis choice A = Σ -1 for the metric in (6.14). How does this compare with A = I? How might you construct a kernel A that

(a) downweighs high-frequency components in the distance metric;

(b) ignores them completely?

Reference no: EM131045033

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