True$/$False Statements with Justifications

A$.$ False: Using a model with less bias isn't always better because it can lead to overfitting, where the model captures noise in the training data, resulting in poor performance on new data.

B$.$ False: Even with the correct step size, gradient descent might not always converge to the optimum in linear regression due to factors like local minima, especially in non$-$convex settings.

C$.$ False: Logistic regression can be adapted for multi$-$class classification problems using methods like One$-$vs$-$Rest $($OvR$)$ or softmax regression.

D$.$ False: Gradient descent can be used for both convex and non$-$convex functions, though it guarantees convergence to a global optimum only for convex functions.

E$.$ True: Cross$-$Entropy Loss is commonly used in classification problems because it effectively measures the performance of models that output probabilities.

F$.$ False: For predicting the probability of an event, logistic regression is preferred over a regression model trained with squared error, as it is specifically designed to handle probability estimation directly.