Transfer Learning by Mapping and Revising Relational Knowledge

transcript

Raymond J. Mooney

University of Texas at Austinwith acknowledgements to

Lily Mihalkova, Tuyen Huynh

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.

Transfer Learning Curves

• Transfer learning increases accuracy in the target domain.

Amount of training data in target domain

NO TRANSFER

TRANSFER FROM SOURCE

Jumpstart

Advantage from Limited target data

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)

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.

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.

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.

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.

Statistical Relational Learning

pacino

brando

coppola

godFather pacino

godFather brando

godFather coppola

streetCar brando

… …

pacino coppola

brando coppola

… …

Actor MovieDirector

WorkedFor

Multi-Relational Data Learning

Algorithm

Probabilistic Graphical Model

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)

TL and SRL and I.I.D.

Standard Machine Learning assumes examples are:

Independent and Identically Distributed

SRL breaks the assumptionthat examples are independent

TL breaks the assumptionthat test examples are drawn from the same distribution as

the training instances

Multi-Relational Domains

• Domains about people– Academic departments (UW-CSE)– Movies (IMDB)

• Biochemical domains– Mutagenesis – Alzheimer drug design

• Linked text domains– WebKB– Cora

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 student’s 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)

Markov logic networks

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

IMDBIMDBDirector(A) Actor(A)

Movie(T, A) WorkedFor(A, B)

UW-CSEUW-CSEProfessor(A) Student(A)

Publication(T, A) AdvisedBy(A, B)

Source: Target:

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)

movieTitle person

First-Order Clauses

• Clause: A disjunction of literals

• Can be rewritten as a set of rules:

Actor(pacino) WorkedFor(pacino, coppola) Movie(godFather, pacino)

Actor(brando) WorkedFor(brando, coppola) Movie(godFather, brando)

Director(coppola) Movie(godFather, coppola)

Representing the Data

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

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.

Markov Networks(Pearl, 1988)

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

Quality of

Reputationof Author

Algorithm Experiments

R A E Q

e e e e 0.7

e e e p 0.1

e e p e 0.03

Same probability distribution can be represented as the

product of a set of functions defined over the cliques of

the graph

Joint distribution

Markov Network Equations

• General form

• Log-linear models

weights features

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.

constants: coppola, brando,

godFather

1.31.20.5

Movie(godFather, brando) Movie(godFather,coppola)

WorkedFor(coppola, brando) WorkedFor(coppola, coppola)

WorkedFor(brando, brando) WorkedFor(brando, coppola)

Director(brando)

Actor(brando)

Director(coppola)

Actor(coppola)

MLN Equations

Compare to log-linear Markov networks:

all groundings of f i

all clauses in the model

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.

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.

WorkedFor(coppola, brando) WorkedFor(coppola, coppola)

WorkedFor(brando, brando) WorkedFor(brando, coppola)

Director(brando)

Actor(brando)

Director(coppola)

Actor(coppola)

Movie(godFather, brando) Movie(godFather,coppola)

0.70.1

0.20.3

MLN Inference Algorithms

• Gibbs Sampling (Richardson & Domingos, 2006)

• MC-SAT (Poon & Domingos, 2006)

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.

WPLL (Kok & Domingos, 2005)

• Weighted pseudo log-likelihood

Compute the likelihood of the data according to the model and take log

For each gliteral, condition on its Markov blanket for tractability

Weight it so that predicates with greater arity do not

dominate

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.

TAMAR(Transfer via Automatic Mapping And Revision)

Target(IMDB)

M-TAMAR

R-TAMAR

Movie(T,A) WorkedFor(A,B) → Movie(T,B)

Movie(T,A) WorkedFor(A,B) Relative(A,B) → Movie(T,B)

Publication(T,A) AdvisedBy(A,B) → Publication(T,B) (clause from UW-CSE)

Predicate Mapping:Publication MovieAdvisedBy WorkedFor

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.

Predicate Mapping Example

Publication(title, person) Movie(name, person)

AdvisedBy(person, person) WorkedFor(person, person)

Consistent Type Mapping: title → name person → person

Predicate Mapping Example 2

Publication(title, person) Gender(person, gend)

AdvisedBy(person, person) SameGender(gend, gend)

Consistent Type Mapping: title → person person → gend

TAMAR(Transfer via Automatic Mapping And Revision)

Target(IMDB)

M-TAMAR

R-TAMAR

Publication(T,A) AdvisedBy(A,B) → Publication(T,B) (clause from UW-CSE)

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.

Source MLN

Top-down Source MLN

Target TrainingData

Data-DrivenRevisionProposer

Bottom-up

R-TAMAR

Relational Data

Clause 1 wtClause 2 wtClause 3 wtClause 4 wtClause 5 wt

Self-diagnosis

0.10.51.3

-0.2Change in WPLL

Clause 1 wtClause 2 wtClause 3 wtClause 4 wtClause 5 wtToo Long

Too ShortGood

Too LongGood

Directed Beam Search

New Candidate ClausesNew Clause 1 wtNew Clause 3 wt

New Clause 5 wt

New clause

discovery

New Clause 6 wtNew Clause 7 wt

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.

Self-Diagnosis: Clause BinsActor(brando) Director(coppola)

Movie(godFather, brando) Movie(godFather, coppola)

Movie(rainMaker, coppola) WorkedFor(brando, coppola)

Current gliteral:

Actor(brando)

– Relevant; Good

Current gliteral:

Actor(brando)

– Relevant; Good

– Relevant; Bad

Current gliteral:

Actor(brando)

– Relevant; Good

– Relevant; Bad

– Irrelevant; Good

Current gliteral:

Actor(brando)

– Relevant; Good

– Relevant; Bad

– Irrelevant; Good

– Irrelevant; Bad

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:

1. Limiting the clauses considered for updates.2. Restricting the type of updates allowed.

New Clause Discovery

• Uses Relational Pathfinding (Richards & Mooney, 1992)

brando coppola

godFather rainMaker

WorkedFor

Movie M

Actor(brando) Director(coppola)Movie(godFather, brando) Movie(godFather, coppola)

WorkedFor

Weight Revision

Target(IMDB)

M-TAMAR

R-TAMAR

Publication(T,A) AdvisedBy(A,B) → Publication(T,B)

MLN Weight Training

0.8 Movie(T,A) WorkedFor(A,B) Relative(A,B) → Movie(T,B)

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,

• WebKB– Entity relations from the original WebKB domain

(Craven et al. 1998)– Predicates include Faculty, Student, Project, CourseTA, etc.

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.

Data Set # Mega-

Examples

Constants

Predicates

# True Gliterals

Total # Gliterals

IMDB 5 316 4 10 1,540 32,615

UW-CSE 5 1,323 9 15 2,673 678,899

WebKB 4 1,700 3 6 2,065 688,193

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.

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.

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.

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.

Metrics to Summarize Curves

• Transfer Ratio (Cohen et al. 2007)

– Gives overall idea of improvement achieved over learning from scratch

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.

AUC Transfer Ratio

WebKB to IMDB UW-CSE to IMDB UW-KB to IMDB WebKB to UW-CSE IMDB to UW-CSE

Experiment

CLL Transfer Ratio

Experiments

Sample Learning Curve

ScrKDTrKD, Hand Mapping

TAMAR, Hand MappingTrKD

Total Training Time in Minutes

200.00

400.00

600.00

800.00

1000.00

1200.00

Experiment

Scr KD

0.89 9.10 9.99 6.75 42.3

Number of seconds to find best mapping:

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)

Multiple Source Transfer

• Transfer from multiple source problems to a given target problem.

• Determine which clauses to map and revise from different source MLNs.

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.

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.

Questions?

Related papers at:http://www.cs.utexas.edu/users/ml/publication/transfer.html

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

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.

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.

Summary of Methodology

1. Learn MLNs for each point on learning curve

2. Perform inference over learned models3. Summarize inference results using 2

metrics: CLL and AUC, thus producing two learning curves

4. Summarize each learning curve using transfer ratio and percentage improvement from one mega-example

CLL Percent Improvement

Experiment

AUC Percent Improvement

Experiment

Transfer Learning by Mapping and Revising Relational Knowledge

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