Relevant Mathematical Derivations, Computer Programs & Plots With Modern Computational Statistical Methods - Computer Science Assignment Help

Assignment Task

This assignment 
1. For all the questions please provide the relevant mathematical derivations, the computer programs (only using R software), and the plots.

The data from this image correspond to two features x1 and x2 and one binary outcome y (0 for red dots and 1 for blue dots). An extract of the first 6 dots are presenting in the following table:
(a) . Load the dataset (available on I learned) and split it into training and test sets. You should have 80% of your data in your train set and the remaining 20% in your test set. Carry out a statistical comparison of your choice between the distribution of the two classes in both the training set and the test set, aiming to show that these are randomly chosen.
(b). Fit a logistic model to the training set using a generalized linear model  (using glm function ) to create a binary classifier using the train data.
(c) . Evaluate the performance of your classifier on the test set. You should provide the confusion matrix as well as the F1 score.
(d) . Now using first principles (not using any specific packages), build a binary classifier using the sigmoid function on the linear combination of the features (including a bias term). You will estimate your parameter by exploiting the cross-entropy loss. Remember that it is equivalent to the logistic model. You will use your own batch gradient descent algorithm for optimizing your cost function. Provide at least two R functions:
i. A first function for getting the estimates of your model. Some arguments of your function might be the initial start values of the parameters, a data matrix containing features and response variable, the tolerance for your stoping rule, the maximum number of iterations, the learning rate, ...
ii. A second function for classifying new data points.
(e) Train your model using the training data. Provide a plot of the loss
function during training to illustrate the convergence of your model. You might try different learning rates.
(f) Evaluate the performance of your classifier on the test set. You should provide the confusion matrix and F1 score and compare them with the results of item 3 above.
A second function for classifying new data points.
(e) Train your model using the training data. Provide a plot of the loss function during training to illustrate the convergence of your model. You might try different learning rates.
(f) Evaluate the performance of your classifier on the test set. You should provide the confusion matrix and F1 score and compare them with the results of item 3above.

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