In This Problem We Will Investigate Minimizing The Training Objective For A Support Vector Machine With Margin Loss 1 (81.74 KiB) Viewed 24 times
In This Problem We Will Investigate Minimizing The Training Objective For A Support Vector Machine With Margin Loss 2 (53.03 KiB) Viewed 24 times
In this problem, we will investigate minimizing the training objective for a Support Vector Machine (with margin loss). The training objective for the Support Vector Machine (with margin loss) can be seen as optimizing a balance between the average hinge loss over the examples and a regularization term that tries to keep the parameters small (increase the margin). This balance is set by the regularization parameter x > 0. Here we only consider the case without the offset parameter (setting it to zero) so that the training objective is given by TO (4.3) A Lossh (yi) x(i) 13 | + 121101²2 = 2²/12/201 Lossh (y) x(i)) + 11011²2 n i=1 where the hinge loss is given by Lossh (y (0x)) = max{0, 1y (0-x)} (4.4) = Argmin, [Lossh (y0.x) + 1011²2 x (1) Note: For all of the exercises on this page, assume that n = 1 where n is the number of training examples and x = Y = = y(¹). and
Minimizing Loss - Numerical Example (1) 2 points possible (graded) Consider minimizing the above objective fuction for the following numerical example: λ = 0.5, y = 1, x = D Note that this is a classification problem where points lie on a two dimensional space. Hence Ô would be a two dimensional vector. Let 0 = [1,2], where 61, 62 are the first and second components of respectively. Solve for 01, 02. Hint: For the above example, show that Lossh (y (Ô · x)) ≤ 0 61₁ - 0₂ =
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