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'''Decision lists''' are a representation for Boolean functions.<ref>{{cite journal|author=Ronald L. Rivest|authorlink=Ronald L. Rivest|title=Learning decision lists|journal=Machine Learning|volume=2|issue=3|pages=229–246|date=Nov 1987|doi=10.1023/A:1022607331053|url=http://people.csail.mit.edu/rivest/pubs/Riv87b.pdf}}</ref>  Single term decision lists are more expressive than [[disjunctions]] and [[conjunctions]], however 1-term decision lists are less expressive than the general [[disjunctive normal form]] and the [[conjunctive normal form]].


The language specified by a k-length decision list includes as a subset the language specified by a k-depth [[decision tree]].


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Learning decision lists can be used for [[attribute efficient learning]].<ref>Adam R. Klivans and Rocco A. Servedio, "Toward Attribute Efficient Learning of Decision Lists and Parities", ''Journal of Machine Learning Research'' '''7''':12:587-602 [http://dl.acm.org/citation.cfm?id=1248567&dl=ACM&coll=DL&CFID=344844478&CFTOKEN=13074001 ACM Digital Library] [http://www.jmlr.org/papers/volume7/klivans06a/klivans06a.pdf full text]</ref>
 
== Definition ==
 
A decision list (DL) of length <math>r</math> is of the form:
 
'''if''' <math>f_1</math> '''then''' output <math>b_1</math>
'''else if''' <math>f_2</math> '''then''' output <math>b_2</math>
...
'''else if''' <math>f_r</math> '''then''' output <math>b_r</math>
 
where <math>f_i</math> is the <math>i</math>th formula and <math>b_i</math> is the <math>i</math>th [[Boolean data type|boolean]] for <math>i \in \{1...r\}</math>. The last if-then-else is the default case, which means formula <math>f_r</math> is always equal to true. A <math>k</math>-DL is a decision list where all of formulas have at most <math>k</math> terms.  Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its [[negation]].
 
==References==
<references/>
 
[[Category:Artificial intelligence]]
[[Category:Machine learning]]
 
 
{{AI-stub}}

Revision as of 21:59, 19 January 2014

Decision lists are a representation for Boolean functions.[1] Single term decision lists are more expressive than disjunctions and conjunctions, however 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form.

The language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree.

Learning decision lists can be used for attribute efficient learning.[2]

Definition

A decision list (DL) of length r is of the form:

if f1 then output b1
else if f2 then output b2
...
else if fr then output br

where fi is the ith formula and bi is the ith boolean for i{1...r}. The last if-then-else is the default case, which means formula fr is always equal to true. A k-DL is a decision list where all of formulas have at most k terms. Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.

References

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  2. Adam R. Klivans and Rocco A. Servedio, "Toward Attribute Efficient Learning of Decision Lists and Parities", Journal of Machine Learning Research 7:12:587-602 ACM Digital Library full text


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