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GO Classes GATE DA | GOAT DPP Series | Machine Learning | DAY 3 | Question: 4

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Consider a binary logistic regression model with labels $Y \in \{0,1\}$. Suppose the class probabilities are obtained from the softmax function using weight vectors $w_0$ and $w_1$.

Which expression correctly gives $P(Y=1\mid x)$?

  1. $ \frac{\exp(w_0^T x)} {\exp(w_0^T x)+\exp(w_1^T x)} $
     
  2. $ \frac{\exp(w_1^T x)} {\exp(w_0^T x)+\exp(w_1^T x)} $
     
  3. $ \frac{1} {1+\exp\left((w_1-w_0)^T x\right)} $
     
  4. $ \frac{\exp\left((w_0-w_1)^T x\right)} {1+\exp\left((w_0-w_1)^T x\right)} $
     

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