Online%20Max-Margin%20Weight%20Learning%20with%20Markov%20Logic%20Networks

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Online Max-Margin Weight Learning with Markov
Logic Networks

• Tuyen N. Huynh and Raymond J. Mooney

Machine Learning Group Department of Computer
Science The University of Texas at Austin
Star AI 2010, July 12, 2010
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Outline

• Motivation
• Background
• Markov Logic Networks
• Primal-dual framework
• New online learning algorithm for structured
  prediction
• Experiments
• Citation segmentation
• Search query disambiguation
• Conclusion

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Motivation

• Most of the existing weight learning for MLNs are
  in the batch setting.
• Need to run inference over all the training
  examples in each iteration
• Usually take a few hundred iterations to converge
• Cannot fit all the training examples in the
  memory
• ? Conventional solution online learning

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Background
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Markov Logic Networks (MLNs)
Richardson Domingos, 2006

• An MLN is a weighted set of first-order formulas
• Larger weight indicates stronger belief that the
  clause should hold
• Probability of a possible world (a truth
  assignment to all ground atoms) x

2.5 Center(i,c) gt InField(Ftitle,i,c) 1.2
InField(f,i,c) Next(j,i) HasPunc(c,i)gt
InField(f,j,c)
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Existing discriminative weight learning methods
for MLNs

• maximize the Conditional Log Likelihood (CLL)
  Singla Domingos, 2005, Lowd Domingos,
  2007, Huynh Mooney, 2008
• maximize the margin, the log ratio between the
  probability of the correct label and the closest
  incorrect one Huynh Mooney, 2009

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Online learning

•  

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Primal-dual framework Shalev-Shwartz et al.,
2006

• A general and latest framework for deriving
  low-regret online algorithms
• Rewriting the regret bound as an optimization
  problem (called the primal problem), then
  considering the dual problem of the primal one
• A condition that guarantees the increase in the
  dual objective in each step
• ? Incremental-Dual-Ascent (IDA) algorithms. For
  example subgradient methods

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Primal-dual framework (cont.)

• Proposed a new class of IDA algorithms called
  Coordinate-Dual-Ascent (CDA) algorithm
• The CDA update rule only optimizes the dual w.r.t
  the last dual variable
• A closed-form solution of CDA update rule ? CDA
  algorithms have the same cost as subgradient
  methods but increase the dual objective more in
  each step ? converging to the optimal value
  faster

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Primal-dual framework (cont.)

•  

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CDA algorithms for max-margin structured
prediction
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Max-margin structured prediction

•  

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Steps for deriving new CDA algorithms

1. Define the regularization and loss functions
2. Find the conjugate functions
3. Derive a closed-form solution for the CDA update
   rule

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1. Define the regularization and loss functions

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Label loss function
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1. Define the regularization and loss functions
(cont.)

•  

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2. Find the conjugate functions

•  

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2. Find the conjugate functions (cont.)

•  

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3. Closed-form solution for the CDA update rule

• Optimization problem
• Solution

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CDA algorithms for max-margin structured
prediction

•  

 
 
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Experiments
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Citation segmentation

• Citeseer dataset Lawrence et.al., 1999 Poon
  and Domingos, 2007
• 1,563 citations, divided into 4 research topics
• Each citation is segmented into 3 fields Author,
  Title, Venue
• Used the simplest MLN in Poon and Domingos,
  2007
• Similar to a linear chain CRF
• Next(j,i) !HasPunc(c,i) InField(c,f,i)
  gt InField(c,f,j)

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Experimental setup

• Systems compared
• MM the max-margin weight learner for MLNs in
  batch setting Huynh Mooney, 2009
• 1-best MIRA Crammer et al., 2005
• Subgradient Ratliff et al., 2007
• CDA1/PA1
• CDA2

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Experimental setup (cont.)

• 4-fold cross-validation
• Metric
• CiteSeer micro-average F1 at the token level
• Used exact MPE inference (Integer Linear
  Programming) for all online algorithms and
  approximate MPE inference (LP-relaxation) for the
  batch one.
• Used Hamming loss as the label loss function

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Average F1
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Average training time in minutes
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Microsoft web search query dataset

• Used the clean-up dataset created by Mihalkova
  Mooney 2009
• Has thousands of search sessions where an
  ambiguous queries was asked
• Goal disambiguate search query based on previous
  related search sessions
• Used 3 MLNs proposed in Mihalkova Mooney, 2009

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Experimental setup

• Systems compared
• Contrastive Divergence (CD) Hinton 2002 used
  in Mihalkova Mooney, 2009
• 1-best MIRA
• Subgradient
• CDA1/PA1
• CDA2
• Metric
• Mean Average Precision (MAP) how close the
  relevant results are to the top of the rankings

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MAP scores
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Conclusion

• Derived CDA algorithms for max-margin structured
  prediction
• Have same computational cost as existing online
  algorithms but increase the dual objective more
• Experimental results on two real-world problems
  show that the new algorithms generally achieve
  better accuracy and also have more consistent
  performance.

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Thank you!
Questions?