ai decision tree s25

8/8/2019 AI Decision Tree s25

1/19

ExampleAttribut

es Goal Alt Bar Fri Hun Pat Price Rain Res Type Est WillWait

X1 Yes No Yes Yes Full $ No No Thai 10-30 Yes

X2 Yes No Yes No Full $$$ No Yes French >60 No

X3 No Yes No Yes Some $$ Yes Yes Italian 0-10 Yes

X4 No Yes No No None $ Yes No Burger 0-10 No

X5 No No No Yes Some $$ Yes Yes Thai 0-10 Yes

X6 No Yes Yes No Full $ Yes No Burger >60 No

X7 Yes Yes Yes Yes Full $$$ No Yes Italian 10-30 No

X8 No No No No None $ No No Thai 0-10 No

X9 Yes Yes Yes Yes Full $ No No Burger 30-60 Yes

X10 Yes No No Yes Some $$$ No Yes French 0-10 Yes

X11 Yes No No Yes Full $ No No Thai 30-60 No

X12 No Yes No No Some $ No No Burger 0-10 Yes

A set of examples X1,, X12 for the restaurant domain is shown in Figure 18.3.The positive examples are ones where the goal WillWait is true (X1, X3,....) and

negative examples are ones where it is false (X2, X4, ...).


2/19

Figure 18.2 A decision tree for deciding whether

to wait for a table.


3/19

Figure 18.4 Splitting

the examples by

testing onattributes.

In (a)Patrons is a

good attribute to

test first;in (b) Type is a poor

one; and

in (c)Hungry is a

fairly good second

test, given that

Patrons is the first

test.


4/19

Figure 18.8 The optimal decision tree induced

from the 12-example training set using ID3


5/19

But if we actually look at this tree we can

perhaps see the logic in the treePatrons=some OR

Patrons=full and Hungry=no and Type=french OR

Patrons=full and Hungry=no and Type=burger OR

Patrons=full and Hungry=no and

Type=Thai and

Fri/Sat=Yes


6/19

Decision Tree

Outlook

Sunny Overcast Rain

Humidity

High Normal

Wind

Strong Weak

No Yes

Yes

YesNo

decision trees represent disjunctions of conjunctions

(Outlook=Sunny Humidity=Normal) (Outlook=Overcast)

(Outlook=Rain

Wind=Weak)


7/19

Representing knowledge as logic Restaurant example from handout (based on

chapter 18).

Alternate(X1) ^ Bar(X1) ^ Fri(X1) ^

Hungry(X1) .... Estimate(10-30,X1)

-> WillWait(X1)

But this is just one example. We wouldneed to encode all 12 examples and join

them with disjunction.


8/19

Representing knowledge as logic But THAT suggests we know only those 12 cases.

In fact, the book has proposed that we know more

through the construction of the decision tree(Figure 18.6)

As LogicForAll x WillWait(x)

Patrons(x,Some)V Patrons(x,Full) ^ Hungry(x) Type(x,French)

V Patrons(x,Full) ^ Hungry(x) ^ Type(x,Thai) ^ Fri(x)

V Patrons(x,Full) ^ Hungry(x) Type(x,Burger)


9/19

Learning over time How do you evolve knowledge over time

when you learn little bit by little bit?

Abstract version the Frinkle


10/19

The Question The Question

How can we build this kind of representation

over time?

The Answer

Rely on the concepts of false positives and false

negatives


11/19

The idea False Positive

An example which is predicted to be positive but whose

known outcome is negative The problem is that our hypothesis is too general.

The solution is to add another condition to ourhypothesis.

False Negative An example which is predicted to be negative but

whose known outcome is positive

The problem is that our hypothesis is too restrictive.

The solution is to remove a condition to our hypothesis

[or to add disjunction]


12/19

Lets try this using the restaurant

problem based on my handout Start with X1

H1: ForAll x WillWait(x) Alt(x)


13/19


problem based on my handout Consider X2 given the current hypothesis

H1: ForAll x WillWait(x) Alt(x)

This yields a result of WillWait but we see

that the known outcome is false.

This is a false positive add a condition

H2: ForAll x WillWait(x) Alt(x) ^ Hun(x)


14/19



H2: ForAll x WillWait(x) Alt(x) ^ Hun(x)

This yields a result of NOT WillWait but wesee that the known outcome is true.

This is a false negative remove a

conditionH3: ForAll x WillWait(x) Hun(x)


15/19


problem based on my handout Notice that the next 3 cases all are correct

given our current hypothesisH3: ForAll x WillWait(x) Hun(x)


16/19



H3: ForAll x WillWait(x) Hun(x)

This yields a result of WillWait but we seethat the known outcome is false.

This is a false positive add a condition

H4: ForAll x WillWait(x) Hun(x) ^ NOTCost(x,$$$).


17/19


problem based on my handout X8 and X9 both are correct given our

current hypothesis.H4: ForAll x WillWait(x) Hun(x)


18/19



H4: ForAll x WillWait(x) Hun(x) ^ NOT Cost(x,$$$).

This yields a result of NOT WillWait but we see thatthe known outcome is true.

This is a false negative remove a condition.

Except, we dont really have a condition we can

remove. Thus, add disjunction.H4: ForAll x WillWait(x) Hun(x) ^ NOT Cost(x,$$$).


19/19


problem based on my handout H4: ForAll x WillWait(x) Hun(x) ^ NOT

Cost(x,$$$).

Except, we dont really have a condition wecan remove.

Thus, add disjunction.

H5: ForAll x WillWait(x)

Hun(x) NOT Cost(x,$$$) V

Hun(x) ^ Cost(x,$$$) ^ Patrons(x,Some)

ai decision tree s25

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