Homework 4 (Chapter 7 and Chapter 8)

  • For a binary classification, describe the possible values of entropy. On what conditions does entropy reach its minimum and maximum values?
  • In a decision tree, how does the algorithm pick the attributes for splitting?
  • John went to see the doctor about a severe headache. The doctor selected John at random to have a blood test for swine flu, which is suspected to affect 1 in 5,000 people in this country. The test is 99% accurate, in the sense that the probability of a false positive is 1%. The probability of a false negative is zero. John’s test came back positive. What is the probability that John has swine flu?
  • Which classifier is considered computationally efficient for high-dimensional problems? Why?
  • A data science team is working on a classification problem in which the dataset contains many correlated variables, and most of them are categorical variables. Which classifier should the team consider using? Why?
  • A data science team is working on a classification problem in which the dataset contains many correlated variables, and most of them are continuous. The team wants the model to output the probabilities in addition to the class labels. Which classifier should the team consider using? Why?
  • Why use autocorrelation instead of autocovariance when examining stationary time series?
  • Provide an example that if the cov(X, Y) = 0, the two random variables, X and Y, are not necessarily independent.
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