Question 1

Question text with a plot of red and blue points in two concentric circles for a logistic regression feature question A logistic regression model is being trained on a dataset of size $2n$. The first $n$ data-points belong to class-1 and the rest in class-0. Note that we are talking about the true label here. $$\begin{aligned} &\text{Class-1} = \{x_1, \cdots, x_n\} \\ &\text{Class-0} = \{x_{n+1}, \cdots, x_{2n}\} \end{aligned}$$ The probability output by the model at any step in the training process is given by: $$P(y = 1 \mid x_i) = p_i$$ Which of the following expressions is the loss of the model? **NOTE:** We use the binary cross entropy loss for logistic regression. Labels are 1 and 0 for the two classes. Figure from the original question paper