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Forest cover type classification using AdaBoost

Download the Cover Type Dataset for multiclass classification. Implement AdaBoost from scratch and run it using decision stumps (binary classification rules based on single features) as base classifiers to train seven binary classifiers, one for each of the seven classes (one-vs-all encoding). Use external cross-validation to evaluate the multiclass classification performance (zero-one loss) for different values of the number T of AdaBoost rounds. In order to use the seven binary classifiers to make multiclass predictions, use the fact that binary classifiers trained by AdaBoost have the form and predict usingwherecorresponds to the binary classifier for class.

Optional: Implement from scratch the multiclass version of AdaBoost (Chapter 10 of this book) and study the cross-validated multiclass classification performance (zero-one loss) on the same dataset.

Digit classification with the Kernel Perceptron

Download the MNIST dataset for multiclass classification of handwritten digits. Implement the kernel Perceptron from scratch and run it to train 10 binary classifiers, one for each of the 10 digits (one-vs-all encoding), using the polynomial kernel. In order to extract a binary classifier, do the following: run the algorithm for a given number of epochs (e.g., cycles over the entire training data) on a random permutation of the training set and collect the ensemble of predictorsused by the Perceptron when predicting each training datapoint . Then use:

the average of the predictors in the ensemble;

the predictor achieving the smallest training error among those in the ensemble.

Based on the given split of the data in training and test set, evaluate the multiclass classification performance (zero-one loss) for different values of the number of epochs (go up to at least 10 epochs) and the degree of the polynomial (go up to at least degree 6). In order to use the 10 binary classifiers to make multiclass predictions, use the fact that binary classifiers trained by the Perceptron have the form  and predict using  wherecorresponds to the binary classifier for class.

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