📗 Enter your ID (the wisc email ID without @wisc.edu) here: and click (or hit enter key) 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15x6
📗 The same ID should generate the same set of questions. Your answers are not saved when you close the browser. You could print the page: , solve the problems, then enter all your answers at the end.
📗 Please do not refresh the page: your answers will not be saved.
📗 [3 points] Suppose you are given a neural network with hidden layers, input units, output units, and hidden units. In one backpropogation step when computing the gradient of the cost (for example, squared loss) with respect to \(w^{\left(1\right)}_{11}\), the weight in layer \(1\) connecting input \(1\) and hidden unit \(1\), how many weights (including \(w^{\left(1\right)}_{11}\) itself, and including biases) are used in the backpropogation step of \(\dfrac{\partial C}{\partial w^{\left(1\right)}_{11}}\)?
📗 The above is a diagram of the network, the nodes labelled "1" are the bias units. You can highlight the edges representing the weights in the diagram, but they are not graded. Note: the backpropogation step assumes the activations in all layers are already known so do not count the weights and biases in the forward step computing the activations.
📗 Answer: .
📗 [3 points] A tweet is ratioed if at least one reply gets more likes than the tweet. Suppose a tweet has replies, and each one of these replies gets more likes than the tweet with probability if the tweet is bad, and probability if the tweet is good. Given a tweet is ratioed, what is the probability that it is a bad tweet? The prior probability of a bad tweet is .
📗 Answer: .
📗 [3 points] A hard margin SVM (Support Vector Machine) is trained on the following dataset. Suppose we restrict \(b\) = , what is the value of \(w\)? Enter a single number, i.e. do not include \(b\). Assume the SVM classifier is \(1_{\left\{w x + b \geq 0\right\}}\) (this means it predict 1 if \(w x + b \geq 0\) and 0 otherwise.
\(x_{i}\)
\(y_{i}\)
📗 Answer: .
📗 [3 points] Consider the Grid World with terminal states "RED" and "GREEN" and 7 other states shown in the table below.
RED
1
2
3
4
5
6
7
GREEN
There are four actions UP, DOWN, LEFT, RIGHT describing the movement between the states on the grid. The grid does not wrap around, i.e. using the action UP in state 1 results in state 1, not state 7.
Suppose the reward on all transitions (from actions UP, DOWN, LEFT, RIGHT) are \(R_{t}\) = , and the discount factor is \(\gamma\) = . The current policy \(\pi\) (probabilities of actions UP, DOWN, LEFT, RIGHT when in each state) is given in the following table.
State
UP
DOWN
LEFT
RIGHT
1
2
3
4
5
6
7
The current value function \(V_{k}\) is given in the table below.
\(0\)
\(0\)
Find the value of state in the next step of value iteration (i.e. \(V_{k+1}\) for state ). Enter one number.
📗 Answer: .
📗 [4 points] Consider the following Markov Decision Process. It has two states \(s\), A and B. It has two actions \(a\): move and stay. The state transition is deterministic: "move" moves to the other state, while "stay" stays at the current state. The reward \(r\) is for move, for stay. Suppose the discount rate is \(\gamma\) = .
Find the Q table \(Q_{i}\) after \(i\) = updates of every entry using Q value iteration (\(i = 0\) initializes all values to \(0\)) in the format described by the following table. Enter a two by two matrix.
State \ Action
stay
move
A
?
?
B
?
?
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 You could save the text in the above text box to a file using the button or copy and paste it into a file yourself .
📗 You could load your answers from the text (or txt file) in the text box below using the button . The first two lines should be "##x: 6" and "##id: your id", and the format of the remaining lines should be "##1: your answer to question 1" newline "##2: your answer to question 2", etc. Please make sure that your answers are loaded correctly before submitting them.