CS4100/CS5100 - Machine-Learning And Statistical Algorithms, Probabilistic Forecasting, Logistic, MSEs Report Writing - Computer Science Assignment Help

Assignment Task

The learning outcomes assessed are
1-develop, validate, evaluate, and use effectively machine-learning and statistical algorithms 
2- apply methods and techniques such as probabilistic forecasting, logistic regression, and gradient descent 
3- extract value and insight from data 
4- implement machine-learning and statistical algorithms in R or MATLAB 

Tasks
1. Implement the logistic regression algorithm using Gradient Descent in analogy with neural networks (as described in the lectures, Chapter 4, or [1], Sections 11.3–11.5) for p attributes. The objective function, which your program should minimize, can be either the training MSE

(as described on slide 44 of Chapter 4); the choice is yours. (Be careful not to confuse p as the number of attributes and p(x) as the predicted probability of 1.) Your program can be written either in R or in MAT LAB. You are not allowed to use any existing implementations of logistic regression or Gradient Descent in R, MATLAB, or any other language, and should code logistic regression from first principles. However, you are allowed to set the number of attributes p to a specific value that allows you to do the following tasks.

Apply your program to the Auto data set and new variable to predict high given horsepower, weight, year, and origin. (In other words, high is the label, and horsepower, weight, year, and origin are the attributes.) Since the origin is a qualitative variable, you will have to create appropriate dummy variables. Normalize the attributes, as described in Lab Worksheet 4, Section 5 or Exercise 9 (or Section 4.6.6 of [2]).

3. Split the data set randomly into two equal parts, which will serve as the training set and the test set. Use your birthday (in the format MMDD) as the seed for the pseudorandom number generator. The same training and test sets should be used throughout this assignment. 
4. Train your algorithm on the training set using independent random numbers in the range [−0.7, 0.7] as the initial weights. Find the MSE on the test set (it is defined by (1) except that the average should be over the test rather than the training set). Try different values of the learning rate η and of the number of training steps (so that your stopping rule is to stop after a given number of steps). Give a small table of test and training MSEs in your report. 
5. Optional: Try different stopping rules, such as: stop when the value of the objective function (the training MSE) does not change by more than 1% of its initial value over the last 10 training steps. 
6. Run your logistic regression program for a fixed value of η and for a fixed stopping rule (producing reasonable results in your experiments so far) 100 times, for different values of the initial weights (produced as above, as independent random numbers in [−0.7, 0.7]). In each of the 100 cases compute the test MSE and show it in your report as a boxplot. 
7. Optional: Redo the experiments in items 4–5 modifying the training procedure as follows. Instead of training logistic regression once using Gradient Descent, train it 4 times using Gradient Descent with different values of the initial weights and then choose the prediction rule with the best training MSE. 
 

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