Math/Physic/Economic/Statistic Problems
1 of 2 Homework Assignment #2
Through this homework assignment, you will refresh on the concepts of derivatives and convexity, and will practice on programming of logistic regression for binary classification.
A) Which of these is the logistic loss” function (for the i-th sample)?
(a) LOVV/Y(0) = (no logry(n) + -Y(0)1.61 -AO
(b) 1400,^01Y(0) = -A01
(c) Lo(1fnyto) = Irv) -Ao12
(4) 44/WM = max(0,y(n-Y44
ram (400010)
Problem 2. Write the derivatives /(x) of the following functions of x
A) (x). 1r.
B) (x) = log(14- rrz)
C) R.) = W. where x E FO and a = [2,3,1],
D) f(x) = xrAx where x E W and A= [2,3;1,2] E
E) R.) = (y – ‘Ja)y where x E = 1 and a = [2,3,1],Problem 3. The softplus function is given by
f(r) = log(1 o
Plot/(z) as a function of z. If you plot by hand, mark a couple of critical points on the curve.
Show that /(z) is convex in z by showing that its second derivative is positive for all.
