Description

1. Consider the following data. The DECISION-TREE-LEARNING algorithm will first select the attribute Length to split on. Finish building the decision tree, and show the computations.
Example Author Thread Length Where Read User Action
e1 known new long home skips
e2 unknown new short work reads
e3 unknown follow Up long work skips
e4 known follow Up long home skips
e5 known new short home reads
e6 known follow Up long work skips
e7 unknown follow Up short work skips
e8 unknown new short work reads
e9 known follow Up long home skips
e10 known new long work skips
e11 unknown follow Up short home skips
e12 known new long work skips
e13 known follow Up short home reads
e14 known new short work reads
e15 known new short home reads
e16 known follow Up short work reads
e17 known new short home reads
e18 unknown new short work reads
2. Consider the candy example from the lecture. Assume that the prior distribution over h1,…,h5 is given by h0.1,0.2,0.4,0.2,0.1i. Suppose that the first 5 candies taste lime, cherry, cherry, lime, and lime. Make predictions for the 6th candy using Bayesian, MAP and ML learning, respectively. Show the computations done to make the predictions.
3. Consider the Boolean function E = (A XOR B) AND (C XOR D). Construct its truth table, and then remove the line for the input A =1,B =1,C =1,D =1. Use Naive Bayes classification to make prediction for this input. Show the computations.
4. Construct a neural network that computes the XOR function of two inputs.
5. Consider the neural net on Page 32 of the course slides for neural nets.
• Suppose we use the sigmoid function as the activate function. Compute ∂Losso1/∂w1.
• Suppose we use the tanh function as the activate function. Compute ∂Losso2/∂w4. Note that tanh(x) = (ex −e−x)/(ex +e−x) = 2g(2x)−1, and tanh0(x) = 1−tanh2(x).
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