Implementations of The Bootstrap - Computer Science Assignment Help

Assignment Task

Question 1 Please submit Question1.pdf on Moodle using the Final Exam -

Question 1 object. You must submit a single PDF. You may submit multiple .py files if you wish. The parts are worth 4 + 6 + 6 + 6 + 3 = 25. In this problem we will consider a slightly different dataset than the one used in Homework 2 question 1, which is provided in Q1.csv with binary response variable Y and 30 continuous features X1, . . . , X30. Recall the set-up for regularized logistic regression in that question. In this question we will use the `1 penalty, i.e., we wish to solve (βˆ 0, βˆ) = arg min β0,β {CL(β0, β) + kβk1} (1) where L(β0, β) is the log-loss and where the penalty is usually not applied to the bias term β0, and C is a hyper-parameter controlling the trade-off between fit and regularization. Assume for the remainder of this question that C = 1000, and work with the entire data set provided. We will use the liblinear solver and l1 penalty throughout. Do not use any existing implementations of the Bootstrap and/or Jackknife algorithms; doing so will result in a grade of zero for this question. In Homework 2 we built confidence intervals using the nonparametric bootstrap. In this question we will explore two different approaches to building the CIs. (a) First, run an analysis identical to the one done in Homework 2 part (d) using the nonparametric bootstrap, and using the new dataset and updated parameter values: B = 500; C = 1000; and set a random seed of 12. Feel free to modify your own code from Homework 2, or modify the code in the sample solution. Be sure to use the correct C value in any sub-models fit in the bootstrap process. Generate a plot where the x-axis represents the different parameters β1, . . . , βp, and plot vertical bars to represent the CIs. For those intervals that contain 0, draw the bar in red, otherwise draw it in blue. Also, indicate on each bar the nonparametric bootstrap mean. Along with your plot, answer the following:

(i) What effect does taking C = 1000 have?

(ii) Do you think that taking C = 1000 will result in more reliable estimates of the confidence intervals relative to taking C to be small (e.g. C = 0.1)? Why? What to submit: a single plot, some commentary, a screen shot of your code for this section, a copy of your Python code in solutions.

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