[] from mxnet import nd, autograd, gluon import matplotlib.pyplot as plt 1. Logistic Regression for Binary Classification (2 points) In multiclass classification we typically use the exponential model exp(oy) p(yo) = softmax(0)y Ey, exp(Oy) 1.1. Show that this parametrization has a spurious degree of freedom. That is, show that both o and o+c with c ER lead to the same probability estimate. 1.2. For binary classification, i.e. whenever we have only two classes {-1,1}, we can arbitrarily set 0-1 = 0. Using the shorthand o = 01 show that this is equivalent to 1 p(y= 10) = 1+ exp(-o) 1.3. Show that the log-likelihood loss (often called logistic loss) for labels y e{-1,1} is thus given by log p(y|0) = log(1 + exp(-y:o)) 1.4. Show that for y=1 the logistic loss asymptotes to 0 for o + and to o for o +-0. [] from mxnet import nd, autograd, gluon import matplotlib.pyplot as plt 1. Logistic Regression for Binary Classification (2 points) In multiclass classification we typically use the exponential model exp(oy) p(yo) = softmax(0)y Ey, exp(Oy) 1.1. Show that this parametrization has a spurious degree of freedom. That is, show that both o and o+c with c ER lead to the same probability estimate. 1.2. For binary classification, i.e. whenever we have only two classes {-1,1}, we can arbitrarily set 0-1 = 0. Using the shorthand o = 01 show that this is equivalent to 1 p(y= 10) = 1+ exp(-o) 1.3. Show that the log-likelihood loss (often called logistic loss) for labels y e{-1,1} is thus given by log p(y|0) = log(1 + exp(-y:o)) 1.4. Show that for y=1 the logistic loss asymptotes to 0 for o + and to o for o +-0