Abductive Plan Recognition By Extending Bayesian Logic Programs
Sindhu V. Raghavan & Raymond J. Mooney
The University of Texas at Austin
1
Plan RecognitionPredict an agent’s top-level plans based on the
observed actions
Abductive reasoning involving inference of cause from effect
ApplicationsStory UnderstandingStrategic Planning Intelligent User Interfaces
2
$ cd test-dir$ cp test1.txt my-dir$ rm test1.txt
$ cd test-dir$ cp test1.txt my-dir$ rm test1.txtWhat task is the user performing?move-file
Which files and directories are involved?test1.txt and test-dir
Plan Recognition in Intelligent User Interfaces
3
Data is relational in nature - several files and directories and several relations between them
Related WorkFirst-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 actions Unable 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
Statistical Relational Learning based approaches Markov Logic Networks for plan recognition [Kate and Mooney, 2009;
Singla and Mooney, 2011]
4
Our Approach
Extend Bayesian Logic Programs (BLPs) [Kersting and
De Raedt, 2001] for plan recognitionBLPs 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
5
Outline
MotivationBackground
Logical AbductionBayesian Logic Programs (BLPs)
Extending BLPs for Plan RecognitionExperimentsConclusions
6
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
7
Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001]
Set of Bayesian clauses a|a1,a2,....,an
Definite clauses that are universally quantifiedRange-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.
8
€
⊆
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
9€
i
∏
BLPs for Plan Recognition
SLD resolution is deductive inference, used for predicting observations from top-level plans
Plan recognition is abductive in nature and involves predicting the top-level plan from observations
10
BLPs cannot be used as is for plan recognition
Extending BLPs for Plan Recognition
11
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.
12
Example – Intelligent User InterfacesTop-level plan predicates
copy-file, move-file, remove-file
Action 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)
13
Abductive Inference
14
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
cp(Filename,Destdir) | copy-file(Filename,Destdir)
Assumed literalAssumed literal
Abductive Inference
15
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
cp(Filename,Destdir) | move-file(Filename,Destdir)
Assumed literalAssumed literal
Abductive Inference
16
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(Filename) | move-file(Filename,Destdir)
rm(test1.txt)
Match existing assumptionMatch existing assumption
Abductive Inference
17
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(Filename) | remove-file(Filename)
rm(test1.txt)
remove-file(test1)
Assumed literalAssumed literal
Structure of Bayesian network
18
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(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
19
Probabilistic Inference
20
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(test1.txt)
remove-file(test1)
Noisy-or Noisy-or
Probabilistic Inference
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
21
Probabilistic Inference
22
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(test1.txt)
remove-file(test1)
Noisy-or Noisy-or
Probabilistic Inference
23
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(test1.txt)
remove-file(test1)
Noisy-or Noisy-or
Evidence
Probabilistic Inference
24
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(test1.txt)
remove-file(test1)
Noisy-or Noisy-or
Evidence
Query variables
Probabilistic Inference
25
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(test1.txt,mydir)
rm(test1.txt)
remove-file(test1)
Noisy-or Noisy-or
Evidence
Query variablesTRUE FALSEFALSE
MPE
Probabilistic Inference
26
copy-file(test1.txt,mydir)
cp(test1.txt,mydir)
move-file(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
27
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 predicate was predicted correctly
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Results on Monroe
31
94.2 *
Co
nve
rgen
ce S
core
BALPs MLN-HCAM Blaylock & Allen
* - Differences are statistically significant wrt BALPs
Results on Linux
32
Co
nve
rgen
ce S
core
BALPs MLN-HCAM Blaylock & Allen
36.1 *
* - Differences are statistically significant wrt BALPs
Experiments with partial observability Limitations of convergence score
Does not account for predicting the plan arguments correctly
Requires all the observations to be seen before plans can be predicted
Early plan recognition with partial set of observationsPerform plan recognition after observing the first 25%,
50%, 75%, and 100% of the observationsAccuracy – Assign partial credit for the predicting plan
predicate and a subset of the arguments correctly
Systems comparedBALPsMLN-HCAM [Singla and Mooney, 2011]
33
Results on Monroe
34Percent observations seen
Ac
cu
rac
y
Results on Linux
35
Ac
cu
rac
y
Percent observations seen
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
36
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
37
Results on Story Understanding
38* - Differences are statistically significant wrt BALPs
* *
Conclusion
BALPS – Extension of 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
39
Future Work
Learn abductive knowledge base automatically from data
Compare BALPs with other probabilistic logics like ProbLog [De Raedt et. al, 2007], PRISM [Sato, 1995] and Poole’s Horn Abduction [Poole, 1993] on plan recognition
40
Questions
41
Backup
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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
43
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
44
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
45
€
∀( )
€
∃( )
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
46
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
47
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
48
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
49
Parameter sharing in SRL
50
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)
51
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)
52
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
53
Noisy-and And Noisy-or Models
54
alarm(james)
burglary(james)
neighborhood(james)
lives(james,yorkshire) tornado(yorkshire)
Noisy-and And Noisy-or Models
55alarm(james)
burglary(james)
neighborhood(james)
lives(james,yorkshire) tornado(yorkshire)
dummy1 dummy2
Noisy/logical-and
Noisy/logical-andNoisy/logical-and
Noisy-or
Logical Inference in BLPs SLD Resolution
56
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
Logical Inference in BLPs SLD Resolution
57
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)
burglary(james)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
58
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)
burglary(james)
neighborhood(james)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
59
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)
burglary(james)
neighborhood(james)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
60
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)
burglary(james)
neighborhood(james)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
61
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)
burglary(james)
neighborhood(james)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
62
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)
burglary(james)
neighborhood(james)
lives(james,Y) tornado(Y)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
63
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)
burglary(james)
neighborhood(james)
lives(james,Y) tornado(Y)
lives(james,yorkshire)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
64
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)
burglary(james)
neighborhood(james)
lives(james,Y) tornado(Y)
lives(james,yorkshire)
tornado(yorkshire)
Example from Ngo and Haddawy, 1997
Logical Inference in BLPs SLD Resolution
65
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)
burglary(james)
neighborhood(james)
lives(james,Y) tornado(Y)
lives(james,yorkshire)
tornado(yorkshire)
Example from Ngo and Haddawy, 1997
Bayesian Network Construction
66
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
Bayesian Network Construction
67
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
Bayesian Network Construction
68
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
Bayesian Network Construction
69
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
Use combining rule to combine multiple CPTs into a single CPT
lives(stefan,freiburg)✖
Probabilistic Inference
70
copy-file(Test1,txt,Mydir)
cp(Test1.txt,Mydir)
move-file(Test1,txt,Mydir)
rm(Test1.txt)
remove-file(Test1)
4 parameters
4 parameters
Probabilistic Inference
71
copy-file(Test1,txt,Mydir)
cp(Test1.txt,Mydir)
move-file(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
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
72
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
73
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
74
*
*
* From SRL tutorial at ECML 07 74
Decomposable Combining Rules
Express different influences using separate nodes
These nodes can be combined using a deterministic function
75
Combining Rules
76alarm(james)
burglary(james)
neighborhood(james)
lives(james,yorkshire) tornado(yorkshire)
dummy1 dummy2
Logical-and
Logical-andLogical-and
Noisy-or
Decomposable Combining Rules
77alarm(james)
burglary(james)
neighborhood(james)
lives(james,yorkshire) tornado(yorkshire)
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
78
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 not there in BLPsPLPs and hence BLPs are more flexible and have a richer
representation
79
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
80
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.
81
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
82
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
83
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
84
Learning Results - Monroe
85
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
86
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 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 o
87
Learning Results - Linux
88
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
89
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 BALPso MLN-HCAM [Singla and Mooney, 2011]
o ACCEL-Simplicity [Ng and Mooney, 1992]
o ACCEL-Coherence [Ng and Mooney, 1992]
– Specific for Story Understanding
90
Results on Story Understanding
91* - Differences are statistically significant wrt BALPs
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
92
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
93
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
94
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