50 Activities for Creativity & Problem Solving by Geof Cox, Chuck Dufault, Walt Hopkins

By Geof Cox, Chuck Dufault, Walt Hopkins

50 actions For reaching swap an entire advisor outlining the method of accepting swap, show the necessity for swap, decreasing clash, enhancing communique talents and extra. education target enhance inventive considering provide new approached to challenge fixing boost techniques to difficulties that won't reply to conventional problem-solving equipment actions conceal challenge research pondering procedure discovering ideas Implementation of inventive problem-solving equipment

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YdF(ylx). \. is referred to as the problem of regression estimation. We now show that under conditions ! 2 r (x)dF(y,x) < x the problem of regression estimation is reduced to the model of minimizing risk based on empirical data. Indeed. on the set f(x, a), a E ,\ (f(x, a) E L 2 (P)). the minimum of the fund iona I R(a) = ! (y - f(x o (~))2 dF(y ... 9) (provided the minimum exists) is attained at the regression function if the regression r(x) belongs to f(x, a), a E A. The minimum of this functional is attained at the function f(x, (y').

5). Thus, the problem of pattern recognition has been reduced to the problem of minimizing the risk on the basis of empirical data. 2. The following restrictions are imposed: • The vector z consists of n + 1 coordinates: coordinate w, which takes on only a finite number of values (two values for a two classes problem). and n coordinates x l , ... , x n which form the vector x . • The set of functions Q(z, a), a E A. is given by Q(z, a) = L(w, ep (x, a)), aEA and also takes on only a finite number of values (zero and one for the simplest loss function).

J=1 In the case when L(wj, ¢) E {O, I} (0 if W = ¢ and 1 if W i- ¢). minimization of the empirical risk functional produced a function which has the smallest number of errors on the training data. 34 1 TWO APPROACHES TO THE LEARNING PROBLEM Least Squares Method for the Regression Estimation Problem. 4. we considered the problem of regression estimation as the probkm of minimization of the functional R(a) = ! (y .. f(x. on the set of functions f(x. a). \, on the basis of empirical data For this functional, the empirical risk functional is I I", .

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