## CS 8751 Take Home Final

### Due December 17th by 5:55 p.m. -- NO LATE EXAMS ALLOWED

You must submit a signed copy of the following page with your exam.

1. Show the initial G and S sets and the G and S sets after each of the data points shown below is presented to the Version Space (Candidate Elimination) algorithm: [15 points]
```	1	2	1	3	1	+
2	1	2	2	2	-
1	2	1	1	2	-
1	1	2	3	1	-
1	2	2	3	2	+
```
2. For a dataset with 5 features, A, B, C, D, and E where A, B, and D have possible values of true and false, and C and E are continuously valued and the following examples:
```     A		B	C	D	E	Class
-----------------------------------------------------
false	true	15	false	20	+ positive
true	false	1	true	5	- negative
false	false	10	true	10	- negative
false	false	8	false	15	+ positive
true	true	13	true	16	+ positive
false	true	9	false	8	- negative
false	false	1	true	5	- negative
true	false	12	false	13	- negative
true	true	15	false	6	+ positive
true	true	15	true	10	+ positive
false	true	13	true	7	- negative
false	true	3	false	5	+ positive

NOTE:
```
• What decision tree would be learned using ID3? [20 points]
• For each of the following data points, what class would be predicted using the 3-Nearest Neighbor algorithm using a Manhattan distance measure where the two continuous features are scaled to be values between 0 and 1? [20 points]
• true    true    5    true    15
• false    true    3    true    9
• false    false    15    false    3
• What predictions would be made using the Naive Bayes learning method for the data points shown in the previous question? [20 points]
• Using the agglomerative single link clustering method, determine the clusters that would be produced from the data points above assuming we ignore the class (the - or + value), that our distance is measured as nearest neighbor question above, and where we have the following threshold values (two points are considered to be connected if their distance is *less* than these thresholds): (i) 0.9, (ii) 1.9, and (iii) 2.9. [20 points]
3. Consider the use of ensembles in machine learning. [30 points]
1. Explain how ensembles address the issue of overfitting avoidance.
2. What is one strength of bagging compared to boosting? Justify your answer.
3. Give a brief argument for the use of an ensemble consisting of one decision tree, one support-vector machine (SVM), and one neural network instead of using an ensemble of three models all produced by the same learning algorithm.
4. What neural network would be generated by KBANN from the following rules assuming the output predicate is J and the input predicates are A, B, C and D? For each unit generated you should connect it to any input unit that it is not already directly connected to with a small weight link. [20 points]
```   A, C -> E
B, not C, D -> E
E, C -> F
not A, D -> F
E, F -> G
B, not E -> G
E, not F -> H
E, G, H -> J
```
5. Given a neural network with 3 input units (A, B, C), two hidden units (D, E), one output unit (F) and one unit that always has an activation value of 1 (ONE) and the following weight connections:
```   ONE->D: 0.0
A->D: 0.5
B->D: 0.0
C->D: -1.0
ONE->E: 0.5
A->E: 0.0
B->E: 0.5
C->E: 0.5
ONE->F: 0.0
D->F: -0.5
E->F: 0.5
```

What would be the weights after each of the following points is presented (in the sequence shown) assuming a learning rate of 0.25 and a momentum term of 0.9. Assume the hidden and output units use a sigmoidal activation function and that the weights are changed using backpropagation. [20 points]

```              A B C   F
Point 1:   1 0 1   1
Point 2:   0 1 1   0
Point 3:   1 1 1   1
```
6. A key concern in supervised learning is overfitting avoidance. Define overfitting and explain its importance. [20 points]

Discuss one key technique (two in total) for addressing the problem of overfitting in (i) decision trees and (ii) neural networks.

7. For the maze world shown in the top of the three diagrams below with actions and rewards shown in the diagram calculate the corresponding V*(s) and Q(s,a) values assuming a discount factor of 0.8. Assume the agent stops moving when they reach the upper right hand state. [20 points]

8. Briefly define and explain the following terms and how they are used in support vector machines: (i) margin, (ii) kernel, and (iii) slack variables. [15 points]
9. For the following points:
```	A	B	C	D	class
-------------------------------------
-1	1	-1	-1	-1
1	1	1	1	1
-1	1	1	1	1
-1	-1	1	1	-1
1	-1	-1	-1	-1
```

Assuming a linear kernel and the use of slack variables give the set of constraint equations generated for these points. [20 points]

10. For the Bayes network and CPTs shown below calculate the following: [20 points]
1. p(e=true|a=true,b=true,c=true)
2. p(d=true|e=true,b=false)
3. p(e=false|a=true,c=false)

11. Define the term association rule. Give the Apriori algorithm for learning association rules. Show an example of how the algorithm works. Give two examples of ways to speedup this algorithm. [20 points]
12. How would you represent the solution to a regression problem in genetic algorithms? Give an example to demonstrate your solution. Discuss what kind of fitness function you would use and how concepts would be selected for reproduction. [20 points]