In these cases, we might try to correct for noise while training the classifier. Consider the following formulation for training a logistic regression classifier w ∈ R d on a noisy training data set (x (1), y(1)), . . . ,(x (n) , y(n) ), where for each i, y (i) ∈ {−1, +1}. For simplicity, we ignore the bias term b. Suppose we know that the noise magnitude is at most r. Then, instead of the standard logistic regression loss, we might want to minimize the following loss: L˜(w) = Pn i=1 L˜ i(w), where, L˜ i(w) = max z (i):kz (i)−x(i)k≤r log(1 + exp(−y (i)w >z (i) )), where kvk means the L2-norm of vector v. (a) (5 points) Prove that for all i, L˜ i(w) = Mi(w), where Mi(w) = log(1 + exp(rkwk − y (i)w >x (i) )). For full credit, show all the steps in your proof.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.

$54.99

step-by-step explanation:

$54.99 includes 500 min. if she does not exceed 500 min then her bill is $54.99