Inductive logic programming: Difference between revisions

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== Probabilistic inductive logic programming ==

Probabilistic inductive logic programming adapts the setting of inductive logic programming to learning [[Probabilistic logic programming|probabilistic logic programs]]. It can be considered as a form of [[statistical relational learning]] within the formalism of probabilistic logic programming.<ref>{{Citation |last1=De Raedt |first1=Luc |title=Probabilistic Inductive Logic Programming |date=2008 |url=http://dx.doi.org/10.1007/978-3-540-78652-8_1 |pages=1–27 |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-540-78651-1 |last2=Kersting |first2=Kristian|doi=10.1007/978-3-540-78652-8_1 }}</ref><ref name="pilp">{{Cite journal |last1=Riguzzi |first1=Fabrizio |last2=Bellodi |first2=Elena |last3=Zese |first3=Riccardo |date=2014-09-18 |title=A History of Probabilistic Inductive Logic Programming |journal=Frontiers in Robotics and AI |volume=1 |doi=10.3389/frobt.2014.00006 |issn=2296-9144 |doi-access=free }}</ref>

Given

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the goal of probabilistic inductive logic programming is to find a probabilistic logic program <math display="inline">H</math> such that the probability of positive examples according to <math display="inline">{H \cup B}</math> is maximized and the probability of negative examples is minimized.<ref name="pilp" />

This problem has two variants: parameter learning and structure learning. In the firstformer, one is given the structure (the clauses) of {{Mvar|H}} and the goal is to infer the probabilities annotations of the given clauses, while in the secondlatter the goal wasis to infer both the structure and the probability parameters of {{Mvar|H}}. Just as in classical inductive logic programming, the examples can be given as examples or as (partial) interpretations.<ref name="pilp" />

=== Parameter Learning ===

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Structure learning was pioneered by [[Daphne Koller]] and Avi Pfeffer in 1997,<ref>{{Cite conference |last1=Koller |first1=Daphne |last2=Pfeffer |first2=Avi |date=August 1997 |title=Learning probabilities for noisy first-order rules |url=http://www.robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:IJCAI97.pdf |conference=[[IJCAI]]}}</ref> where the authors learn the structure of [[First-order logic|first-order]] rules with associated probabilistic uncertainty parameters. Their approach involves generating the underlying [[graphical model]] in a preliminary step and then applying expectation-maximisation.<ref name="pilp" />

In 2008, [[Luc De Raedt|De Raedt]] et al. presented an algorithm for performing [[theory compression]] on [[ProbLog]] programs, where theory compression meansrefers to a process of removing as many clauses as possible from the theory in order to maximize the probability that no new clause can be added to the theory.<ref name="pilp" />

In the same year, Meert, W. et al. introduced a method for learning parameters and structure of [[Ground term|ground]] probabilistic logic programs by considering the [[Bayesian network]]s equivalent to them and applying techniques for learning Bayesian networks.<ref>{{Citation |last1=Blockeel |first1=Hendrik |title=Towards Learning Non-recursive LPADs by Transforming Them into Bayesian Networks |url=http://dx.doi.org/10.1007/978-3-540-73847-3_16 |work=Inductive Logic Programming |pages=94–108 |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-540-73846-6 |last2=Meert |first2=Wannes|series=Lecture Notes in Computer Science |date=2007 |volume=4455 |doi=10.1007/978-3-540-73847-3_16 }}</ref><ref name="pilp" />