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final.dvi

shattered by the chosen family of functions 1 2 3 4x=0 Figure Four points that cannot be shattered by sinx despite in nite VC dimension 0.2 0.4 0.6 0.8 1 1.2 1.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 V C C on [...] that trained machine in the series whose sum of empirical risk and VC condence is minimal h1h2h3h4 h1 < h2 < h3 ... Figure Nested subsets of functions ordered by VC dimension We have now laid the groundwork [...] We could equally well have chosen H to again be R and x p x x xx x x A 0.2 0.4 0.6 0.8 1 -1 -0.5 0 0.5 1 0 0.2 0.4 0.6 0.8 1 Figure Image in H of the square R under the mapping or H to be …