Abductive Plan Recognition By Extending Bayesian Logic Programs

Abductive Plan Recognition By Extending Bayesian Logic Programs Sindhu V. Raghavan & Raymond J. Mooney The University of Texas at Austin 1

Plan Recognition q Predict an agent’s top-level plans based on the observed actions q Abductive reasoning involving inference of cause from effect q Applications ² Story Understanding ² Strategic Planning ² Intelligent User Interfaces 2

Plan Recognition in Intelligent User Interfaces $ cd test-dir $ cp test 1. txt my-dir $ rm test 1. txt What task is the user performing? move-file Which files and directories are involved? test 1. txt and test-dir Data is relational in nature - several files and directories and several relations between them 3

Related Work q First-order logic based approaches [Kautz and Allen, 1986; Ng and Mooney, 1992] ² Knowledge base of plans and actions ² Default reasoning or logical abduction to predict the best plan based on the observed actions ² Unable to handle uncertainty in data or estimate likelihood of alternative plans q Probabilistic graphical models [Charniak and Goldman, 1989; Huber et al. , 1994; Pynadath and Wellman, 2000; Bui, 2003; Blaylock and Allen, 2005] ² Encode the domain knowledge using Bayesian networks, abstract hidden Markov models, or statistical n-gram models ² Unable to handle relational/structured data q Statistical Relational Learning based approaches ² Markov Logic Networks for plan recognition Singla and Mooney, 2011] [Kate and Mooney, 2009; 4

Our Approach q Extend Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001] for plan recognition q BLPs integrate first-order logic and Bayesian networks q Why BLPs? ² Efficient grounding mechanism that includes only those variables that are relevant to the query ² Easy to extend by incorporating any type of logical inference to construct networks ² Well suited for capturing causal relations in data 5

Outline ü Motivation q Background ² Logical Abduction ² Bayesian Logic Programs (BLPs) q Extending BLPs for Plan Recognition q Experiments q Conclusions 6

Logical Abduction q Abduction ² Process of finding the best explanation for a set of observations q Given ² Background knowledge, B, in the form of a set of (Horn) clauses in first-order logic ² Observations, O, in the form of atomic facts in first-order logic q Find ² A hypothesis, H, a set of assumptions (atomic facts) that logically entail the observations given theory: B H O ² Best explanation is the one with the fewest assumptions 7

Bayesian Logic Programs (BLPs) [Kersting and De Raedt, 2001] q Set of Bayesian clauses a|a 1, a 2, . . , an ² Definite clauses that are universally quantified ² Range-restricted, i. e variables{head} variables{body} ² Associated conditional probability table (CPT) o P(head|body) q Bayesian predicates a, a 1, a 2, …, an have finite domains ² Combining rule like noisy-or for mapping multiple CPTs into a single CPT. 8

Inference in BLPs [Kersting and De Raedt, 2001] q Logical inference ² Given a BLP and a query, SLD resolution is used to construct proofs for the query q Bayesian network construction ² Each ground atom is a random variable ² Edges are added from ground atoms in the body to the ground atom in head ² CPTs specified by the conditional probability distribution for the corresponding clause ² P(X) = P(Xi | Pa(Xi)) q Probabilistic inference ² Marginal probability given evidence ² Most Probable Explanation (MPE) given evidence 9

BLPs for Plan Recognition q SLD resolution is deductive inference, used for predicting observations from top-level plans q Plan recognition is abductive in nature and involves predicting the top-level plan from observations BLPs cannot be used as is for plan recognition 10

Extending BLPs for Plan Recognition BLPs + Logical Abduction = BALPs – Bayesian Abductive Logic Programs 11

Logical Abduction in BALPs q Given ² A set of observation literals O = {O 1, O 2, …. On} and a knowledge base KB q Compute a set abductive proofs of O using Stickel’s abduction algorithm [Stickel 1988] ² Backchain on each Oi until it is proved or assumed ² 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 q Construct a Bayesian network using the resulting set of proofs as in BLPs. 12

Example – Intelligent User Interfaces q Top-level plan predicates ² copy-file, move-file, remove-file q Action predicates ² cp, rm q Knowledge Base (KB) ² cp(Filename, Destdir) | copy-file(Filename, Destdir) ² cp(Filename, Destdir) | move-file(Filename, Destdir) ² rm(Filename) | remove-file(Filename) q Observed actions ² cp(test 1. txt, mydir) ² rm(test 1. txt) 13

Abductive Inference Assumed literal copy-file(test 1. txt, mydir) cp(Filename, Destdir) | copy-file(Filename, Destdir) 14

Abductive Inference Assumed literal copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) cp(Filename, Destdir) | move-file(Filename, Destdir) 15

Abductive Inference Match existing assumption copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) cp(test 1. txt, mydir) rm(test 1. txt) rm(Filename) | move-file(Filename, Destdir) 16

Abductive Inference Assumed literal copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) cp(test 1. txt, mydir) rm(test 1. txt) rm(Filename) | remove-file(Filename) 17

Structure of Bayesian network copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) cp(test 1. txt, mydir) rm(test 1. txt) 18

Probabilistic Inference q Specifying probabilistic parameters ² Noisy-and o Specify the CPT for combining the evidence from conjuncts in the body of the clause ² Noisy-or o Specify the CPT for combining the evidence from disjunctive contributions from different ground clauses with the same head o Models “explaining away” ² Noisy-and noisy-or models reduce the number of parameters learned from data 19

Probabilistic Inference copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) Noisy-or cp(test 1. txt, mydir) Noisy-or rm(test 1. txt) 20

Probabilistic Inference q Most Probable Explanation (MPE) ² For multiple plans, compute MPE, the most likely combination of truth values to all unknown literals given this evidence q Marginal Probability ² For single top level plan prediction, compute marginal probability for all instances of plan predicate and pick the instance with maximum probability ² When exact inference is intractable, Sample. Search [Gogate and Dechter, 2007], an approximate inference algorithm for graphical models with deterministic constraints is used 21

Probabilistic Inference copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) Noisy-or cp(test 1. txt, mydir) Noisy-or rm(test 1. txt) 22

Probabilistic Inference copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) Noisy-or cp(test 1. txt, mydir) Noisy-or rm(test 1. txt) Evidence 23

Probabilistic Inference Query variables copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) Noisy-or cp(test 1. txt, mydir) Noisy-or rm(test 1. txt) Evidence 24

Probabilistic Inference MPE Query variables FALSE TRUE copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) remove-file(test 1) Noisy-or cp(test 1. txt, mydir) Noisy-or rm(test 1. txt) Evidence 25

Probabilistic Inference MPE Query variables FALSE TRUE copy-file(test 1. txt, mydir) move-file(test 1. txt, mydir) Noisy-or cp(test 1. txt, mydir) remove-file(test 1) Noisy-or rm(test 1. txt) Evidence 26

Parameter Learning q Learn noisy-or/noisy-and parameters using the EM algorithm adapted for BLPs [Kersting and De Raedt, 2008] q Partial observability ² In plan recognition domain, data is partially observable ² Evidence is present only for observed actions and top-level plans; sub-goals, noisy-or, and noisy-and nodes are not observed q Simplify learning problem ² Learn noisy-or parameters only ² Used logical-and instead of noisy-and to combine evidence from conjuncts in the body of a clause 27

Experimental Evaluation q Monroe (Strategic planning) q Linux (Intelligent user interfaces) q Story Understanding (Story understanding) 28

Monroe and Linux [Blaylock and Allen, 2005] q Task ² Monroe involves recognizing top level plans in an emergency response domain (artificially generated using HTN planner) ² Linux involves recognizing top-level plans based on linux commands ² Single correct plan in each example q Data 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 29

Monroe and Linux q Methodology ² Manually encoded the knowledge base ² Learned noisy-or parameters using EM ² Computed marginal probability for plan instances q Systems compared ² BALPs ² MLN-HCAM [Singla and Mooney, 2011] o MLN-PC and MLN-HC do not run on Monroe and Linux due to scaling issues ² Blaylock and Allen’s system [Blaylock and Allen, 2005] q Performance metric ² Convergence score - measures the fraction of examples for which the plan predicate was predicted correctly 30

Convergence Score Results on Monroe 94. 2 * BALPs MLN-HCAM Blaylock & Allen * - Differences are statistically significant wrt BALPs 31

Convergence Score Results on Linux 36. 1 * BALPs MLN-HCAM Blaylock & Allen * - Differences are statistically significant wrt BALPs 32

Experiments with partial observability q Limitations of convergence score ² Does not account for predicting the plan arguments correctly ² Requires all the observations to be seen before plans can be predicted q Early plan recognition with partial set of observations ² Perform plan recognition after observing the first 25%, 50%, 75%, and 100% of the observations ² Accuracy – Assign partial credit for the predicting plan predicate and a subset of the arguments correctly q Systems compared ² BALPs ² MLN-HCAM [Singla and Mooney, 2011] 33

Accuracy Results on Monroe Percent observations seen 34

Accuracy Results on Linux Percent observations seen 35

Story Understanding [Charniak and Goldman, 1991; Ng and Mooney, 1992] q Task ² Recognize character’s top level plans based on actions described in narrative text ² Multiple top-level plans in each example q Data ² 25 examples in development set and 25 examples in test set ² 12. 6 observations per example ² 8 top-level plan predicates 36

Story Understanding q Methodology ² Knowledge base was created for ACCEL [Ng and Mooney, 1992] ² Parameters set manually o Insufficient number of examples in the development set to learn parameters ² Computed MPE to get the best set of plans q Systems compared ² BALPs ² MLN-HCAM [Singla and Mooney, 2011] o Best performing MLN model ² ACCEL-Simplicity [Ng and Mooney, 1992] ² ACCEL-Coherence [Ng and Mooney, 1992] o Specific for Story Understanding 37

Results on Story Understanding * * - Differences are statistically significant wrt BALPs * 38

Conclusion q BALPS – Extension of BLPs for plan recognition by employing logical abduction to construct Bayesian networks q Automatic learning of model parameters using EM q Empirical results on all benchmark datasets demonstrate advantages over existing methods 39

Future Work q Learn abductive knowledge base automatically from data q Compare BALPs with other probabilistic logics like Prob. Log [De Raedt et. al, 2007], PRISM [Sato, 1995] and Poole’s Horn Abduction [Poole, 1993] on plan recognition 40

Questions 41

Backup 42

Completeness in First-order Logic q Completeness - If a sentence is entailed by a KB, then it is possible to find the proof that entails it q 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 q Resolution is complete in first-order logic ² If a set of sentences is unsatisfiable, then it is possible to find a contradiction 43

First-order Logic q Terms ² Constants – individual entities like anna, bob ² Variables – placeholders for objects like X, Y q Predicates ² Relations over entities like works. For, capital. Of q Literal – predicate or its negation applied to terms ² Atom – Positive literal like works. For(X, Y) ² Ground literal – literal with no variables like works. For(anna, bob) q Clause – disjunction of literals ² Horn clause has at most one positive literal ² Definite clause has exactly one positive literal 44

First-order Logic q Quantifiers ² Universal quantification - true for all objects in the domain ² Existential quantification - true for some objects in the domain q Logical Inference ² Forward Chaining– For every implication p q, if p is true, then q is concluded to be true ² Backward Chaining – For a query literal q, if an implication p q is present and p is true, then q is concluded to be true, otherwise backward chaining tries to prove p 45

Forward chaining q For every implication p q, if p is true, then q is concluded to be true q Results in addition of a new fact to KB q Efficient, but incomplete q Inference can explode and forward chaining may never terminate ² Addition of new facts might result in rules being satisfied q It is data-driven, not goal-driven ² Might result in irrelevant conclusions 46

Backward chaining q For a query literal q, if an implication p q is present and p is true, then q is concluded to be true, otherwise backward chaining tries to prove p q Efficient, but not complete q May never terminate, might get stuck in infinite loop q Exponential q Goal-driven 47

Herbrand Model Semantics q Herbrand universe ² All constants in the domain q Herbrand base ² All ground atoms over Herbrand universe q Herbrand interpretation ² A set of ground atoms from Herbrand base that are true q Herbrand model ² Herbrand interpretation that satisfies all clauses in the knowledge base 48

Advantages of SRL models over vanilla probabilistic models q Compactly represent domain knowledge in firstorder logic q Employ logical inference to construct ground networks q Enables parameter sharing 49

Parameter sharing in SRL father(john) θ 1 parent(john) father(mary) θ 2 parent(mary) father(alice) θ 3 parent(alice) dummy 50

Parameter sharing in SRL father(X) parent(X) father(john) θ parent(john) θ father(mary) θ parent(mary) father(alice) θ parent(alice) dummy 51

Noisy-and Model q Several causes ci have to occur simultaneously if event e has to occur q ci fails to trigger e with probability pi q 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 q Several causes ci cause event e has to occur q ci independently triggers e with probability pi q leak accounts for some unknown cause due to which e has triggered P(e) = 1 – [(I – inh) Πi (1 -pi)^(1 -ci)] q Models explaining away ² 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 neighborhood(james) burglary(james) lives(james, yorkshire) tornado(yorkshire) alarm(james) 54

Noisy-and And Noisy-or Models neighborhood(james) Noisy/logical-and burglary(james) lives(james, yorkshire) Noisy/logical-and tornado(yorkshire) Noisy/logical-and dummy 2 dummy 1 Noisy-or alarm(james) 55

Logical Inference in BLPs SLD Resolution BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). Proof alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query alarm(james) Example from Ngo and Haddawy, 1997 56

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query alarm(james) Example from Ngo and Haddawy, 1997 57

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query neighborhood(james) alarm(james) Example from Ngo and Haddawy, 1997 58

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query neighborhood(james) alarm(james) Example from Ngo and Haddawy, 1997 59

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query neighborhood(james) alarm(james) Example from Ngo and Haddawy, 1997 60

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query neighborhood(james) alarm(james) Example from Ngo and Haddawy, 1997 61

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query lives(james, Y) tornado(Y) neighborhood(james) alarm(james) Example from Ngo and Haddawy, 1997 62

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query lives(james, Y) tornado(Y) neighborhood(james) lives(james, yorkshire) alarm(james) Example from Ngo and Haddawy, 1997 63

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query lives(james, Y) tornado(Y) neighborhood(james) lives(james, yorkshire) alarm(james) tornado(yorkshire) Example from Ngo and Haddawy, 1997 64

Logical Inference in BLPs SLD Resolution Proof BLP lives(james, yorkshire). lives(stefan, freiburg). neighborhood(james). tornado(yorkshire). alarm(james) burglary(X) | neighborhood(X). alarm(X) | burglary(X). alarm(X) | lives(X, Y), tornado(Y). Query lives(james, Y) tornado(Y) neighborhood(james) lives(james, yorkshire) alarm(james) tornado(yorkshire) Example from Ngo and Haddawy, 1997 65

Bayesian Network Construction neighborhood(james) burglary(james) lives(james, yorkshire) tornado(yorkshire) alarm(james) 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 66

Bayesian Network Construction neighborhood(james) burglary(james) lives(james, yorkshire) tornado(yorkshire) alarm(james) 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 67

Bayesian Network Construction neighborhood(james) burglary(james) lives(james, yorkshire) tornado(yorkshire) alarm(james) 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 68

Bayesian Network Construction ✖ neighborhood(james) burglary(james) lives(stefan, freiburg) lives(james, yorkshire) tornado(yorkshire) alarm(james) 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 69

Probabilistic Inference copy-file(Test 1, txt, Mydir) move-file(Test 1, txt, Mydir) remove-file(Test 1) rm(Test 1. txt) cp(Test 1. txt, Mydir) rs e t e 4 p m ara 4 m a r pa rs e t e 70

Probabilistic Inference copy-file(Test 1, txt, Mydir) move-file(Test 1, txt, Mydir) remove-file(Test 1) θ 1 θ 2 cp(Test 1. txt, Mydir) 2 parameters θ 3 θ 4 rm(Test 1. txt) 2 parameters Noisy models require parameters linear in the number of parents 71

Learning in BLPs [Kersting and De Raedt, 2008] q Parameter learning ² Expectation Maximization ² Gradient-ascent based learning ² Both approaches optimize likelihood q Structure learning ² Hill climbing search through the space of possible structures ² Initial structure obtained from CLAUDIEN [De Raedt and Dehaspe, 1997] ² Learns from only positive examples 72

Probabilistic Inference and Learning q Probabilistic inference ² Marginal probability given evidence ² Most Probable Explanation (MPE) given evidence q Learning [Kersting and De Raedt, 2008] ² Parameters o Expectation Maximization o Gradient-ascent based learning ² Structure o 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 * From SRL tutorial at ECML 07 * 74 74

Decomposable Combining Rules q Express different influences using separate nodes q These nodes can be combined using a deterministic function 75

Combining Rules neighborhood(james) Logical-and burglary(james) lives(james, yorkshire) Logical-and tornado(yorkshire) Logical-and dummy 2 dummy 1 Noisy-or alarm(james) 76

Decomposable Combining Rules neighborhood(james) Logical-and burglary(james) lives(james, yorkshire) tornado(yorkshire) Logical-and dummy 2 dummy 1 Noisy-or dummy 1 -new dummy 2 -new Logical-or alarm(james) 77

BLPs vs. PLPs q Differences in representation ² 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 ² Instead of having neighborhood(x) = bad, in PLPs, we have neighborhood(x, bad) ² To compute probability of a query alarm(james), PLPs have to construct one proof tree for all possible values for all predicates ² Inference is cumbersome q BLPs subsume PLPs 78

BLPs vs. Poole's Horn Abduction q Differences in representation ² For example, if P(x) and R(x) are two competing hypothesis, then either P(x) could be true or R(x) could be true ² Prior probabilities of P(x) and R(x) should sum to 1 ² Restrictions of these kind are not there in BLPs ² PLPs and hence BLPs are more flexible and have a richer representation 79

BLPs vs. PRMs q BLPs subsume PRMs q PRMs use entity-relationship models to represent knowledge and they use KBMC-like construction to construct a ground Bayesian network ² Each attribute becomes a random variable in the ground network and relations over the entities are logical constraints ² In BLP, each attribute becomes a Bayesian atom and relations become logical atoms ² Aggregator functions can be transformed into combining rules 80

BLPs vs. RBNs q BLPs subsume RBNs q In RBNs, each node in BN is a predicate and probability formulae are used to specify probabilities ² Combining rules can be used to represent these probability formulae in BLPs. 81

BALPs vs. BLPs q Like BLPs, BALPs use logic programs as templates for constructing Bayesian networks q Unlike BLPs, BALPs uses logical abduction instead of deduction to construct the network 82

Monroe [Blaylock and Allen, 2005] q Task ² Recognize top level plans in an emergency response domain (artificially generated using HTN planner) ² Plans include set-up-shelter, clear-road-wreck, providemedical-attention ² Single correct plan in each example ² Domain consists of several entities and sub-goals ² Test the ability to scale to large domains q Data ² Contains 1000 examples 83

Monroe q Methodology ² Knowledge base constructed based on the domain knowledge encoded in planner ² Learn noisy-or parameters using EM ² Compute marginal probability for instances of top level plans and pick the one with the highest marginal probability ² Systems compared o BALPs o MLN-HCAM [Singla and Mooney, 2011] o Blaylock and Allen’s system [Blaylock and Allen, 2005] ² Convergence score - measures the fraction of examples for which the plan schema was predicted correctly 84

Learning Results - Monroe MW Conv Score 98. 4 Acc-100 79. 16 Acc-75 46. 06 Acc-50 20. 67 Acc-25 7. 2 MW-Start 98. 4 79. 16 44. 63 20. 26 7. 33 85 Rand-Start 98. 4 79. 86 44. 73 19. 7 10. 46

Linux q Task [Blaylock and Allen, 2005] ² Recognize top level plans based on Linux commands ² Human users asked to perform tasks in Linux and commands were recorded ² Top-level plans include find-file-by-ext, remove-file-by-ext, copy-file, move-file ² Single correct plan in each example ² Tests 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-byname have identical actions q Data ² Contains 457 examples 86

Linux q Methodology ² Knowledge base constructed based on the knowledge of Linux commands ² Learn noisy-or parameters using EM ² Compute marginal probability for instances of top level plans and pick the one with the highest marginal probability ² Systems compared o BALPs o MLN-HCAM [Singla and Mooney, 2011] o Blaylock and Allen’s system [Blaylock and Allen, 2005] ² Convergence score - measures the fraction of examples for which the plan schema was predicted correctly o 87

Accuracy Learning Results - Linux Partial Observability Conv Score MW MW-Start Rand-Start 39. 82 46. 6 41. 57 88

Story Understanding [Charniak and Goldman, 1991; Ng and Mooney, 1992] q Task ² Recognize character’s top level plans based on actions described in narrative text ² Logical representation of actions literals provided ² Top-level plans include shopping, robbing, restaurant dining, partying ² Multiple top-level plans in each example ² Tests the ability to predict multiple plans q Data ² 25 development examples ² 25 test examples 89

Story Understanding q Methodology ² Knowledge base constructed for ACCEL by Ng and Mooney [1992] ² Insufficient number of examples to learn parameters o Noisy-or parameters set to 0. 9 o Noisy-and parameters set to 0. 9 o Priors tuned on development set ² Compute MPE to get the best set of plans ² Systems compared o BALPs o 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 * - Differences are statistically significant wrt BALPs 91

Other Applications of BALPs q Medical diagnosis q Textual entailment q Computational biology ² Inferring gene relations based on the output of micro-array experiments q Any application that requires abductive reasoning 92

ACCEL [Ng and Mooney, 1992] q First-order logic based system for plan recognition q Simplicity metric selects explanations that have the least number of assumptions q Coherence metric selects explanations that connect maximum number of observations ² Measures explanatory coherence ² Specific to text interpretation 93

System by Blaylock and Allen [2005] q Statistical n-gram models to predict plans based on observed actions q Performs plan recognition in two phases ² Predicts the plan schema first ² Predicts arguments based on the predicted schema 94