Assignment 2 – Classification

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Assignment 2 – Classification

For Students Taking Machine Learning and Intelligent Data Analysis (Extended)

1 Gradient Descent (3 marks)

Carefully read the code provided in the Jupyter notebook build-logistic-regression-model.ipynb to work out what it is doing. Then, run the statement below to produce a Logistic Regression model for a problem where input variables can assume values in [0, 1]:

gradientDescent([[1,0.3,0.1],[1,0.3,0.2],[1,0.6,0.7], [1,0.8,0.2]], [0,0,1,1], 5, 0.1, 1000)

● Is the resulting model appropriate for the task being learned? Justify your answer.

● Discuss one positive and one negative point regarding the choice of ar-guments in the Python statement above in the context of the problem being solved. Your discussion should be supported by evidence whenever possible.

Instructions:

● It is part of the question to think about what evidence you could provide to support your discussion.

● You may add additional functions or lines of code to the Jupyter notebook to gather evidence to help you with answering this question.

● If you do so, please submit the modified Jupyter notebook as part of your assignment, with Python comments explicitly showing which lines of code or functions you have added.

● You must not use any external libraries, except for numpy, matplotlib, math and sys.

2 Newton-Raphson Weight Update Rule (3 marks)

Consider a problem where the following function is to be minimised:

E(x) = x⁴ − 5x − 3.

        Would the iterative application of the Newton-Raphson rule be likely to work well to find the optimum value of x for this problem? Justify your answer.

3 Multiclass Logistic Regression (4 marks)

We have learned in Lecture 7e one way to use Logistic Regression to deal with multi-class problems. Section 4.3.4 of Chris Bishop’s book on Pattern Recogni-tion and Machine Learning shows a different way. Briefly explain with your own words your understanding of how this method works and how it differs from the one learned in Lecture 7e.

Instructions:

● You may use up to 400 words. Any text beyond 400 words will be consid-ered as not being part of the answer.

● You do not need to type any equations – you can reference the equations of the book if you wish.

● You do not need to explain Newton-Raphson or Iterative Reweighted Least Squares for this question. Reading until the calculation of the gradient in Eq. 4.109 is enough for the purpose of this question.

● Note that Bishop’s book makes use of a different notation, where yn repre-sents the probability p1 for example n and tn represents the output value for example n. For the purpose of this assignment, you can also interpret φn as the vector of input values of example n.