Understanding Knowledge Representation: Decision Tables, Decision Trees, and Rules, Slides of Computer Fundamentals

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Knowledge

Representation

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Outline:

Output - Knowledge representation

 Decision tables

 Decision trees  Decision rules  Rules involving relations  Instance-based representation  Prototypes, Clusters

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Decision tables

 Simplest way of representing output:  Use the same format as input!  Decision table for the weather problem:

 What do you think is the main problem?

Outlook Humidity Play Sunny High No Sunny Normal Yes Overcast High Yes Overcast Normal Yes Rainy High No Rainy Normal No

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Decision tables

 Decision table for the weather problem:

 Main problem: selecting the right attributes  Also, not flexible enough

Outlook Humidity Play Sunny High No Sunny Normal Yes Overcast High Yes Overcast Normal Yes Rainy High No Rainy Normal No

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Decision trees, 2

 Build a decision tree using this information:

Outlook Humidity Play Sunny High No Sunny Normal Yes Overcast High Yes Overcast Normal Yes Rainy High No Rainy Normal No

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overcast

high normal

sunny (^) rain

No

No

Yes

Yes

Decision trees, 3

Outlook

Humidity

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Missing values

 Does absence of value have some significance?  Yes ⇒ “missing” is a separate value

 No ⇒ “missing” must be treated in a special way  Solution A: assign instance to most popular branch  Solution B: split instance into pieces  Pieces receive weight according to fraction of training instances that go down each branch  Classifications from leave nodes are combined using the weights that have percolated to them

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Classification rules

 Popular alternative to decision trees

 Antecedent (pre-condition): a series of tests (just

like the tests at the nodes of a decision tree)

 Tests are usually logically ANDed together (but may also be general logical expressions)

 Consequent (conclusion): classes, set of classes, or

probability distribution assigned by rule

 Individual rules are often logically ORed together  Conflicts arise if different conclusions apply

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overcast

high normal

sunny (^) rain

No

No

Yes

Yes

From trees to rules, 2

Outlook

Humidity

Write rules for this tree.

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From trees to rules, 3

If outlook=sunny and humidity=high

then play=no

If outlook=sunny and humidity=normal

then play=yes

If outlook=overcast then play=yes

If outlook=rain then play=no

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A tree for a simple disjunction

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The exclusive-or problem

If x = 1 and y = 0 then class = a If x = 0 and y = 1 then class = a If x = 0 and y = 0 then class = b If x = 1 and y = 1 then class = b

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“Nuggets” of knowledge

 Are rules independent pieces of knowledge? (It seems easy to add a rule to an existing rule base.)

 Problem: ignores how rules are executed

 Two ways of executing a rule set:

 Ordered set of rules (“decision list”)  Order is important for interpretation  Unordered set of rules  Rules may overlap and lead to different conclusions for the same instance

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Interpreting rules

 What if two or more rules conflict?

 Give no conclusion at all?  Go with rule that is most popular on training data?  …

 What if no rule applies to a test instance?

 Give no conclusion at all?  Go with class that is most frequent in training data?  …