Question $1(15$ points$)$:

Please explain the technique of Gaussian Mixture and how it is used for anomaly detection. $(5$ points$)$

Please draw the diagram of Convolutional Neural Networks $($CNN$).$ Then explain the functionality of each layer of CNN$.$ Name several latest algorithms of CNN $($e$.$g$.,$ AlexNet etc.$).(5$ points$)$

What are the vanishing and exploding gradients problems in Backpropagation? Name several techniques to address these problems. $(5$ points$)$