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Recitation 1 April 9

Recitation 1 April 9. Polynomial regression Ridge regression Lasso. Polynomial regression. lm( y ~ poly(x, degree = d ) , data =dataset) Find the optimal degree Check the residual plots Training and test set Cross-validation R demo 1. Ridge regression – R package.

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Recitation 1 April 9

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  1. Recitation 1April 9 Polynomial regression Ridge regression Lasso

  2. Polynomial regression • lm( y ~ poly(x, degree = d), data=dataset) • Find the optimal degree • Check the residual plots • Training and test set • Cross-validation • R demo 1

  3. Ridge regression – R package • lm.ridge() in library(“MASS”) • lm.ridge( y ~ . , data = dataset, lambda = seq(0, 0.01, by=0.001) ) • R demo 2

  4. Ridge regression – from sketch • Ridge regression estimators have closed form solutions: • How to deal with intercept? • Tuning parameter: • Effective degrees of freedom • Implement: HW 2

  5. Lasso – R package • l1ce() in library(“lasso2”) or lars() in library(“lars”) • l1ce( y ~ . , data = dataset, bound = shrinkage.factor) • Lasso doesn’t have EDF (why?) . We can use the shrinkage factor to get a sense of the penalty. • R demo 3

  6. Lasso – from sketch • Shooting algorithm (stochastic gradient descent) • At each iteration, randomly sample one dimension j, and update • How to deal with intercept • Center x and y • Standardize x • Tuning parameter • Shrinkage factor for a given • Convergence criterion • Implement: HW 2 Bonus problem

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