Description
1 Bootstrap Description
Suppose that we have a dataset (xi
, yi)
n
i=1, and we fix a value ¯x. Further suppose that we are going to
build a predictor for the response ¯y associated to ¯x using some statistical learning method. Describe how
we might estimate the standard deviation of our prediction. You must explicitly define every variable
and equation.
2 Bootstrap for Estimating Standard Errors of Logistic Regression Coefficients
Solve exercise 6 from Chapter 5 of ISLR, in python.
You can use either the statsmodels or sklearn package for this. I recommend using statsmodels,
since it has better support for this kind of statistical analysis (note also that sklearn regularizes by
default, so you must turn that off if you use sklearn).
For statsmodels, after building a model m, you can use m.summary() to get the standard errors of
the coefficients.
For 6.b, write a function boot fn that works as described in ISLR. Instead of the R library function
boot, you must write your own: write a function boot(data, fn, R) where data is a pandas dataframe,
fn is a function that computes a statistic, and R is the number of replicates. You can use resample from
sklearn to generate individual bootstrap samples.
3 Cross-Validation on Simulated Data
Solve exercise 8 from Chapter 5 of ISLR, in python.
4 Ridge Regression Effect of λ
Solve exercise 4 in Chapter 6 of ISLR
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IEOR E4525
Christian Kroer
Assignment 3
Due: Oct 29th, at 11:59pm
5 Comparing Lasso, Ridge, and Least Squares
Solve exercise 9 from Chapter 6 of ISLR. You only need to complete questions (a),(b),(c),(d), and (g).
For question (g), you only need to compare the three approaches from (b), (c), and (d).
You can use scikitlearn LinearRegression, Ridge, Lasso.
If you prefer statsmodels, then you can use regularized for lasso and ridge.
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