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Homework 8 Implement Logitboost

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Homework 8,

1. Implement Logitboost using 1D linear regressors as weak learners. At each boosting
iteration choose the weak learner that obtains the largest reduction in the loss function
on the training set D = {(xi
, yi), i = 1, …, N}, with yi ∈ {0, 1}:
L =
X
N
i=1
ln(1 + exp[−y˜ih(xi)]) (1)
where y˜i = 2yi − 1 take values ±1 and h(x) = h1(x) + … + hk(x) is the boosted
classifier. Please note that the Logitboost algorithm from the slides uses yi ∈ {0, 1}
and the loss uses y˜ ∈ {−1, 1}.
a) Using the Gisette data, train a Logitboost classifier on the training set, with
k ∈ {10, 30, 100, 300, 500} boosted iterations. Plot the training loss vs iteration
number for k = 500. Report in a table the misclassification errors on the training
and test set for the models obtained for all these k. Plot the misclassification
errors on the training and test set vs k. (5 points)
b) Repeat point a) on the dexter dataset. (2 points)
c) Repeat point a) on the madelon dataset. (2 points)