You use your favorite decision tree algorithm to learn a decision tree for binary classification. Your tree has J leaves indexed j = 1, . . . , J. Leaf j contains nj training examples, mj of which are positive. However, instead of predicting a label, you would like to use this tree to predict the probability P(Y = 1 | X) (where Y is the binary class and X are the input attributes). Therefore, you decide to have each leaf predict a real value pj ∈ [0, 1]. -What are the values pj that yield the largest log likelihood? Show your work.

can you please give correct and proper solution.

Give an instance of STABLEMATCHING where the Propose-Dispose algorithm yields a matching where strictly more women get their most preferred man than men get their most preferred woman.

5. For the following game tree, each player maximizes their respective utility. Let x, y respectively denotes the top and bottom values in a node. Player 1 uses the utility function U1(x, y) = x. Both players know that Player 2 uses the utility function U2(x, y) = x - y. DA P1 P2 P2 P2 1 7 3 1 3 10 A. Fill in the rectangles in the figure above with pair of values returned by each max node. B. You want to save computation time by using pruning in your game tree search. On the game tree above, put an 'X' on branches that do not need to be explored or simply write 'None'. Assume that branches are explored from left to right.

Consider the hypothesis space defined over instances shown below, we characterize each hypothesis (apple taste) by 4-tuples. Please hand trace the ID3 classifier to build a decision tree, then predict the target value Taste=Sweet/Tart for the following instances: a) <Red, High, Some, No> b) <Red, Low, Some, Yes> c) <Yellow, Low, Some, No> d) <Green, High, None, No> e) <Green, Mid, Some, Yes> Now suppose the actual taste of the five apples above are actually “Sweet, Sweet, Sweet, Tart, Tart”, what is the accuracy of the decision tree? Please show all the steps and include the corresponding confusion matrix for accuracy calculation. (please................ as soon as give correct solution)

Modify tic-tac-toe: the 1st player x wins if she gets 3-in-a-row, otherwise the 2nd player owins. What is the first-player minimax value for this game (win, lose)? For this game, givea proof tree for x to play from the position above right.

Let's look at the minimax search tree illustrated in Figure 2. In this diagram, black nodes represent decisions made by the MAX player, while white nodes represent decisions made by the MIN player. The squares at the terminal nodes represent payments, with the number indicating the amount paid from MIN to MAX (a 0 indicates no payment from MIN to MAX). MAX aims to maximize the payment they receive, while MIN aims to minimize the payment they make. If we apply the α-β pruning algorithm, we can analyze the minimax tree as shown in Figure 2. (a) Assume that we iterate over nodes from right to left; what are the arcs that are pruned by α-β pruning, if any? (b)Does you answer change if we iterate over nodes from left to right?