CMPT 317 Assignment 5 Bayesian Netowrks, and Linear Learning Models solution

Description

Overview
In this assignment, we’ll exercise a few ideas, but there is no signicant programming. This assignment should
take you about 2-4 hours.
Questions 1,2 can be done on paper (then scanned and submitted electronically), or using a word processor.
Whatever you decide, make it legible, keep it simple, and prefer PDF and JPG le formats.
Questions 3 and 4 are very short exercises exploring linear classiers. Most of the work is done for you,
but it has to be completed using Jupyter Notebook. This is a way of working with scripts in various languages,
combining documentation, code, and output.
A version of Jupyter Notebook is available on Linux machines in the lab. Furthermore, the department has
a cloud service set up for Jupyter Lab, which you can use:
• https://trux.usask.ca
The only trick will be getting the les you need on the lab lesystem.
Jupyter Notebook is easy to install on your own computers, especially if you use the Anaconda 3 installation
tools for Python 3. If you installed Python using Anaconda 3, it may already be installed for you. If not, Google
for help. This might take an extra 15 or 20 minutes.
CMPT 317
Introduction to Artificial Intelligence
Question 1 (12 points):
Purpose: To reinforce the concepts of Bayesian networks.
Consider the Bayesian network given below.
X1
X2 X3 X4 X5
(a) (5 points) What are the Conditional Probability Distributions implied by the network diagram above?
List them using the notation P(. . .). You do not need to indicate any probabilities. Just provide the
notation.
(b) (2 points) Assume that each variable Xi has 10 domain values. How many entries in each Conditional
Probability table that you listed? In other words, how many numbers would be required if you were to
ll in each table (which you thankfully don’t have to do). What’s the total number of entries, when you
add up all the entries for all the CPDs?
(c) (1 point) Express the Joint Probability Distribution in terms of the Conditional Probability Distributions
you outlined above.
(d) (4 points) Derive a formula for the query P(X1|X2, X3, X4).
What to Hand In
Hand in a document containing the answers to the above questions. You may submit a text document,
or you can complete the work on paper, and submit an image of it (scanned, or captured by your phone).
Before you submit, make sure it’s legible.
• The answers to the questions above.
Be sure to include your name, NSID, student number, and course number at the top of all documents.
Evaluation
• 4 marks: You described the Conditional Probability tables using the P() notation, indicating the correct
dependencies as implied in the network structure.
• 2 marks: You calculated the correct number of entries for each CPD, and in total.
• 1 mark: Your JPD was correctly dened in terms of the CPDs.
• 4 marks: Your formula was derived correctly.
If the submission is not legible, the marker may deduct up to 100% of the grade.
Page 2
CMPT 317
Introduction to Artificial Intelligence
Question 2 (12 points):
Purpose: To reinforce the concepts of Bayesian networks.
Consider the Bayesian network given below.
X1
X2 X3 X4 X5
(a) (5 points) What are the Conditional Probability Distributions implied by the network diagram above?
List them using the notation P(. . .). You do not need to indicate any probabilities. Just provide the
notation.
(b) (2 points) Assume that each variable Xi has 10 domain values. How many entries in each Conditional
Probability table that you listed? In other words, how many numbers would be required if you were to
ll in each table (which you thankfully don’t have to do). What’s the total number of entries, when you
add up all the entries for all the CPDs?
(c) (1 point) Express the Joint Probability Distribution in terms of the Conditional Probability Distributions
you outlined above.
(d) (4 points) Derive a formula for the query P(X1|X2, X3, X4).
What to Hand In
Hand in a document containing the answers to the above questions. You may submit a text document,
or you can complete the work on paper, and submit an image of it (scanned, or captured by your phone).
Before you submit, make sure it’s legible.
• The answers to the questions above.
Be sure to include your name, NSID, student number, and course number at the top of all documents.
Evaluation
• 4 marks: You described the Conditional Probability tables using the P() notation, indicating the correct
dependencies as implied in the network structure.
• 2 marks: You calculated the correct number of entries for each CPD, and in total.
• 1 mark: Your JPD was correctly dened in terms of the CPDs.
• 4 marks: Your formula was derived correctly.
If the submission is not legible, the marker may deduct up to 100% of the grade.
Page 3
Question 3 (5 points):
Purpose: To work experiment with a simple implementation of a Linear Classier.
On the Moodle Assignment page, you’ll nd the les linclass.py and A5Q3.ipynb. Download them both.
Using Jupyter Notebook, open A5Q3.ipynb. Read through the document.
Complete the TO DO items in the notebook:
(a) (2 points) TO DO: Choose a dierent line
(b) (1 point) TO DO: Add a point to the line
(c) (2 points) TO DO: Increase the number of learning steps
What to Hand In
The Jupyter Notebook A5Q3.ipynb with the TO DO items complete.
Be sure to include your name, NSID, student number, and course number at the top of all documents.
Evaluation
1. (2 marks) Your new line separates the original data.
2. (1 mark) The point you added was misclassied by the line from the previous task.
3. (2 marks) You increase the number of learning steps, and the tted line separates the two classes.
Page 4
Question 4 (4 points):
Purpose: To work experiment with a simple implementation of a Linear Classier.
On the Moodle Assignment page, you’ll nd the les linclass.py and A5Q4.ipynb. Download them both.
Using Jupyter Notebook, open A5Q4.ipynb. Read through the document.
Complete the TO DO items in the notebook:
(a) (2 points) TO DO: Increase the number of learning steps (linear classier)
(b) (2 points) TO DO: Increase the number of learning steps (logistic classier)
What to Hand In
The Jupyter Notebook A5Q4.ipynb with the TO DO items complete.
Be sure to include your name, NSID, student number, and course number at the top of all documents.
Evaluation
(a) (2 marks) You increased the number of learning steps, and changed the alpha parameter. Your linear
classifying line does not perfectly classify the data.
(b) (2 marks) You increased the number of learning steps, and changed the alpha parameter. The Logistic
Classier gets all but one data point correctly classied.
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