Consider a multi-class logistic regression with two classes using the softmax function. Let zo = 21= wfx, and z = [20,21

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Consider A Multi Class Logistic Regression With Two Classes Using The Softmax Function Let Zo 21 Wfx And Z 20 21 1 (15.1 KiB) Viewed 37 times

Consider A Multi Class Logistic Regression With Two Classes Using The Softmax Function Let Zo 21 Wfx And Z 20 21 2 (9.02 KiB) Viewed 37 times

Consider A Multi Class Logistic Regression With Two Classes Using The Softmax Function Let Zo 21 Wfx And Z 20 21 3 (17.12 KiB) Viewed 37 times

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Consider a multi-class logistic regression with two classes using the softmax function. Let zo = 21= wfx, and z = [20,21]. Express the softmax outputs P(y=0|x) = go(zo, 21) and P(y = 1x) = 91 (20, 21) in terms of zo and 2₁. wr, and
90(20, 21) = symbolic expression 91(20, 21) = symbolic expression
Now, you will show that using two softmax outputs is equivalent to using one sigmoid output. Rewrite the expression for P(y = 1|x) in the form of a sigmoid, where the argument is in terms of zo and 21, i.e. P(y= 1x) = 1te but z is expressed in terms of 20 and 2₁.
P(y = 1x) = symbolic expression The expression go(zo, 21) is equivalent to σ(2), when 2 = symbolic expression