📗 [4 points] Which order of goal check is possible with , without specifying the order of successors when putting them in the queue (i.e. you can rearrange the order of the branches)? Enter the correct choices as a list, comma separated, without parentheses, for example, "1, 2, 4".

📗 Choices:

📗 Answer (comma separated vector):

📗 [4 points] Consider a zero-sum sequential move game with Chance. Min player moves first, then Chance, then Max. The values of the terminal states are shown in the diagram (they are the values for the Max player). What is the (expected) value of the game (for the Max player)?

📗 Note: in case the diagram is not clear, the probabilities from left to right is: , and the rewards are .

📗 Answer: . Calculate

📗 [4 points] What is the projected variance of and onto the principal component ? Use the MLE (Maximum Likelihood Estimate) formula for the variance: \(\sigma^{2} = \dfrac{1}{n} \displaystyle\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}\) with \(\mu = \dfrac{1}{n} \displaystyle\sum_{i=1}^{n} x_{i}\).

📗 Answer: . Calculate

📗 [4 points] Enter the largest integer value of \(A\) such that \(B\) will be alpha-beta pruned? Min player moves first. In the case alpha = beta, prune the node. Enter 100 if you think the answer is infinity.

📗 Answer: .

📗 [3 points] Consider a state space where the states are positive integers between 1 and . State \(i\) has two neighbors \(i - 1\) and \(i + 1\) (subject to the boundary constraints). State \(i\) has score . If one runs the hill climbing algorithm, which initial states can reach the global minimum? Break ties by moving towards the global minimum. If there are multiple global minima, list the states that lead to all of them.

📗 Answer (comma separated vector): .

📗 [3 points] Let \(h_{1}\) be an admissible heuristic from a state to the optimal goal, A* search with which ones of the following \(h\) will be admissible? Enter the correct choices as a list, comma separated, without parentheses, for example, "1, 2, 4".

📗 Choices:

📗 Answer (comma separated vector): .

📗 [3 points] Given the variance matrix \(\hat{\Sigma}\) = . If one original data point is \(x\) = . What is the reconstructed vector using only the first principal components?

📗 Answer (comma separated vector):

📗 [3 points] Given data and initial k-means cluster centers \(c_{1}\) = and \(c_{2}\) = , what is the initial total distortion (do not take the square root). Use Euclidean distance. Break ties by assigning points to the first cluster.

📗 Answer: . Calculate

📗 [3 points] You have a dataset with unique data points which you want to use k-means clustering on. You setup the experiment as follows: you apply k-means with different k's: \(k\) = . Which \(k\) value will minimize the total distortion? Enter -1 if the answer depends on the data points.

📗 Answer: .

📗 [4 points] Run search algorithm on the following graph, starting from state 0 with the goal state being . Write down the expansion path (in the order of the states expanded). The heuristic function \(h\) is shown as subscripts. Break tie by expanding the state with a smaller index.

📗 In case the diagram is not clear: the weights are (with heuristic values on the diagonal entries): .

📗 Answer (comma separated vector): .

📗 [3 points] What is the distance between clusters \(C_{1}\) = {} and \(C_{2}\) = {} using linkage?

📗 Answer: . Calculate

📗 [3 points] In the following graph coloring problem, each node is either labeled as + or -. The score of the graph is the number of edges connecting two nodes with the same label (color). We are minimizing the score. If the successor function is to change the label of a single node, in hill climbing (here, valley finding), which node should we change in the following graph? Enter the index of the node (subscript in the diagram) or -1 if we are at a local minimum. Break ties by entering the node with the smaller index.

📗 Answer: .

📗 [4 points] Given the dataset , the cluster centers are computed by k-means clustering algorithm with \(k = 2\). The first cluster center is \(x\) and the second cluster center is . What is the imum value of \(x\) such that the second cluster is empty (contains 0 instances). In case of a tie in distance, the point belongs to cluster 1.

📗 Answer: . Calculate

📗 [1 points] Please enter any comments including possible mistakes and bugs with the questions or your answers. If you have no comments, please enter "None": do not leave it blank.

📗 Answer: .