ex2_reg.m

Sure, let me explain each part of the code in more detail:

Part 1: Regularized Logistic Regression
The first thing this script does is to load a dataset from a text file "ex2data2.txt" which contains two features and a binary output label. The plotData function is then called to create a scatter plot of the data, with blue dots indicating positive labels (y = 1) and yellow dots representing negative labels (y = 0). The xlabel and ylabel functions are used to label the x- and y-axes with the feature names.

Next, polynomial features are added to the input data using the mapFeature function, which takes as input the original input data X and returns a matrix containing higher-order combinations of the input features up to degree 6. This is done because the decision boundary between the two classes of data is not a straight line. By adding polynomial features, complex nonlinear decision boundaries can be fit using logistic regression.

After creating the polynomial features, the initial values for the model parameters theta are set to zero, and the regularization parameter lambda is set to 1. The costFunctionReg function is then called to compute the cost and gradient of the regularized logistic regression model, given the input features X, output labels y, model parameters theta, and regularization parameter lambda. The costFunctionReg function uses the sigmoid function to compute the predicted probabilities of the output labels, and then evaluates the error between the predicted probabilities and the actual output labels. The regularization term is added to the cost function to prevent overfitting.

Finally, the cost of the model with initial parameters set to zero is printed, and the user is prompted to press Enter to continue.

Part 2: Regularization and Accuracies
In this part, different values of the regularization parameter lambda are tried to see how the decision boundary changes and how the training set accuracy varies. Three different values of lambda (0, 1, and 100) are tried, by calling the costFunctionReg function inside the fminunc optimization function. fminunc finds the optimal values of the model parameters theta that minimize the cost function. The exit_flag variable is a scalar output indicating whether the optimization terminated successfully (0) or not (nonzero).

After computing the optimal values of theta for each value of lambda, the plotDecisionBoundary function is called to plot the decision boundary along with the input data points. The title function is used to label the plot with the value of lambda used, and the xlabel, ylabel, and legend functions are used to label the axis and add a legend to the plot.

Finally, the predict function is called to compute the accuracy of the trained model on the training set, and the user is prompted to press Enter to continue.

I hope this helps clarify the code! Let me know if you have any more questions.