Transfer Learning With Markov Logic Networks

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Transfer Learning With Markov Logic Networks

• Lilyana Mihalkova Raymond Mooney
• University of Texas at Austin

ICML-06 Workshop on Structural Knowledge Transfer
for Machine Learning June 29, 2006
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Markov Logic Networks
Richardson Domingos 2006

• Set of first-order formulae, each with a weight
  attached
• Templates for constructing Markov networks, when
  a set of constants is provided
• Include a node for each grounding of each
  predicate in the MLN
• Include a feature for each grounding of each
  formula in the MLN

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MLNs Inference
Richardson Domingos 2006

• Given a set of unknown query ground literals Q
  and a set of evidence ground literals E, find
  P(QE)
• Done using Gibbs sampling

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MLNs Inference Cont.
Richardson Domingos 2006

• Recomputing P(XMBX) in basic Gibbs step

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MLN Structure Learning
Kok Domingos 2005

• Can start from scratch or from provided MLN
• Proceeds by using greedy beam-search
• Refinements to a clause are generated by
• Adding a literal in all possible ways
• Trying all possible literal deletions (only from
  clauses of the original source MLN)
• Trying all possible sign flips of the literals
• Candidates are scored using a weighted pseudo
  log-likelihood measure
• The best b candidates are kept and in the next
  iteration new refinements are generated from them

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Setting and Assumptions

• Given
• MLN, S, learned in source relational domain
• Mapping between predicates in source and target
  domains
• Find out which parts of S are still valid in new
  domain and which need to be relearned
• Perform relearning of incorrect structure

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Transfer Learning as Revision

• Regard source MLN as an incorrect model for the
  target task that needs to be accurately and
  efficiently revised
• Thus our general approach is similar to that
  taken by revision systems Richards Mooney,
  1995
• Revisions are proposed in a bottom-up fashion

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New Algorithm
Relational Data
Change in pseudo log-likelihood
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Self-Diagnosis Preliminaries

• From the perspective of a particular ground
  literal, a clause can be in one of four
  diagnostic bins
• Applies, good
• Applies, bad
• Does not apply, good
• Does not apply, bad

Student(Ann) !HasJob(Ann,J) Sleepy(Ann),
Sociable(Ann) InClass(Ann,C)
InClass(Ann,C) gt Student(Ann)
Sociable(Ann) gt !Student(Ann)
Too General
!Sleepy(Ann) gt !Student(Ann)
HasJob(Ann,J) gt Student(Ann)
Too Specific
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Self-Diagnosis

• Perform Gibbs sampling with each predicate P in
  turn serving as query
• In addition to recomputing probability of each
  ground literal, calculate bin memberships of
  participating clauses

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Structure Updates

• Using directed beam search
• Literal deletions attempted only from clauses
  marked as too specific
• Literal additions only to clauses determined to
  be too general
• Restrictions carry over to derivatives of
  original clauses
• Search space constrained by
• Limiting the clauses considered for updates
• Restricting the type of update allowed

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Experiments Domains
Academic Industrial
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Experiments Data

• Each training mega-example is a world
  representing the domain
• Consists of roughly 50-150 true ground literals
• Generated by fixing the values of some predicate
  groundings and performing MAP inference over a
  hand-crafted MLN to set the rest

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Experiments Details

• Systems compared
• ScratchAlchemy Kok Domingos 2005
• TransferAlchemy Kok Domingos 2005
• TransferNew
• Metrics
• Conditional log likelihood (CLL)
• Area under the precision-recall curve (AUC)
• Running time
• Number of candidate clauses considered
• Test predicates SupervisedBy and Secretary

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Results CLL
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Results AUC
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Results Running Time
TransferAlchemy
TransferNew
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Results Number of Candidates
TransferAlchemy
TransferNew
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Conclusions

• Presented new transfer learning algorithm that
• Explicitly takes advantage of similarities
  between tasks
• Focuses on relearning only incorrect portions of
  the domain
• Decreases both search space and running time