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Transfer Learning by Mapping and Revising
Relational Knowledge

• Raymond J. Mooney
• University of Texas at Austin
• with acknowledgements to
• Lily Mihalkova, Tuyen Huynh

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Transfer Learning

• Most machine learning methods learn each new task
  from scratch, failing to utilize previously
  learned knowledge.
• Transfer learning concerns using knowledge
  acquired in a previous source task to facilitate
  learning in a related target task.
• Usually assume significant training data was
  available in the source domain but limited
  training data is available in the target domain.
• By exploiting knowledge from the source, learning
  in the target can be
• More accurate Learned knowledge makes better
  predictions.
• Faster Training time is reduced.

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Transfer Learning Curves

• Transfer learning increases accuracy in the
  target domain.

Predictive Accuracy
Amount of training data in target domain
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Recent Work on Transfer Learning

• Recent DARPA program on Transfer Learning has led
  to significant recent research in the area.
• Some work focuses on feature-vector
  classification.
• Hierarchical Bayes (Yu et al., 2005 Lawrence
  Platt, 2004)
• Informative Bayesian Priors (Raina et al., 2005)
• Boosting for transfer learning (Dai et al., 2007)
• Structural Correspondence Learning (Blitzer et
  al., 2007)
• Some work focuses on Reinforcement Learning
• Value-function transfer (Taylor Stone, 2005
  2007)
• Advice-based policy transfer (Torrey et al.,
  2005 2007)

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Similar Research Problems

• Multi-Task Learning (Caruana, 1997)
• Learn multiple tasks simultaneously each one
  helped by the others.
• Life-Long Learning (Thrun, 1996)
• Transfer learning from a number of prior source
  problems, picking the correct source problems to
  use.

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Logical Paradigm

• Represents knowledge and data in binary symbolic
  logic such as First Order Predicate Calculus.
• Rich representation that handles arbitrary
  sets of objects, with properties, relations,
  quantifiers, etc.
• ? Unable to handle uncertain knowledge and
  probabilistic reasoning.

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Probabilistic Paradigm

• Represents knowledge and data as a fixed set of
  random variables with a joint probability
  distribution.
• Handles uncertain knowledge and probabilistic
  reasoning.
• ? Unable to handle arbitrary sets of objects,
  with properties, relations, quantifiers, etc.

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Statistical Relational Learning (SRL)

• Most machine learning methods assume i.i.d.
  examples represented as fixed-length feature
  vectors.
• Many domains require learning and making
  inferences about unbounded sets of entities that
  are richly relationally connected.
• SRL methods attempt to integrate methods from
  predicate logic and probabilistic graphical
  models to handle such structured,
  multi-relational data.

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Statistical Relational Learning
Actor
Movie
Director
WorkedFor
Multi-Relational Data
Learning Algorithm
Probabilistic Graphical Model
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Multi-Relational Data Challenges

• Examples cannot be effectively represented as
  feature vectors.
• Predictions for connected facts are not
  independent. (e.g. WorkedFor(brando,
  coppolo), Movie(godFather, brando))
• Data is not i.i.d.
• Requires collective inference (classification)
  (Taskar et al., 2001)
• A single independent example (mega-example) often
  contains information about a large number of
  interconnected entities and can vary in length.
• Leave one university out testing (Craven et al.,
  1998)

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TL and SRL and I.I.D.

• Standard Machine Learning assumes examples are
• Independent and Identically Distributed

TL breaks the assumption that test examples
are drawn from the same distribution as the
training instances
SRL breaks the assumption that examples are
independent
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Multi-Relational Domains

• Domains about people
• Academic departments (UW-CSE)
• Movies (IMDB)
• Biochemical domains
• Mutagenesis
• Alzheimer drug design
• Linked text domains
• WebKB
• Cora

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Relational Learning Methods

• Inductive Logic Programming (ILP)
• Produces sets of first-order rules
• Not appropriate for probabilistic reasoning
• If a student wrote a paper with a professor, then
  the professor is the students advisor
• SRL models learning algorithms
• SLPs (Muggleton, 1996)
• PRMs (Koller, 1999)
• BLPs (Kersting De Raedt, 2001)
• RMNs (Taskar et al., 2002)
• MLNs (Richardson Domingos, 2006)

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MLN Transfer(Mihalkova, Huynh, Mooney, 2007)

• Given two multi-relational domains, such as
• Transfer a Markov logic network learned in the
  Source to the Target by
• Mapping the Source predicates to the Target
• Revising the mapped knowledge

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First-Order Logic Basics

• Literal A predicate (or its negation) applied to
  constants and/or variables.
• Gliteral Ground literal WorkedFor(brando,
  coppola)
• Vliteral Variablized literal ?WorkedFor(A, B)
• We assume predicates have typed arguments.
• For example Movie(godFather, coppola)

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First-Order Clauses

• Clause A disjunction of literals

• Can be rewritten as a set of rules

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Representing the Data

• Makes a closed world assumption
• The gliterals listed are true the rest are false

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Markov Logic Networks(Richardson Domingos,
2006)

• Set of first-order clauses, each assigned a
  weight.
• Larger weight indicates stronger belief that the
  clause should hold.
• The clauses are called the structure of the MLN.

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Markov Networks(Pearl, 1988)

• A concise representation of the joint probability
  distribution of a set of random variables using
  an undirected graph.

Joint distribution
Reputation of Author
Quality of Paper
Same probability distribution can be represented
as the product of a set of functions defined over
the cliques of the graph
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Markov Network Equations

• General form
• Log-linear models

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Ground Markov Network for an MLN

• MLNs are templates for constructing Markov
  networks for a given set of constants
• Include a node for each type-consistent grounding
  (a gliteral) of each predicate in the MLN.
• Two nodes are connected by an edge if their
  corresponding gliterals appear together in any
  grounding of any clause in the MLN.
• Include a feature for each grounding of each
  clause in the MLN with weight equal to the weight
  of the clause.

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• constants
• coppola,
• brando,
• godFather

1.3
1.2
0.5
Actor(brando)
Director(brando)
WorkedFor(brando, brando)
WorkedFor(brando, coppola)
Movie(godFather, brando)
Movie(godFather,coppola)
WorkedFor(coppola, brando)
WorkedFor(coppola, coppola)
Director(coppola)
Actor(coppola)
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MLN Equations
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MLN Equation Intuition

• A possible world (a truth assignment to all
  gliterals) becomes exponentially less likely as
  the total weight of all the grounded clauses it
  violates increases.

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MLN Inference

• Given truth assignments for given set of evidence
  gliterals, infer the probability that each member
  of set of unknown query gliterals is true.

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Actor(brando)
Director(brando)
WorkedFor(brando, brando)
WorkedFor(brando, coppola)
Movie(godFather, brando)
Movie(godFather,coppola)
WorkedFor(coppola, brando)
WorkedFor(coppola, coppola)
Director(coppola)
Actor(coppola)
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MLN Inference Algorithms

• Gibbs Sampling (Richardson Domingos, 2006)
• MC-SAT (Poon Domingos, 2006)

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MLN Learning

• Weight-learning (Richardson Domingos, 2006
  Lowd Domingos, 2007)
• Performed using optimization methods.
• Structure-learning (Kok Domingos, 2005)
• Proceeds in iterations of beam search, adding the
  best-performing clause after each iteration to
  the MLN.
• Clauses are evaluated using WPLL score.

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WPLL (Kok Domingos, 2005)

• Weighted pseudo log-likelihood

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Alchemy

• Open-source package of MLN software provided by
  UW that includes
• Inference algorithms
• Weight learning algorithms
• Structure learning algorithm
• Sample data sets
• All our software uses and extends Alchemy.

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TAMAR(Transfer via Automatic Mapping And
Revision)
Target (IMDB) Data
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Predicate Mapping

• Each clause is mapped independently of the
  others.
• The algorithm considers all possible ways to map
  a clause such that
• Each predicate in the source clause is mapped to
  some target predicate.
• Each argument type in the source is mapped to
  exactly one argument type in the target.
• Each mapped clause is evaluated by measuring its
  WPLL for the target data, and the most accurate
  mapping is kept.

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Predicate Mapping Example
Consistent Type Mapping title ?
name person ? person
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Predicate Mapping Example 2
Consistent Type Mapping title ?
person person ? gend
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TAMAR(Transfer via Automatic Mapping And
Revision)
Target (IMDB) Data
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Transfer Learning as Revision

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

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R-TAMAR
Relational Data
New clause discovery
New Candidate Clauses
Change in WPLL
0.1
-0.2
0.5
1.7
1.3
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R-TAMAR Self-Diagnosis

• Use mapped source MLN to make inferences in the
  target and observe the behavior of each clause
• Consider each predicate P in the domain in turn.
• Use Gibbs sampling to infer truth values for the
  gliterals of P, using the remaining gliterals as
  evidence.
• Bin the clauses containing gliterals of P based
  on whether they behave as desired.
• Revisions are focused only on clauses in the
  Bad bins.

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Self-Diagnosis Clause Bins
Actor(brando) Director(coppola) Movie(godFather,
brando) Movie(godFather, coppola) Movie(rainMaker,
coppola) WorkedFor(brando, coppola)
Current gliteral Actor(brando)

• Relevant

Good
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Self-Diagnosis Clause Bins
Actor(brando) Director(coppola) Movie(godFather,
brando) Movie(godFather, coppola) Movie(rainMaker,
coppola) WorkedFor(brando, coppola)
Current gliteral Actor(brando)

• Relevant

Good

• Relevant

Bad
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Self-Diagnosis Clause Bins
Actor(brando) Director(coppola) Movie(godFather,
brando) Movie(godFather, coppola) Movie(rainMaker,
coppola) WorkedFor(brando, coppola)
Current gliteral Actor(brando)

• Relevant

Good

• Relevant

Bad

• Irrelevant

Good
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Self-Diagnosis Clause Bins
Actor(brando) Director(coppola) Movie(godFather,
brando) Movie(godFather, coppola) Movie(rainMaker,
coppola) WorkedFor(brando, coppola)
Current gliteral Actor(brando)

• Relevant

Good

• Relevant

Bad

• Irrelevant

Good

• Irrelevant

Bad
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Structure Revisions

• Using directed beam search
• Literal deletions attempted only from clauses
  marked for shortening.
• Literal additions attempted only for clauses
  marked for lengthening.
• Training is much faster since search space is
  constrained by
• Limiting the clauses considered for updates.
• Restricting the type of updates allowed.

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New Clause Discovery

• Uses Relational Pathfinding (Richards Mooney,
  1992)

Actor(brando) Director(coppola) Movie(godFather,
brando) Movie(godFather, coppola) Movie(rainMaker,
coppola) WorkedFor(brando, coppola)
WorkedFor
WorkedFor
brando
coppola
Movie
Movie
Movie
godFather
rainMaker
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Weight Revision
Publication(T,A) ? AdvisedBy(A,B) ?
Publication(T,B)
Target (IMDB) Data
Movie(T,A) ? WorkedFor(A,B) ? Movie(T,B)
Movie(T,A) ? WorkedFor(A,B) ? Relative(A,B) ?
Movie(T,B)
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Experiments Domains

• UW-CSE
• Data about members of the UW CSE department
• Predicates include Professor, Student, AdvisedBy,
  TaughtBy, Publication, etc.
• IMDB
• Data about 20 movies
• Predicates include Actor, Director, Movie,
  WorkedFor, Genre, etc.
• WebKB
• Entity relations from the original WebKB domain
  (Craven et al. 1998)
• Predicates include Faculty, Student, Project,
  CourseTA, etc.

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Dataset Statistics
Data is organized as mega-examples

• Each mega-example contains information about a
  group of related entities.
• Mega-examples are independent and disconnected
  from each other.

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Manually Developed Source KB

• UW-KB is a hand-built knowledge base (set of
  clauses) for the UW-CSE domain.
• When used as a source domain, transfer learning
  is a form of theory refinement that also includes
  mapping to a new domain with a different
  representation.

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Systems Compared

• TAMAR Complete transfer system.
• ScrKD Algorithm of Kok Domingos (2005)
  learning from scratch.
• TrKD Algorithm of Kok Domingos (2005)
  performing transfer, using M-TAMAR to produce a
  mapping.

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Methodology Training Testing

• Generated learning curves using leave-one-out
  CV
• Each run keeps one mega-example for testing and
  trains on the remaining ones, provided one by
  one.
• Curves are averages over all runs.
• Evaluated learned MLN by performing inference for
  all gliterals of each predicate in turn,
  providing the rest as evidence, and averaging the
  results.

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Methodology Metrics Kok Domingos (2005)

• CLL Conditional Log Likelihood
• The log of the probability predicted by the model
  that a gliteral has the correct truth value given
  in the data.
• Averaged over all test gliterals.
• AUC Area under the precision recall (PR) curve
• Produce a PR curve by varying the probability
  threshold.
• Compute the area under this curve.

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Metrics to Summarize Curves

• Transfer Ratio (Cohen et al. 2007)
• Gives overall idea of improvement achieved over
  learning from scratch

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Transfer Scenarios

• Source/target pairs tested
• WebKB ? IMDB
• UW-CSE ? IMDB
• UW-KB ? IMDB
• WebKB ? UW-CSE
• IMDB ? UW-CSE
• WebKB not used as a target since one mega-example
  is sufficient to learn an accurate theory for its
  limited predicate set.

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Sample Learning Curve
ScrKD TrKD, Hand Mapping TAMAR, Hand
Mapping TrKD TAMAR
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Future Research Issues

• More realistic application domains.
• Application to other SRL models (e.g. SLPs,
  BLPs).
• More flexible predicate mapping
• Allow argument ordering or arity to change.
• Map 1 predicate to conjunction of 1 predicates
• AdvisedBy(X,Y) ?? Movie(M,X) ? Director(M,Y)

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Multiple Source Transfer

• Transfer from multiple source problems to a given
  target problem.
• Determine which clauses to map and revise from
  different source MLNs.

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Source Selection

• Select useful source domains from a large number
  of previously learned tasks.
• Ideally, picking source domain(s) is sub-linear
  in the number of previously learned tasks.

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Conclusions

• Presented TAMAR, a complete transfer system for
  SRL that
• Maps relational knowledge in the source to the
  target domain.
• Revises the mapped knowledge to further improve
  accuracy.
• Showed experimentally that TAMAR improves speed
  and accuracy over existing methods.

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Questions?

• Related papers at
• http//www.cs.utexas.edu/users/ml/publication/tran
  sfer.html

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Why MLNs?

• Inherit the expressivity of first-order logic
• Can apply insights from ILP
• Inherit the flexibility of probabilistic
  graphical models
• Can deal with noisy uncertain environments
• Undirected models
• Do not need to learn causal directions
• Subsume all other SRL models that are special
  cases of first-order logic or probabilistic
  graphical models Richardson 04
• Publicly available software package Alchemy

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Predicate Mapping Comments

• A particular source predicate can be mapped to
  different target predicates in different clauses.
• This makes our approach context sensitive.
• More scalable.
• In the worst-case, the number of mappings is
  exponential in the number of predicates.
• The number of predicates in a clause is generally
  much smaller than the total number of predicates
  in a domain.

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Relationship to Structure Mapping Engine
(Falkenheiner et al., 1989)

• A system for mapping relations using analogy
  based on a psychological theory.
• Mappings are evaluated based only on the
  structural relational similarity between the two
  domains.
• Does not consider the accuracy of mapped
  knowledge in the target when determining the
  preferred mapping.
• Determines a single global mapping for a given
  source target.

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Summary of Methodology

• Learn MLNs for each point on learning curve
• Perform inference over learned models
• Summarize inference results using 2 metrics CLL
  and AUC, thus producing two learning curves
• Summarize each learning curve using transfer
  ratio and percentage improvement from one
  mega-example

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