Problem Set 6

Problem Set 6

This is to be completed by November 30th, 2017.

Exercises

1. Datacamp
• Complete the lesson:
a. Text Mining: Bag of Words
2. Exercises from Elements of Statistical Learning
• Complete exercises:
a. 4.2
b. 4.6
3. Run the perceptron learning algorithm by hand for the two class classification problem with $(X,Y)$-pairs (given by bitwise or): $((0,0), 0), ((1,0),1), ((0,1),1)), ((1,1),1)$.

4. R Lab:

• Update the LDA Classifier from last week as follows.
a. After fitting an LDA Classifier, produce a function which projects an input sample onto the hyperplane containing the class centroids.
b. Update the classifier to use these projections for classification. Compare the runtimes of prediction of the two methods when the number of features is large relative to the number of classes.
• Construct a perceptron classifier for two class classification. Put an upper bound on the number of steps.
a. Evaluate the perceptron on the above problem and for the bitwise xor problem: $((0,0), 0), ((1,0),1), ((0,1),1)), ((1,1),0)$.