Introduction to Artificial Intelligence The University of Birmingham
Autumn Semester 2016 School of Computer Science
November 3, 2016 Jeremy L Wyatt
Unassessed Worksheet - Machine Learning
Basic Comprehension
Regression
1. Here is a small data set
i) Calculate the averages for X and for T.
ii) Calculate the variance of X and T.
iii) Calculate the co-variance of X and T.
iv) Now calculate the parameters of y = ax + b, where y is the best fit straight line.
2. Taking the data set from 1. Start with a=1 and b=0. Now apply the batch LMS rule to this
regression problem (this will yield 14 updates which you save in batch, 7 for a and 7 for b).
What are a and b after the update at the end of the first epoch?
3. Explain the difference between classification and regression.
4. Explain the difference between supervised and unsupervised learning.
5. This question requires downloading and using Matlab, with which you may be unfamiliar. If
you can’t download it you can use matlab installed on the school network. Type matlab into
a terminal you invoke on a Linux machine. Download the associated matlab (.m) files
associated with this exercise sheet. To run them you should be able to download and install
matlab from mysoftware.bham.ac.uk . It should also run with Octave (https://www.gnu.org/
software/octave/download.html) though I haven’t tried it myself, and so I give no
guarantees.
You may need to add the folder in which you store these files to the Matlab path. Look on
the Mathworks website to see how to do this.
Now run the file “linear_data_regression_script” from the Matlab engine. You should see
three figures, with movies of the convergence of batch and incremental LMS, as I showed
in the lectures.
If you want you can check your answer for Q1, as least_squares_fit is precisely this
procedure.
X
1
3
4
6
9
10
12
T
0.5
5
12
9
19
24
19
