Read e-book online From Statistics to Neural Networks: Theory and Pattern PDF

By Jerome H. Friedman (auth.), Vladimir Cherkassky, Jerome H. Friedman, Harry Wechsler (eds.)

ISBN-10: 3642791190

ISBN-13: 9783642791192

ISBN-10: 3642791212

ISBN-13: 9783642791215

The NATO complicated learn Institute From records to Neural Networks, thought and development reputation purposes happened in Les Arcs, Bourg Saint Maurice, France, from June 21 via July 2, 1993. The assembly delivered to­ gether over a hundred individuals (including 19 invited academics) from 20 nations. The invited teachers whose contributions look during this quantity are: L. Almeida (INESC, Portugal), G. chippie (Boston, USA), V. Cherkassky (Minnesota, USA), F. Fogelman Soulie (LRI, France), W. Freeman (Berkeley, USA), J. Friedman (Stanford, USA), F. Girosi (MIT, united states and IRST, Italy), S. Grossberg (Boston, USA), T. Hastie (AT&T, USA), J. Kittler (Surrey, UK), R. Lippmann (MIT Lincoln Lab, USA), J. Moody (OGI, USA), G. Palm (U1m, Germany), B. Ripley (Oxford, UK), R. Tibshirani (Toronto, Canada), H. Wechsler (GMU, USA), C. Wellekens (Eurecom, France) and H. White (San Diego, USA). The ASI consisted of lectures overviewing significant facets of statistical and neural community studying, their hyperlinks to organic studying and non-linear dynamics (chaos), and real-life examples of development popularity purposes. because of energetic interactions among the contributors, the subsequent issues emerged as significant subject matters of the assembly: (1) Unified framework for the examine of Predictive studying in facts and synthetic Neural Networks (ANNs); (2) variations and similarities among statistical and ANN tools for non­ parametric estimation from examples (learning); (3) primary connections among synthetic studying platforms and organic studying systems.

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Extra info for From Statistics to Neural Networks: Theory and Pattern Recognition Applications

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Given the sizes of the respective (learning and test) samples (NLand NT) the ambiguity associated with the particular assignments to each can be eliminated by computing (20) (45) for all (~) possible assignments and then minimizing the average of (45) over these replications. This is of course not feasible for even moderately small values of N, so it can be approximated by many repeated random divisions and averaging the results. Even this can represent too much of a computational burden when the evaluation of (20) is computationally intensive, so generally only a few replications are performed.

However, even in this case, there is no guarantee that the bias increases monotonically with increasing A-value or even that it achieves its maximum value for A = 00 (starting point). When the A 0 solution is biased (target not a member ofthe parametric family) then it may not even be the one corresponding to minimum bias. Therefore, this type of regularization (40) provides variance control through choice of A-value but very little control over the corresponding bias that is produced in its place.

The number of parameters p, however is usually equal to the training sample size N. For example, solutions to (20) with penalty (41) (42) lead to basis function expansions (32) with p = Nand BA: z ( ) - { r2n+l A: , r~n log rA:, = n odd n = even (42a) with rA: = [(z - zA:f(z - ZA:)p/2 being the Euclidean distance from z to each sample point ZA:. Wahba (1990) and Girosi, Jones and Poggio (1993) establish similar relationships for a wide variety of other penalties based on differential operators and their corresponding parametric representations in terms of basis function expansions (32).

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From Statistics to Neural Networks: Theory and Pattern Recognition Applications by Jerome H. Friedman (auth.), Vladimir Cherkassky, Jerome H. Friedman, Harry Wechsler (eds.)

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