extending bayesian logic programs for plan recognition and machine reading sindhu v. raghavan...

Extending Bayesian Logic Programsfor Plan Recognition and Machine Reading

Sindhu V. Raghavan

Advisor: Raymond Mooney

PhD ProposalMay 12th, 2011

1

$ cd my-dir$ cp test1.txt test-dir$ rm test1.txt

$ cd my-dir$ cp test1.txt test-dir$ rm test1.txtWhat task is the user performing?move-file

Which files and directories are involved?test1.tx and test-dir

Plan Recognition in Intelligent User Interfaces

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Can the task be performed more efficiently?

Data is relational in nature - several files and directories and several relations between them

Characteristics of Real World Data

Relational or structured dataSeveral entities in the domainSeveral relations between entitiesDo not always follow the i.i.d assumption

Presence of noise or uncertaintyUncertainty in the types of entitiesUncertainty in the relations

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Traditional approaches like first-order logic or probabilistic models can handle either structured data or uncertainty, but not both.

Statistical Relational Learning (SRL)

Integrates first-order logic and probabilistic graphical models [Getoor and Taskar, 2007]

– Combines strengths of both first-order logic and probabilistic models

SRL formalisms– Stochastic Logic Programs (SLPs) [Muggleton, 1996]

– Probabilistic Relational Models (PRMs) [Friedman et al., 1999]

– Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001] – Markov Logic Networks (MLNs) [Richardson and Dominogs, 2006]

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Statistical Relational Learning (SRL)

Integrates first-order logic and probabilistic graphical models [Getoor and Taskar, 2007]

– Combines strengths of both first-order logic and probabilistic models

SRL formalisms– Stochastic Logic Programs (SLPs) [Muggleton, 1996]

– Probabilistic Relational Models (PRMs) [Friedman et al., 1999]

– Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001] – Markov Logic Networks (MLNs) [Richardson and Dominogs, 2006]

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Bayesian Logic Programs (BLPs)

Integrate first-order logic and Bayesian networks

Why BLPs?Efficient grounding mechanism that includes only those

variables that are relevant to the queryEasy to extend by incorporating any type of logical

inference to construct networksWell suited for capturing causal relations in data

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Objectives

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BLPs for Plan RecognitionBLPs for Plan Recognition

BLPs for Machine ReadingBLPs for Machine Reading

Objectives

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Plan recognition involves predicting the top-level plan of an agent based on its actions

Plan recognition involves predicting the top-level plan of an agent based on its actions

BLPs for Machine ReadingBLPs for Machine Reading

Objectives

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BLPs for Plan RecognitionBLPs for Plan Recognition

Machine Reading involves automatic extraction of knowledge from natural language text

Machine Reading involves automatic extraction of knowledge from natural language text

Outline

MotivationBackground

First-order logicLogical AbductionBayesian Logic Programs (BLPs)

Completed WorkPart 1 – Extending BLPs for Plan RecognitionPart 2 – Extending BLPs for Machine Reading

Proposed WorkConclusions

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First-order LogicTerms

Constants – individual entities like anna, bobVariables – placeholders for objects like X, Y

Predicates Relations over entities like worksFor, capitalOf

Literal – predicate or its negation applied to terms Atom – Positive literal like worksFor(X,Y)Ground literal – literal with no variables like

worksFor(anna,bob)

Clause – disjunction of literalsHorn clause has at most one positive literalDefinite clause has exactly one positive literal

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First-order Logic

QuantifiersUniversal quantification - true for all objects in the domain

Existential quantification - true for some objects in the domain

Logical InferenceForward Chaining– For every implication pq, if p is true,

then q is concluded to be trueBackward Chaining – For a query literal q, if an implication

pq is present and p is true, then q is concluded to be true, otherwise backward chaining tries to prove p

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€

∀( )

€

∃( )

Logical AbductionAbduction

Process of finding the best explanation for a set of observations

GivenBackground knowledge, B, in the form of a set of (Horn) clauses in

first-order logicObservations, O, in the form of atomic facts in first-order logic

FindA hypothesis, H, a set of assumptions (atomic facts) that logically

entail the observations given the theory:

B H OBest explanation is the one with the fewest assumptions

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Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001]

Set of Bayesian clauses a|a1,a2,....,an

Definite clauses that are universally quantifiedHead of the clause - aBody of the clause - a1, a2, …, an

Range-restricted, i.e variables{head} variables{body}Associated conditional probability table (CPT)

o P(head|body)

Bayesian predicates a, a1, a2, …, an have finite domainsCombining rule like noisy-or for mapping multiple CPTs into

a single CPT.14

€

⊆

Logical Inference in BLPs SLD Resolution

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BLP

lives(james,yorkshire).lives(stefan,freiburg).neighborhood(james).tornado(yorkshire).

burglary(X) | neighborhood(X).alarm(X) | burglary(X).alarm(X) | lives(X,Y), tornado(Y).

Queryalarm(james)

Proof

alarm(james)

Example from Ngo and Haddawy, 1997


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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)

lives(james,Y) tornado(Y)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)


lives(james,yorkshire)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



tornado(yorkshire)



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BLP



Queryalarm(james)

Proof

alarm(james)

burglary(james)

neighborhood(james)



tornado(yorkshire)


Bayesian Network Construction

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alarm(james)

burglary(james)

neighborhood(james)

lives(james,yorkshire) tornado(yorkshire)

Each ground atom becomes a node (random variable) in the Bayesian network

Edges are added from ground atoms in the body of a clause to the ground atom in the head

Specify probabilistic parameters using the CPTs associated with Bayesian clauses


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alarm(james)

burglary(james)

neighborhood(james)






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alarm(james)

burglary(james)

neighborhood(james)






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alarm(james)

burglary(james)

neighborhood(james)





Use combining rule to combine multiple CPTs into a single CPT

lives(stefan,freiburg)✖

Probabilistic Inference and Learning

Probabilistic inferenceMarginal probability given evidenceMost Probable Explanation (MPE) given evidence

Learning [Kersting and De Raedt, 2008]

Parameterso Expectation Maximizationo Gradient-ascent based learning

Structureo Hill climbing search through the space of possible

structures

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Part 1Extending BLPs for Plan Recognition

[Raghavan and Mooney, 2010]

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Plan RecognitionPredict an agent’s top-level plans based on the observed

actionsAbductive reasoning involving inference of cause from

effectApplications

Story Understandingo Recognize character’s motives or plans based on its actions to

answer questions about the story

Strategic planningo Predict other agents’ plans so as to work co-operatively

Intelligent User Interfaceso Predict the task that the user is performing so as to provide

valuable tips to perform the task more efficiently

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Related Work

First-order logic based approaches [Kautz and Allen, 1986; Ng and Mooney, 1992]

Knowledge base of plans and actions Default reasoning or logical abduction to predict the best plan

based on the observed actionsUnable to handle uncertainty in data or estimate likelihood of

alternative plans

Probabilistic graphical models [Charniak and Goldman, 1989; Huber et al., 1994; Pynadath and Wellman, 2000; Bui, 2003; Blaylock and Allen, 2005]

Encode the domain knowledge using Bayesian networks, abstract hidden Markov models, or statistical n-gram models

Unable to handle relational/structured data

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Related WorkMarkov Logic based approaches [Kate and Mooney, 2009; Singla and

Mooney, 2011]

Logical inference in MLNs is deductive in nature MLN-PC [Kate and Mooney, 2009]

o Add reverse implications to handle abductive reasoningo Does not scale to large domains

MLN-HC [Singla and Mooney, 2011]

o Improves over MLN-PC by adding hidden causeso Still does not scale to large domains

MLN-HCAM [Singla and Mooney, 2011] uses logical abduction to constrain groundingo Incorporates ideas from the BLP approach for plan recognition

[Raghavan and Mooney, 2010]

o MLN-HCAM performs better than MLN-PC and MLN-HC

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BLPs for Plan Recognition

Why BLPs ?Directed model captures causal relationships wellEfficient grounding process results in smaller networks, unlike

in MLNs

SLD resolution is deductive inference, used for predicting observed actions from top-level plans

Plan recognition is abductive in nature and involves predicting the top-level plan from observed actions

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BLPs cannot be used as is for plan recognition

Extending BLPs for Plan Recognition

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BLPsBLPs Logical Abduction

Logical Abduction

BALPsBALPs

BALPs – Bayesian Abductive Logic Programs

Logical Abduction in BALPs

Given A set of observation literals O = {O1, O2,….On} and a

knowledge base KB

Compute a set abductive proofs of O using Stickel’s abduction algorithm [Stickel 1988]

Backchain on each Oi until it is proved or assumed

A literal is said to be proved if it unifies with a fact or the head of some rule in KB, otherwise it is said to be assumed

Construct a Bayesian network using the resulting set of proofs as in BLPs.

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Example – Intelligent User InterfacesTop-level plans predicates

copy-file, move-file, remove-file

Actions predicatescp, rm

Knowledge Base (KB)cp(filename,destdir) | copy-file(filename,destdir)cp(filename,destdir) | move-file(filename,destdir) rm(filename) | move-file(filename,destdir) rm(filename) | remove-file(filename)

Observed actionscp(Test1.txt, Mydir) rm(Test1.txt)

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Abductive Inference

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copy-file(Test1.txt,Mydir)

cp(Test1.txt,Mydir)

cp(filename,destdir) | copy-file(filename,destdir)

Assumed literalAssumed literal

Abductive Inference

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cp(Test1.txt,Mydir)

move-file(Test1.txt,Mydir)

cp(filename,destdir) | move-file(filename,destdir)


Abductive Inference

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cp(Test1.txt,Mydir)


rm(filename) | move-file(filename,destdir)

rm(Test1.txt)

Match existing assumptionMatch existing assumption

Abductive Inference

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cp(Test1.txt,Mydir)


rm(filename) | remove-file(filename)

rm(Test1.txt)

remove-file(Test1)


Structure of Bayesian network

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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Probabilistic Inference

Specifying probabilistic parametersNoisy-and

o Specify the CPT for combining the evidence from conjuncts in the body of the clause

Noisy-oro Specify the CPT for combining the evidence from

disjunctive contributions from different ground clauses with the same head

o Models “explaining away”Noisy-and and noisy-or models reduce the number of

parameters learned from data

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copy-file(Test1,txt,Mydir)

cp(Test1.txt,Mydir)

move-file(Test1,txt,Mydir)

rm(Test1.txt)

remove-file(Test1)

4 parameters

4 parameters


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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

2 parameters 2 parameters

θ1 θ2 θ3θ4

Noisy models require parameters linear in the number of parents


Most Probable Explanation (MPE)For multiple plans, compute MPE, the most likely

combination of truth values to all unknown literals given this evidence

Marginal ProbabilityFor single top level plan prediction, compute marginal

probability for all instances of plan predicate and pick the instance with maximum probability

When exact inference is intractable, SampleSearch [Gogate

and Dechter, 2007], an approximate inference algorithm for graphical models with deterministic constraints is used

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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Noisy-or Noisy-or


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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Noisy-or Noisy-or

Evidence


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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Noisy-or Noisy-or

Evidence

Query variables


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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Noisy-or Noisy-or

Evidence

Query variablesTRUE FALSEFALSE

MPE


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cp(Test1.txt,Mydir)


rm(Test1.txt)

remove-file(Test1)

Noisy-or Noisy-or

Evidence

Query variablesTRUE FALSEFALSE

MPE

Parameter Learning

Learn noisy-or/noisy-and parameters using the EM algorithm adapted for BLPs [Kersting and De Raedt, 2008]

Partial observability In plan recognition domain, data is partially observableEvidence is present only for observed actions and top-level

plans; sub-goals, noisy-or, and noisy-and nodes are not observed

Simplify learning problemLearn noisy-or parameters onlyUsed logical-and instead of noisy-and to combine evidence

from conjuncts in the body of a clause

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Experimental Evaluation

Monroe (Strategic planning)

Linux (Intelligent user interfaces)

Story Understanding (Story understanding)

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Monroe and Linux [Blaylock and Allen, 2005]

TaskMonroe involves recognizing top level plans in an

emergency response domain (artificially generated using HTN planner)

Linux involves recognizing top-level plans based on linux commands

Single correct plan in each example

Data

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No. examples

Avg. observations/ example

Total top-level plan predicates

Total observed action predicates

Monroe 1000 10.19 10 30

Linux 457 6.1 19 43

Monroe and Linux

MethodologyManually encoded the knowledge base Learned noisy-or parameters using EMComputed marginal probability for plan instances

Systems comparedBALPsMLN-HCAM [Singla and Mooney, 2011]

o MLN-PC and MLN-HC do not run on Monroe and Linux due to scaling issues

Blaylock and Allen’s system [Blaylock and Allen, 2005]

Performance metricConvergence score - measures the fraction of examples for

which the plan schema was predicted correctly

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Results on Monroe

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94.2 *

Co

nve

rgen

ce S

core

BALPs MLN-HCAM Blaylock & Allen

* - Differences are statistically significant wrt BALPs

Results on Linux

57

Co

nve

rgen

ce S

core

BALPs MLN-HCAM Blaylock & Allen

36.1 *

* - Differences are statistically significant wrt BALPs

Story Understanding [Charniak and Goldman, 1991; Ng and Mooney, 1992]

TaskRecognize character’s top level plans based on actions

described in narrative textMultiple top-level plans in each example

Data25 examples in development set and 25 examples in test

set12.6 observations per example8 top-level plan predicates

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Story UnderstandingMethodology

Knowledge base was created for ACCEL [Ng and Mooney, 1992]

Parameters set manuallyo Insufficient number of examples in the development set to learn

parameters

Computed MPE to get the best set of plans

Systems comparedBALPsMLN-HCAM [Singla and Mooney, 2011]

o Best performing MLN model

ACCEL-Simplicity [Ng and Mooney, 1992]

ACCEL-Coherence [Ng and Mooney, 1992]

o Specific for Story Understanding

59

Results on Story Understanding

60* - Differences are statistically significant wrt BALPs

Results on Story Understanding

61* - Differences are statistically significant wrt BALPs

* *

Summary of BALPs for Plan Recognition

Extend BLPs for plan recognition by employing logical abduction to construct Bayesian networks

Automatic learning of model parameters using EM

Empirical results on all benchmark datasets demonstrate advantages over existing methods

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Part 2Extending BLPs for Machine Reading

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Machine Reading

Machine reading involves automatic extraction of knowledge from natural language text

Information extraction (IE) systems extract factual information like entities and relations between entities that occur in text [Cohen, 1999; Craven et al., 2000; Bunescu and Mooney, 2007; Etzioni et al, 2008]

Extracted information can be used for answering queries automatically

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Limitations of IE Systems

Extract information that is stated explicitly in text Natural language text is not necessarily completeCommonsense information is not explicitly stated in textWell known facts are omitted from the text

Missing information cannot be inferred from textHuman brain performs deeper inference using

commonsense knowledge IE systems have no access to commonsense knowledge

Errors in extraction process result in some facts not being extracted

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Our Objective

Improve performance of IELearn general knowledge or commonsense information in

the form of rules using the facts extracted by the IE system

Infer additional facts that are not stated explicitly in text using the learned rules

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Example

67

“Malaysian Prime Minister Mahathir Mohamad Wednesday announced for the first time that he has appointed his deputy Abdullah Ahmad Badawi as his successor.’’


Example

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“Malaysian Prime Minister Mahathir Mohamad Wednesday announced for the first time that he has appointed his deputy Abdullah Ahmad Badawi as his successor."


Extracted facts

nationState(malaysian)Person(mahathir-mohamad)isLedBy(malaysian,mahathir-mohamad)

Extracted facts


Example

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Query

isLedBy(X,Y)

Query

isLedBy(X,Y)

Extracted facts


Extracted facts


Example

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Extracted facts

nationState(malaysian)Person(mahathir-mohamad)isLedBy(malaysian,mahatir-mohamad)

Extracted facts


Query

isLedBy(X,Y)

Query

isLedBy(X,Y)X = malaysian

Y = mahathir-mohamadX = malaysian

Y = mahathir-mohamad

Example

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Query

citizenOf(mahathir-mohamad,Y)

Query


Extracted facts


Extracted facts


Example

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Extracted facts


Extracted facts


Query


Query


Y = ?Y = ?

Related Work

Learning propositional rules [Nahm and Mooney, 2000]

Learn propositional rules from the output of an IE system on computer-related job postings

Perform deductive inference to infer new facts

Learning first-order rules [Carlson at el., 2010, Schoenmackers et al., 2010; Doppa et al., 2010]

Carlson et al. and Doppa et al. modify existing rule learners like FOIL and FARMER to learn probabilistic ruleso Perform deductive inference to infer additional facts

Schoenmackers et al. develop a new first-order rule learner based on statistical relevanceo Use MLN based approach to infer additional facts

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Our Approach

Use an off-the shelf IE system to extract factsLearn commonsense knowledge from the extracted

facts in the form of first-order-rulesInfer additional facts based on the learned rules

using BLPsPure logical deduction results in inferring a large number of

facts Inference using BLPs is probabilistic in nature, i.e inferred facts

are assigned probabilities. Probabilities can be used to filter out facts with high confidence from the rest

Efficient grounding mechanism in BLPs enables our approach to scale to natural language text

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Extending BLPs for Machine Reading

SLD resolution does not result in inference of new factsGiven a query, SLD resolution will generated deductive

proofs that prove the query

Employ forward chaining to infer additional factsForward chain on extracted facts to infer new facts

Use the deductive proofs from forward chaining to construct Bayesian network for probabilistic inference

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Learning First-order Rules

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“Barack Obama is the current President of USA……. Obama was born on August 4, 1961, in Hawaii, USA…….’’

“Barack Obama is the current President of USA……. Obama was born on August 4, 1961, in Hawaii, USA…….’’

Extracted facts

nationState(USA)Person(BarackObama)isLedBy(USA,BarackObama)hasBirthPlace(BarackObama,USA)citizenOf(BarackObama,USA)

Extracted facts

nationState(USA)Person(BarackObama)isLedBy(USA,BarackObama)hasBirthPlace(BarackObama,USA)citizenOf(BarackObama,USA)

Learning Patterns from Extracted Facts

nationState(USA) ∧ isLedBy(USA,BarackObama)

citizenOf(BarackObama,USA)

nationState(USA) ∧ isLedBy(USA,BarackObama)

hasBirthPlace(BarackObama,USA)

hasBirthPlace(BarackObama,USA)

citizenOf(BarackObama,USA)

.

.

.

.

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Generalizing Patterns to Rules

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nationState(Y) ∧ isLedBy(Y,X) citizenOf(X,Y)

nationState(Y) ∧ isLedBy(Y,X) hasBirthPlace(X,Y)

hasBirthPlace(X,Y) citizenOf(X,Y)

nationState(Y) ∧ isLedBy(Y,X) citizenOf(X,Y)

nationState(Y) ∧ isLedBy(Y,X) hasBirthPlace(X,Y)

hasBirthPlace(X,Y) citizenOf(X,Y)

Inductive Logic Programming (ILP)[Muggleton, 1992]

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ILP Rule Learner

ILP Rule Learner

Target relationcitizenOf(X,Y)

Positive instancescitizenOf(BarackObama, USA)citizenOf(GeorgeBush, USA)citizenOf(IndiraGandhi,India)

.

.

Negative instancescitizenOf(BarackObama, India)citizenOf(GeorgeBush, India)citizenOf(IndiraGandhi,USA)

.

.

KBhasBirthPlace(BarackObama,USA)person(BarackObama)nationState(USA)nationState(India)

.

.

RulesnationState(Y) ∧ isLedBy(Y,X) citizenOf(X,Y)

..

RulesnationState(Y) ∧ isLedBy(Y,X) citizenOf(X,Y)

..

Example

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Extracted facts


Extracted facts


Learned rule

nationState(B) ∧ isLedBy(B,A) citizenOf(A,B)

Learned rule

nationState(B) ∧ isLedBy(B,A) citizenOf(A,B)



Inference of Additional Facts

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nationState(B) ∧ isLedBy(B,A) citizenOf(A,B)nationState(B) ∧ isLedBy(B,A) citizenOf(A,B)

nationState(malaysian)nationState(malaysian) isLedBy(malaysian,mahathir-mohamad)isLedBy(malaysian,mahathir-mohamad)

citizenOf(mahathir-mohamad, malaysian)citizenOf(mahathir-mohamad, malaysian)


DataDARPA’s intelligent community (IC) data setConsists of news articles on politics, terrorism, and others

international events2000 documents, split into training and test in the ratio 9:1Approximately 30,000 sentences

Information Extraction Information extraction using SIRE, IBM’s information

extraction system [Florin et al., 2004]

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Experimental EvaluationLearning first-order rules using LIME [McCreath and Sharma,

1998]

Learns rules from only positive instancesHandles noise in data

ModelsBLP-Pos-Only

o Learn rules using only positive instancesBLP-Pos-Neg

o Learn rules using both positive and negative instanceso Apply closed world assumption to automatically generate

negative instancesBLP-All

o Includes rules learned from BLP-Pos-Only and BLP-Pos-Neg

83


Specifying probabilistic parametersManually specified parametersLogical-and model to combine evidence from conjuncts in

the body of the clauseSet noisy-or parameters to 0.9Set priors to maximum likelihood estimates

84

Experimental EvaluationMethodology

Learned rules for 13 relations including hasCitizenship, hasMember, attendedSchool

Baseline o Perform pure logical deduction to infer all possible

additional factsBLP-0.9

o Facts inferred using the BLP approach with marginal probability greater or equal to 0.9

BLP-0.95o Facts inferred using the BLP approach with marginal

probability greater or equal to 0.95

85

Performance Evaluation

Precision Evaluate if the inferred facts are correct, i.e if they can be

inferred from the documento No ground truth information availableo Perform manual evaluationo Sample 20 documents randomly from the test set and

evaluate inferred facts manually for all models

86

Precision (preliminary results)

Model BLP-ALL BLP-Pos-Neg BLP-Pos-Only

Baseline – Purely logical approach [No. facts inferred]

3813 75 1849

Precision 24.94 16.00 31.80

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3813 75 1849

Precision 24.94 16.00 31.80

BLP-0.9 [No. facts inferred] 1208 66 1158

Precision 34.68 13.63 35.49

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3813 75 1849

Precision 24.94 16.00 31.80

BLP-0.9 [No. facts inferred] 1208 66 1158Precision 34.68 13.63 35.49

BLP-0.95 [No. of facts inferred] 56 1 0Precision 91.07 100 Nil

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Performance Evaluation

Estimated recallFor each target relation, eliminate instances of it from the

extracted facts in the test setTry to infer the eliminated instances correctly based on the

remaining facts using the BLP approach o For each threshold point (0.1 to 1), compute fraction of

eliminated instances that were inferred correctlyo True recall cannot be calculated because of lack of

ground truth

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Estimated Recall (preliminary results)

91

Est

imat

ed r

ecal

l

Confidence threshold


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Est

imat

ed r

ecal

l



93

Est

imat

ed r

ecal

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Est

imat

ed r

ecal

l


First-order Rules from LIME

politicalParty(A) ^ employs(A,B) hasMemberPerson(A,B)

building(B) ^ eventLocation(A,B) ^ bombing(A) thingPhysicallyDamaged(A,B)

employs(A,B) hasMember(A,B)

citizenOf(A,B) hasCitizenship(A,B)

nationState(B) ^ person(A) ^ employs(B,A) hasBirthPlace(A,B)

95

Proposed WorkLearning parameters automatically from data

EM or gradient-ascent based algorithm adapted for BLPs by Kersting and De Raedt [2008]

EvaluationHuman evaluation for inferred facts using Amazon

Mechanical Turk [Callison-Burch and Dredze, 2010]

Use inferred facts to answer queries constructed for evaluation in the DARPA sponsored machine reading project

Comparison to existing approaches like MLNs

Develop a structure learner for incomplete and uncertain data

96

Future ExtensionsMultiple predicate learning

Learn rules for multiple relations at the same time

Discriminative parameter learning for BLPsEM and gradient-ascent based algorithms for learning BLP

parameters optimize likelihood of the dataNo algorithm that learns parameters discriminatively for

BLPs has been developed to date

Comparison of BALPs to other probabilistic logics for plan recognitionComparison to PRISM [Sato, 1995], Poole’s Horn Abduction

[Poole, 1993], Abductive Stochastic Logic Programs [Tammadoni-Nezhad et al., 2006]

97

Conclusions

Extended BLPs to abductive plan recognitionEnhance BLPs with logical abduction, resulting in

Bayesian Abductive Logic Programs (BALPs)BALPs outperform state-of-the-art approaches to plan

recognition on several benchmark data sets

Extended BLPs to machine readingPreliminary results on the IC data set are encouragingPerform an extensive evaluation in immediate futureDevelop a first-order rule learner that learns from

incomplete and uncertain data in future

98

Questions

99

Backup

100

Timeline Additional experiments comparing MLN-HCAM and

BALPs for plan recognition [Target completion – August 2011] Use Sample Search to perform inference in MLN-HCAM

Evaluation of BLPs for Machine Reading [Target completion – November 2011]

Learn parameters automatically Evaluation using Amazon Mechanical Turk Evaluation of BLPs for answering queries Comparison of BLPs with MLNs for machine reading Developing structure learner from positive and uncertain

examples [Target completion – May 2012]

Proposed defense and graduation [August 2012] 101

Completeness in First-order Logic

Completeness - If a sentence is entailed by a KB, then it is possible to find the proof that entails it

Entailment in first-order logic is semidecidable, i.e it is not possible to know if a sentence is entailed by a KB or not

Resolution is complete in first-order logic If a set of sentences is unsatisfiable, then it is possible to

find a contradiction

102

Forward chaining

For every implication pq, if p is true, then q is concluded to be true

Results in addition of a new fact to KBEfficient, but incompleteInference can explode and forward chaining may

never terminateAddition of new facts might result in rules being satisfied

It is data-driven, not goal-drivenMight result in irrelevant conclusions

103

Backward chaining

For a query literal q, if an implication pq is present and p is true, then q is concluded to be true, otherwise backward chaining tries to prove p

Efficient, but not completeMay never terminate, might get stuck in infinite

loopExponentialGoal-driven

104

Herbrand Model Semantics

Herbrand universeAll constants in the domain

Herbrand baseAll ground atoms atoms over Herbrand universe

Herbrand interpretationA set of ground atoms from Herbrand base that are true

Herbrand modelHerbrand interpretation that satisfies all clauses in the

knowledge base

105

Advantages of SRL models over vanilla probabilistic models

Compactly represent domain knowledge in first-order logic

Employ logical inference to construct ground networks

Enables parameter sharing

106

Parameter sharing in SRL

107

father(john)father(john)

parent(john)parent(john)

father(mary)father(mary)

parent(mary)parent(mary)

father(alice)father(alice)

parent(alice)parent(alice)

dummydummy

θ1θ1 θ2θ2 θ3θ3

Parameter sharing in SRL

father(X) parent(X)

108

father(john)father(john)

parent(john)parent(john)

father(mary)father(mary)

parent(mary)parent(mary)

father(alice)father(alice)

parent(alice)parent(alice)

dummydummy

θθ θθ θθ

θθ

Noisy-and Model

Several causes ci have to occur simultaneously if event e has to occur

ci fails to trigger e with probability pi

inh accounts for some unknown cause due to which e has failed to trigger

P(e) = (I – inh) Πi(1-pi)^(1-ci)

109

Noisy-or Model

Several causes ci cause event e has to occur

ci independently triggers e with probability pi

leak accounts for some unknown cause due to which e has triggered

P(e) = 1 – [(I – inh) Πi (1-pi)^(1-ci)]

Models explaining away If there are several causes of an event, and if there is

evidence for one of the causes, then the probability that the other causes have caused the event goes down

110

Noisy-and And Noisy-or Models

111

alarm(james)

burglary(james)

neighborhood(james)


Noisy-and And Noisy-or Models

112alarm(james)

burglary(james)

neighborhood(james)


dummy1 dummy2

Noisy/logical-and

Noisy/logical-andNoisy/logical-and

Noisy-or

Inference in BLPs[Kersting and De Raedt, 2001]

Logical inferenceGiven a BLP and a query, SLD resolution is used to construct

proofs for the query

Bayesian network constructionEach ground atom is a random variableEdges are added from ground atoms in the body to the ground

atom in headCPTs specified by the conditional probability distribution for the

corresponding clauseP(X) = P(Xi | Pa(Xi))

Probabilistic inferenceMarginal probability given evidenceMost Probable Explanation (MPE) given evidence

113€

i

∏

Learning in BLPs[Kersting and De Raedt, 2008]

Parameter learningExpectation Maximization Gradient-ascent based learningBoth approaches optimize likelihood

Structure learningHill climbing search through the space of possible

structures Initial structure obtained from CLAUDIEN [De Raedt and

Dehaspe, 1997]

Learns from only positive examples

114

Expectation Maximization for BLPs/BALPs

• Perform logical inference to construct a ground Bayesian network for each example

• Let r denote rule, X denote a node, and Pa(X) denote parents of X

• E Step

• The inner sum is over all groundings of rule r

• M Step

115

*

*

* From SRL tutorial at ECML 07 115

Decomposable Combining Rules

Express different influences using separate nodes

These nodes can be combined using a deterministic function

116

Combining Rules

117alarm(james)

burglary(james)

neighborhood(james)


dummy1 dummy2

Logical-and

Logical-andLogical-and

Noisy-or

Decomposable Combining Rules

118alarm(james)

burglary(james)

neighborhood(james)


dummy1 dummy2

Logical-and

Logical-andLogical-and

Noisy-or Noisy-or

dummy1-new dummy2 -new

Logical-or

BLPs vs. PLPs

Differences in representation In BLPs, Bayesian atoms take finite set of values, but in

PLPs, each atom is logical in nature and it can take true or false

Instead of having neighborhood(x) = bad, in PLPs, we have neighborhood(x,bad)

To compute probability of a query alarm(james), PLPs have to construct one proof tree for all possible values for all predicates

Inference is cumbersome

BLPs subsume PLPs

119

BLPs vs. Poole's Horn Abduction

Differences in representationFor example, if P(x) and R(x) are two competing

hypothesis, then either P(x) could be true or R(x) could be true

Prior probabilities of P(x) and R(x) should sum to 1 Restrictions of these kind are are not these in BLPsPLPs and hence BLPs are more flexible and have a richer

representation

120

BLPs vs. PRMs

BLPs subsume PRMsPRMs use entity-relationship models to represent

knowledge and they use KBMC-like construction to construct a ground Bayesian networkEach attribute becomes a random variable in the ground

network and relations over the entities are logical constraints In BLP, each attribute becomes a Bayesian atom and

relations become logical atoms Aggregator functions can be transformed into combining

rules

121

BLPs vs. RBNs

BLPs subsume RBNs In RBNs, each node in BN is a predicate and

probability formulae are used to specify probabilitiesCombining rules can be used to represent these

probability formulae in BLPs.

122

BALPs vs. BLPs

Like BLPs, BALPs use logic programs as templates for constructing Bayesian networks

Unlike BLPs, BALPs uses logical abduction instead of deduction to construct the network

123

Monroe [Blaylock and Allen, 2005]

TaskRecognize top level plans in an emergency response

domain (artificially generated using HTN planner)Plans include set-up-shelter, clear-road-wreck, provide-

medical-attentionSingle correct plan in each exampleDomain consists of several entities and sub-goalsTest the ability to scale to large domains

DataContains 1000 examples

124

Monroe

MethodologyKnowledge base constructed based on the domain knowledge

encoded in plannerLearn noisy-or parameters using EMCompute marginal probability for instances of top level plans

and pick the one with the highest marginal probabilitySystems compared

o BALPso MLN-HCAM [Singla and Mooney, 2011]

o Blaylock and Allen’s system [Blaylock and Allen, 2005]

Convergence score - measures the fraction of examples for which the plan schema was predicted correctly

125

Learning Results - Monroe

126

MW MW-Start Rand-Start

Conv Score 98.4 98.4 98.4

Acc-100 79.16 79.16 79.86

Acc-75 46.06 44.63 44.73

Acc-50 20.67 20.26 19.7

Acc-25 7.2 7.33 10.46

Linux [Blaylock and Allen, 2005]

TaskRecognize top level plans based on Linux commandsHuman users asked to perform tasks in Linux and commands

were recordedTop-level plans include find-file-by-ext, remove-file-by-ext,

copy-file, move-fileSingle correct plan in each exampleTests the ability to handle noise in data

o Users indicate success even when they have not achieved the task correctly

o Some top-level plans like find-file-by-ext and file-file-by-name have identical actions

DataContains 457 examples

127

Linux

MethodologyKnowledge base constructed based on the knowledge of Linux

commandsLearn noisy-or parameters using EMCompute marginal probability for instances of top level plans

and pick the one with the highest marginal probabilitySystems compared


o Blaylock and Allen’s system [Blaylock and Allen, 2005]

Convergence score - measures the fraction of examples for which the plan schema was predicted correctly o

128

Learning Results - Linux

129

Acc

ura

cy

Partial Observability

MW MW-Start Rand-Start

Conv Score 39.82 46.6 41.57

Story Understanding [Charniak and Goldman, 1991; Ng and Mooney, 1992]

TaskRecognize character’s top level plans based on actions

described in narrative textLogical representation of actions literals providedTop-level plans include shopping, robbing, restaurant

dining, partying Multiple top-level plans in each exampleTests the ability to predict multiple plans

Data25 development examples25 test examples

130

Story UnderstandingMethodology

Knowledge base constructed for ACCEL by Ng and Mooney [1992]

Insufficient number of examples to learn parameterso Noisy-or parameters set to 0.9o Noisy-and parameters set to 0.9o Priors tuned on development set

Compute MPE to get the best set of plansSystems compared


o ACCEL-Simplicity [Ng and Mooney, 1992]

o ACCEL-Coherence [Ng and Mooney, 1992]

– Specific for Story Understanding

131

Other Applications of BALPs

Medical diagnosisTextual entailmentComputational biology

Inferring gene relations based on the output of micro-array experiments

Any application that requires abductive reasoning

132

ACCEL[Ng and Mooney, 1992]

First-order logic based system for plan recognition

Simplicity metric selects explanations that have the least number of assumptions

Coherence metric selects explanations that connect maximum number of observationsMeasures explanatory coherenceSpecific to text interpretation

133

System by Blaylock and Allen[2005]

Statistical n-gram models to predict plans based on observed actions

Performs plan recognition in two phasesPredicts the plan schema firstPredicts arguments based on the predicted schema

134

Machine Reading

Machine reading involves automatic extraction of knowledge from natural language text

Approaches to machine readingExtract factual information like entities and relations

between entities that occur in text [Cohen, 1999; Craven et al., 2000; Bunescu and Mooney, 2007; Etzioni et al, 2008]

Extract commonsense knowledge about the domain [Nahm and Mooney, 2000; Carlson at el., 2010, Schoenmackers et al., 2010; Doppa et al., 2010]

135

Natural Language Text

Natural language text is not necessarily completeCommonsense information is not explicitly stated in textWell known facts are omitted from the text

Missing information has to be inferred from textHuman brain performs deeper inference using

commonsense knowledge IE systems have no access to commonsense knowledge

136

IE systems are limited to extracting information stated explicitly in text

IC ontology

57 entities 79 relations

137

Estimated Precision (preliminary results)


Baseline [No. facts inferred] 38,151 1,510 18,501

Estimated precision 24.94 (951/3813)*

16.00 (12/75)*

31.80 (588/1849)*

138

Total facts extracted – 12,254* - x out of y inferred facts were correct. These inferred facts are from the 20 randomly sampled documents from test set for manual evaluation



Baseline [No. facts inferred] 38,151 1,510 18,501


16.00 (12/75)*

31.80 (588/1849)*

BLP-0.9 [No. facts inferred] 12,823 880 11,717


13.63 (9/66)*

35.49 (411/1158)*

139




Baseline [No. facts inferred] 38,151 1,510 18,501Estimated precision 24.94

(951/3813)*16.00 (12/75)*

31.80 (588/1849)*

BLP-0.9 [No. facts inferred] 12,823 880 11,717Estimated precision 34.68

(419/1208)*13.63 (9/66)*

35.49 (411/1158)*

BLP-0.95 [No. of facts inferred] 826 119 49Estimated precision 91.07

(51/56)*100 (1/1)*

Nil(0/0)*

140


Estimated Recall

141

“Barack Obama is the current President of USA……. Obama was born on August 4, 1961, in Hawaii, USA……."

“Barack Obama is the current President of USA……. Obama was born on August 4, 1961, in Hawaii, USA……."

Extracted facts

nationState(USA) hasBirthPlace(BarackObama,USA)Person(BarackObama) citizenOf(BarackObama,USA)isLedBy(USA,BarackObama)

Extracted facts


Rule

hasBirthPlace(A,B) citizenOf(A,B)

Rule

hasBirthPlace(A,B) citizenOf(A,B)

Estimated Recall for citizenOf

142

Extracted facts


Extracted facts


hasBirthPlace(A,B) citizenOf(A,B)hasBirthPlace(A,B) citizenOf(A,B)

hasBirthPlace(BarackObama,USA)hasBirthPlace(BarackObama,USA)

citizenOf(BarackObama,USA)citizenOf(BarackObama,USA)Estim

ated Recall – 1/1

Estimated Recall – 1/1

Estimated Recall for hasBirthPlace

143

Extracted facts


Extracted facts


hasBirthPlace(A,B) citizenOf(A,B)hasBirthPlace(A,B) citizenOf(A,B)



??

Proposed WorkLearn first-order rules from incomplete and uncertain

dataFacts extracted from natural language text are incomplete

o Existing rule/structure learners assume that data is completeExtractions from IE system have associated confidence scores

o Existing structure learners cannot use these extraction probabilities

Absence of negative instanceso Most rule learners require both positive and negative

instanceso Closed world assumption does not hold for machine reading

144

extending bayesian logic programs for plan recognition and machine reading sindhu v. raghavan...

Documents

bayesian networkswhy

plan recognitionblps

plan recognitionpart

toplevel plan

yground literal literal

machine readingobjectives

ypredicates relations

domainseveral relations