Consider a binary classification problem where data from class$-1$ follows N$([01],[10$;$01])$ and data from class$-2$ follows N$([12],[20$; $01])$:

$-$Generate $1000$ samples from each class for training and $1000$ samples for testing.

$-$Solve the classification problem using a neural network. Tune number of nodes in the hidden layer and the learning rate alpha for best accuracy. Try two values of alpha between $0$ and $1,$ two values of nodes between $2$ and $10.$ Pick the values randomly. Use tanh nonlinearity. Use $50$ iterations. Plot the ROC curve.

$-$Use minibatch training with a batch$-$size of $16.$ Use L$2$ regularization with Lambda$=0\mathrm{.}2.$ Use dropout with p$=0\mathrm{.}4.$ Use two hidden layers with tanh in the first hidden layer and relu in the second hidden layer. Use $5$ nodes in the first hidden layer. Tune the learning rate alpha and the number of neurons in the second hidden layer for best accuracy in the test set.