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(a) Explain A(9w,b, (i, yi)) as a function of z; — Yi9w,b(7₁). (b) Design a loss function (2) as proxy for A(z) that is (i) convex, (ii) has a derivative defined for all z, and (iii) for all values of z satisfies la(z) > A(Z).

(a) Explain A(9w,b, (i, yi)) as a function of z; — Yi9w,b(7₁). (b) Design a loss function (2) as proxy for A(z) that is (i) convex, (ii) has a derivative defined for all z, and (iii) for all values of z satisfies la(z) > A(Z).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a family of lincar classifiers defined by the sign of function gu,b(x) - (w, x) + b, where z E R² and so w e R² and b e R. Given a data point r; and label y; € {-1,+1}. We require that ||w|| – 1. Now consider a uncertainty zone misclassification goal A (in place of A). In this setting, we want to penalize a classifier with a cost of 1/4 for any point within a distance of 2 of the classification boundary – even if it has the correct sign. So the cost is if (ri, Yi) is misclassified and [gw,b(r;)| > 2 1/4 if 0 < |gu,b(r;)| <2 if (ri, Yi) is classified correctly and [gw ,b(T;)| > 2 A(gw,b, (Ti, Yi)) - (a) Explain A(gm,b, (Xi, Yi)) as a function of z = Y:gw,b(X;). (b) Design a loss function la(2) as proxy for A(2) that is (i) convex, (ii) has a derivative defined for all z, and (iii) for all values of z satisfies la(2) 2 A(2).
Transcribed Image Text:Consider a family of lincar classifiers defined by the sign of function gu,b(x) - (w, x) + b, where z E R² and so w e R² and b e R. Given a data point r; and label y; € {-1,+1}. We require that ||w|| – 1. Now consider a uncertainty zone misclassification goal A (in place of A). In this setting, we want to penalize a classifier with a cost of 1/4 for any point within a distance of 2 of the classification boundary – even if it has the correct sign. So the cost is if (ri, Yi) is misclassified and [gw,b(r;)| > 2 1/4 if 0 < |gu,b(r;)| <2 if (ri, Yi) is classified correctly and [gw ,b(T;)| > 2 A(gw,b, (Ti, Yi)) - (a) Explain A(gm,b, (Xi, Yi)) as a function of z = Y:gw,b(X;). (b) Design a loss function la(2) as proxy for A(2) that is (i) convex, (ii) has a derivative defined for all z, and (iii) for all values of z satisfies la(2) 2 A(2).
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