Machine Learning Algorithms

This is a collection of notes and code for machine learning algorithms.

Most of these will be Matlab/Octave files. Would like to add some Python/Numpy implementations later.

Linear regression

Regularized linear regression has the following cost function:

Correspondingly, the partial derivative of regularized linear regression's cost for θj is defined as:

To plot the learning curve, we need a training and cross validation set error for different training set sizes. To obtain different training set sizes, use different subsets of the original training set X. Specifically, for a training set size of i, you should use the first i examples (i.e., X(1:i,:) and y(1:i)).

You can use the trainLinearRegression() function to find the θ parameters. Note that the lambda is passed as a parameter to the learningCurve function. After learning the θ parameters, you should compute the error on the training and cross validation sets. Recall that the training error for a dataset is defined as:

In particular, note that the training error does not include the regularization term. One way to compute the training error is to use your existing cost function and set λ to 0 only when using it to compute the training error and cross validation error. When you are computing the training set error, make sure you compute it on the training subset (i.e., X(1:n,:) and y(1:n)) (instead of the entire training set). However, for the cross validation error, you should compute it over the entire cross validation set.

Logistic Regression

coming soon

Multi-class Classification

coming soon

Neural Networks

coming soon

Neural Network Learning

coming soon

Regularized Linear Regression

coming soon

Support Vector Machines

coming soon