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Solved–Artificial Intelligence Lab 7– Solution

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Q1) Data in the file logistic is given in the form (xi; yi)n , where xi 2 R 2, and yi 2 f 1; +1 g . 1 i=1 (y = +1; x; w) = and (y = 1; x; w) = 1+exp( (w(2)x(2)+w(1)x(1)+w(0))) L(w) = Pi Li(w), where Li(w) = log (yi; xi; w).…

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Q1) Data in the file

logistic

is

given in the form (xi; yi)n

, where xi

2 R

2, and yi

2 f

1; +1

g

.

1

i=1

(y = +1; x; w) =

and (y =

1; x; w) =

1+exp( (w(2)x(2)+w(1)x(1)+w(0)))

L(w) = Pi Li(w), where Li(w) =

log (yi; xi; w). [50 Marks]

Let w = (w(2); w(1); w(0)) 2 R3. Let . Learn the optimal w for loss function

Q2) Data in the file linear is given in the form (xi; yi)ni=1, where xi 2 R, and yi 2 R. Let w = (w(1); w(0)) 2 R2. Learn the optimal w for loss function L(w) = Pi Li(w), where Li(w) = (w(1)xi + w(0) yi)2. [50 Marks]