STA314 Homework 1 

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  1. 1. For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer.
  • The sample size n is extremely large, and the number of predictors p is small.
  • The number of predictors p is extremely large, and the number of observations n is small.
  • The relationship between the predictors and response is highly non-linear.
  • The variance of the error terms, i.e. σ2 = Var(), is extremely high.
  1. 2. We now revisit the bias-variance decomposition.
  • Provide a sketch of typical (squared) bias, variance, training error, test error, and Bayes (or irreducible) error curves, on a single plot, as we go from less flexible statistical learning methods towards more flexible approaches. The x-axis should represent the amount of flexibility in the method, and the y-axis should represent the values for each curve. There should be five curves. Make sure to label each one.
  • Explain why each of the five curves has the shape displayed in part (a).
  1. 3. What are the advantages and disadvantages of a very flexible (versus a less flexible) approach for regression or classification? Under what circumstances might a more flexible approach be preferred to a less flexible approach? When might a less flexible approach be preferred?
  2. 4. Describe the differences between a parametric and a non-parametric statistical learning approach. What are the advantages of a parametric approach to regression or classification (as opposed to a nonparametric approach)? What are its disadvantages?