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Markov Logic in Natural Language Processing Hoifung Poon Dept. of Computer Science & Eng. University of Washington Overview Motivation Foundational areas Markov logic NLP applications Basics Supervised learning Unsupervised learning 2 Holy Grail of NLP: Automatic Language Understanding Natural language search Answer questions Knowledge discovery …… Text Meaning 3 Reality: Increasingly Fragmented Parsing Semantics Tagging Information Morphology Extraction 4 Time for a New Synthesis? Speed up progress New opportunities to improve performance But we need a new tool for this … 5 Languages Are Structural governments lm$pxtm (according to their families) 6 Languages Are Structural S govern-ment-s NP VP l-m$px-t-m (according to their families) V NP IL-4 induces CD11B Involvement of p70(S6)-kinase George Walker Bush was the activation in IL-10 up-regulation 43rd President of the United in human monocytes by gp41...... States. involvement …… Theme Cause Bush was the eldest son of up-regulation activation President G. H. W. Bush and Babara Bush. Theme Cause Site Theme ……. human In November 1977, he met IL-10 gp41 p70(S6)-kinase Laura Welch at a barbecue. 7 monocyte Languages Are Structural S govern-ment-s NP VP l-m$px-t-m (according to their families) V NP IL-4 induces CD11B Involvement of p70(S6)-kinase George Walker Bush was the activation in IL-10 up-regulation 43rd President of the United in human monocytes by gp41...... States. involvement …… Theme Cause Bush was the eldest son of up-regulation activation President G. H. W. Bush and Babara Bush. Theme Cause Site Theme ……. human In November 1977, he met IL-10 gp41 p70(S6)-kinase Laura Welch at a barbecue. 8 monocyte Processing Is Complex Morphology POS Tagging Chunking Semantic Role Labeling Syntactic Parsing Coreference Resolution Information Extraction …… 9 Pipeline Is Suboptimal Morphology POS Tagging Chunking Semantic Role Labeling Syntactic Parsing Coreference Resolution Information Extraction …… 10 First-Order Logic Main theoretical foundation of computer science General language for describing complex structures and knowledge Trees, graphs, dependencies, hierarchies, etc. easily expressed Inference algorithms (satisfiability testing, theorem proving, etc.) 11 Languages Are Statistical I saw the man with the telescope Microsoft buys Powerset NP Microsoft acquires Powerset I saw the man with the telescope Powerset is acquired by Microsoft Corporation NP The Redmond software giant buys Powerset ADVP I saw the man with the telescope Microsoft’s purchase of Powerset, … …… Here in London, Frances Deek is a retired teacher … G. W. Bush …… In the Israeli town …, Karen London says … …… Laura Bush …… Now London says … Mrs. Bush …… London PERSON or LOCATION? Which one? 12 Languages Are Statistical Languages are ambiguous Our information is always incomplete We need to model correlations Our predictions are uncertain Statistics provides the tools to handle this 13 Probabilistic Graphical Models Mixture models Hidden Markov models Bayesian networks Markov random fields Maximum entropy models Conditional random fields Etc. 14 The Problem Logic is deterministic, requires manual coding Statistical models assume i.i.d. data, objects = feature vectors Historically, statistical and logical NLP have been pursued separately We need to unify the two! 15 Also, Supervision Is Scarce Supervised learning needs training examples Tons of texts … but most are not annotated Labeling is expensive (Cf. Penn-Treebank) Need to leverage indirect supervision 16 A Promising Solution: Statistical Relational Learning Emerging direction in machine learning Unifies logical and statistical approaches Principal way to leverage direct and indirect supervision 17 Key: Joint Inference Models complex interdependencies Propagates information from more certain decisions to resolve ambiguities in others Advantages: Better and more intuitive models Improve predictive accuracy Compensate for lack of training examples SRL can have even greater impact when direct supervision is scarce 18 Challenges in Applying Statistical Relational Learning Learning is much harder Inference becomes a crucial issue Greater complexity for user 19 Progress to Date Probabilistic logic [Nilsson, 1986] Statistics and beliefs [Halpern, 1990] Knowledge-based model construction [Wellman et al., 1992] Stochastic logic programs [Muggleton, 1996] Probabilistic relational models [Friedman et al., 1999] Relational Markov networks [Taskar et al., 2002] Etc. This talk: Markov logic [Domingos & Lowd, 2009] 20 Markov Logic: A Unifying Framework Probabilistic graphical models and first-order logic are special cases Unified inference and learning algorithms Easy-to-use software: Alchemy Broad applicability Goal of this tutorial: Quickly learn how to use Markov logic and Alchemy for a broad spectrum of NLP applications 21 Overview Motivation Foundational areas Probabilistic inference Statistical learning Logical inference Inductive logic programming Markov logic NLP applications Basics Supervised learning Unsupervised learning 22 Markov Networks Undirected graphical models Smoking Cancer Asthma Cough Potential functions defined over cliques 1 Smoking Cancer Ф(S,C) P( x) c ( xc ) Z c False False 4.5 False True 4.5 Z c ( xc ) True False 2.7 x c True True 4.5 23 Markov Networks Undirected graphical models Smoking Cancer Asthma Cough Log-linear model: 1 P( x) exp wi f i ( x) Z i Weight of Feature i Feature i 1 if Smoking Cancer f1 (Smoking, Cancer ) 0 otherwise w1 1.5 24 Markov Nets vs. Bayes Nets Property Markov Nets Bayes Nets Form Prod. potentials Prod. potentials Potentials Arbitrary Cond. probabilities Cycles Allowed Forbidden Partition func. Z = ? Z=1 Indep. check Graph separation D-separation Indep. props. Some Some Inference MCMC, BP, etc. Convert to Markov 25 Inference in Markov Networks Goal: compute marginals & conditionals of 1 P( X ) exp wi f i ( X ) Z exp wi fi ( X ) Z i X i Exact inference is #P-complete Conditioning on Markov blanket is easy: P( x | MB( x )) w f ( x) exp i i i exp w f ( x 0) exp w f ( x 1) i i i i i i Gibbs sampling exploits this 26 MCMC: Gibbs Sampling state ← random truth assignment for i ← 1 to num-samples do for each variable x sample x according to P(x|neighbors(x)) state ← state with new value of x P(F) ← fraction of states in which F is true 27 Other Inference Methods Belief propagation (sum-product) Mean field / Variational approximations 28 MAP/MPE Inference Goal: Find most likely state of world given evidence max P( y | x) y Query Evidence 29 MAP Inference Algorithms Iterated conditional modes Simulated annealing Graph cuts Belief propagation (max-product) LP relaxation 30 Overview Motivation Foundational areas Probabilistic inference Statistical learning Logical inference Inductive logic programming Markov logic NLP applications Basics Supervised learning Unsupervised learning 31 Generative Weight Learning Maximize likelihood Use gradient ascent or L-BFGS No local maxima log Pw ( x) ni ( x) Ew ni ( x) wi No. of times feature i is true in data Expected no. times feature i is true according to model Requires inference at each step (slow!) 32 Pseudo-Likelihood PL ( x) P ( xi | neighbors ( xi )) i Likelihood of each variable given its neighbors in the data Does not require inference at each step Widely used in vision, spatial statistics, etc. But PL parameters may not work well for long inference chains 33 Discriminative Weight Learning Maximize conditional likelihood of query (y) given evidence (x) log Pw ( y | x) ni ( x, y ) Ew ni ( x, y ) wi No. of true groundings of clause i in data Expected no. true groundings according to model Approximate expected counts by counts in MAP state of y given x 34 Voted Perceptron Originally proposed for training HMMs discriminatively Assumes network is linear chain Can be generalized to arbitrary networks wi ← 0 for t ← 1 to T do yMAP ← Viterbi(x) wi ← wi + η [counti(yData) – counti(yMAP)] return wi / T 35 Overview Motivation Foundational areas Probabilistic inference Statistical learning Logical inference Inductive logic programming Markov logic NLP applications Basics Supervised learning Unsupervised learning 36 First-Order Logic Constants, variables, functions, predicates E.g.: Anna, x, MotherOf(x), Friends(x, y) Literal: Predicate or its negation Clause: Disjunction of literals Grounding: Replace all variables by constants E.g.: Friends (Anna, Bob) World (model, interpretation): Assignment of truth values to all ground predicates 37 Inference in First-Order Logic Traditionally done by theorem proving (e.g.: Prolog) Propositionalization followed by model checking turns out to be faster (often by a lot) Propositionalization: Create all ground atoms and clauses Model checking: Satisfiability testing Two main approaches: Backtracking (e.g.: DPLL) Stochastic local search (e.g.: WalkSAT) 38 Satisfiability Input: Set of clauses (Convert KB to conjunctive normal form (CNF)) Output: Truth assignment that satisfies all clauses, or failure The paradigmatic NP-complete problem Solution: Search Key point: Most SAT problems are actually easy Hard region: Narrow range of #Clauses / #Variables 39 Stochastic Local Search Uses complete assignments instead of partial Start with random state Flip variables in unsatisfied clauses Hill-climbing: Minimize # unsatisfied clauses Avoid local minima: Random flips Multiple restarts 40 The WalkSAT Algorithm for i ← 1 to max-tries do solution = random truth assignment for j ← 1 to max-flips do if all clauses satisfied then return solution c ← random unsatisfied clause with probability p flip a random variable in c else flip variable in c that maximizes # satisfied clauses return failure 41 Overview Motivation Foundational areas Probabilistic inference Statistical learning Logical inference Inductive logic programming Markov logic NLP applications Basics Supervised learning Unsupervised learning 42 Rule Induction Given: Set of positive and negative examples of some concept Example: (x1, x2, … , xn, y) y: concept (Boolean) x1, x2, … , xn: attributes (assume Boolean) Goal: Induce a set of rules that cover all positive examples and no negative ones Rule: xa ^ xb ^ … y (xa: Literal, i.e., xi or its negation) Same as Horn clause: Body Head Rule r covers example x iff x satisfies body of r Eval(r): Accuracy, info gain, coverage, support, etc. 43 Learning a Single Rule head ← y body ← Ø repeat for each literal x rx ← r with x added to body Eval(rx) body ← body ^ best x until no x improves Eval(r) return r 44 Learning a Set of Rules R←Ø S ← examples repeat learn a single rule r R←RU{r} S ← S − positive examples covered by r until S = Ø return R 45 First-Order Rule Induction y and xi are now predicates with arguments E.g.: y is Ancestor(x,y), xi is Parent(x,y) Literals to add are predicates or their negations Literal to add must include at least one variable already appearing in rule Adding a literal changes # groundings of rule E.g.: Ancestor(x,z) ^ Parent(z,y) Ancestor(x,y) Eval(r) must take this into account E.g.: Multiply by # positive groundings of rule still covered after adding literal 46 Overview Motivation Foundational areas Markov logic NLP applications Basics Supervised learning Unsupervised learning 47 Markov Logic Syntax: Weighted first-order formulas Semantics: Feature templates for Markov networks Intuition: Soften logical constraints Give each formula a weight (Higher weight Stronger constraint) P(world) exp weights of formulasit satisfies 48 Example: Coreference Resolution Mentions of Obama are often headed by "Obama" Mentions of Obama are often headed by "President" Appositions usually refer to the same entity Barack Obama, the 44th President of the United States, is the first African American to hold the office. …… 49 Example: Coreference Resolution x MentionOf ( x, Obama) Head( x,"Obama ") x MentionOf ( x, Obama) Head( x,"President ") x, y, c Apposition( x, y ) MentionOf ( x, c) MentionOf ( y, c) 50 Example: Coreference Resolution 1.5 x MentionOf ( x, Obama) Head( x,"Obama ") 0.8 x MentionOf ( x, Obama) Head( x,"President ") 100 x, y, c Apposition( x, y ) MentionOf ( x, c) MentionOf ( y, c) 51 Example: Coreference Resolution 1.5 x MentionOf ( x, Obama) Head( x,"Obama ") 0.8 x MentionOf ( x, Obama) Head( x,"President ") 100 x, y, c Apposition( x, y ) MentionOf ( x, c) MentionOf ( y, c) Two mention constants: A and B Apposition(A,B) Head(A,“President”) Head(B,“President”) MentionOf(A,Obama) MentionOf(B,Obama) Head(A,“Obama”) Head(B,“Obama”) Apposition(B,A) 52 Markov Logic Networks MLN is template for ground Markov nets Probability of a world x: 1 P( x) exp wi ni ( x) Z i Weight of formula i No. of true groundings of formula i in x Typed variables and constants greatly reduce size of ground Markov net Functions, existential quantifiers, etc. Can handle infinite domains [Singla & Domingos, 2007] and continuous domains [Wang & Domingos, 2008] 53 Relation to Statistical Models Special cases: Obtained by making all Markov networks predicates zero-arity Markov random fields Bayesian networks Markov logic allows Log-linear models objects to be Exponential models interdependent Max. entropy models (non-i.i.d.) Gibbs distributions Boltzmann machines Logistic regression Hidden Markov models Conditional random fields 54 Relation to First-Order Logic Infinite weights First-order logic Satisfiable KB, positive weights Satisfying assignments = Modes of distribution Markov logic allows contradictions between formulas 55 MLN Algorithms: The First Three Generations Problem First Second Third generation generation generation MAP Weighted Lazy Cutting inference satisfiability inference planes Marginal Gibbs MC-SAT Lifted inference sampling inference Weight Pseudo- Voted Scaled conj. learning likelihood perceptron gradient Structure Inductive ILP + PL Clustering + learning logic progr. (etc.) pathfinding 56 MAP/MPE Inference Problem: Find most likely state of world given evidence max P( y | x) y Query Evidence 57 MAP/MPE Inference Problem: Find most likely state of world given evidence 1 max exp wi ni ( x, y) y Zx i 58 MAP/MPE Inference Problem: Find most likely state of world given evidence max y w n ( x, y ) i i i 59 MAP/MPE Inference Problem: Find most likely state of world given evidence max y w n ( x, y ) i i i This is just the weighted MaxSAT problem Use weighted SAT solver (e.g., MaxWalkSAT [Kautz et al., 1997] ) 60 The MaxWalkSAT Algorithm for i ← 1 to max-tries do solution = random truth assignment for j ← 1 to max-flips do if weights(sat. clauses) > threshold then return solution c ← random unsatisfied clause with probability p flip a random variable in c else flip variable in c that maximizes weights(sat. clauses) return failure, best solution found 61 Computing Probabilities P(Formula|MLN,C) = ? MCMC: Sample worlds, check formula holds P(Formula1|Formula2,MLN,C) = ? If Formula2 = Conjunction of ground atoms First construct min subset of network necessary to answer query (generalization of KBMC) Then apply MCMC 62 But … Insufficient for Logic Problem: Deterministic dependencies break MCMC Near-deterministic ones make it very slow Solution: Combine MCMC and WalkSAT → MC-SAT algorithm [Poon & Domingos, 2006] 63 Auxiliary-Variable Methods Main ideas: Use auxiliary variables to capture dependencies Turn difficult sampling into uniform sampling Given distribution P(x) 1, if 0 u P( x) f ( x, u ) 0, otherwise f ( x, u) du P( x) Sample from f (x, u), then discard u 64 Slice Sampling [Damien et al. 1999] U P(x) Slice u(k) X x(k) x(k+1) 65 Slice Sampling Identifying the slice may be difficult 1 P( x ) i ( x ) Z i Introduce an auxiliary variable ui for each Фi 1 if 0 ui i ( x) f ( x, u1, , un ) 0 otherwise 66 The MC-SAT Algorithm Select random subset M of satisfied clauses With probability 1 – exp ( – wi ) Larger wi Ci more likely to be selected Hard clause (wi ): Always selected Slice States that satisfy clauses in M Uses SAT solver to sample x | u. Orders of magnitude faster than Gibbs sampling, etc. 67 But … It Is Not Scalable 1000 researchers Coauthor(x,y): 1 million ground atoms Coauthor(x,y) Coauthor(y,z) Coauthor(x,z): 1 billion ground clauses Exponential in arity 68 Sparsity to the Rescue 1000 researchers Coauthor(x,y): 1 million ground atoms But … most atoms are false Coauthor(x,y) Coauthor(y,z) Coauthor(x,z): 1 billion ground clauses Most trivially satisfied if most atoms are false No need to explicitly compute most of them 69 Lazy Inference LazySAT [Singla & Domingos, 2006a] Lazy version of WalkSAT [Selman et al., 1996] Grounds atoms/clauses as needed Greatly reduces memory usage The idea is much more general [Poon & Domingos, 2008a] 70 General Method for Lazy Inference If most variables assume the default value, wasteful to instantiate all variables / functions Main idea: Allocate memory for a small subset of “active” variables / functions Activate more if necessary as inference proceeds Applicable to a diverse set of algorithms: Satisfiability solvers (systematic, local-search), Markov chain Monte Carlo, MPE / MAP algorithms, Maximum expected utility algorithms, Belief propagation, MC-SAT, Etc. Reduce memory and time by orders of magnitude 71 Lifted Inference Consider belief propagation (BP) Often in large problems, many nodes are interchangeable: They send and receive the same messages throughout BP Basic idea: Group them into supernodes, forming lifted network Smaller network → Faster inference Akin to resolution in first-order logic 72 Belief Propagation x f ( x) hn ( x ) \{ f } h x ( x) Nodes Features (x) (f) wf ( x ) f x ( x) e \{}y f ( y) ~{ x} yn ( f ) x 73 Lifted Belief Propagation x f ( x) hn ( x ) \{ f } h x ( x) Nodes Features (x) (f) wf ( x ) f x ( x) e \{}y f ( y) ~{ x} yn ( f ) x 74 Lifted Belief Propagation , : Functions of edge x f ( x) h x ( x) counts hn ( x ) \{ f } Nodes Features (x) (f) wf ( x ) f x ( x) e \{}y f ( y) ~{ x} yn ( f ) x 75 Learning Data is a relational database Closed world assumption (if not: EM) Learning parameters (weights) Learning structure (formulas) 76 Parameter Learning Parameter tying: Groundings of same clause log P ( x) ni ( x) Ex ni ( x) wi No. of times clause i is true in data Expected no. times clause i is true according to MLN Generative learning: Pseudo-likelihood Discriminative learning: Conditional likelihood, use MC-SAT or MaxWalkSAT for inference 77 Parameter Learning Pseudo-likelihood + L-BFGS is fast and robust but can give poor inference results Voted perceptron: Gradient descent + MAP inference Scaled conjugate gradient 78 Voted Perceptron for MLNs HMMs are special case of MLNs Replace Viterbi by MaxWalkSAT Network can now be arbitrary graph wi ← 0 for t ← 1 to T do yMAP ← MaxWalkSAT(x) wi ← wi + η [counti(yData) – counti(yMAP)] return wi / T 79 Problem: Multiple Modes Not alleviated by contrastive divergence Alleviated by MC-SAT Warm start: Start each MC-SAT run at previous end state 80 Problem: Extreme Ill-Conditioning Solvable by quasi-Newton, conjugate gradient, etc. But line searches require exact inference Solution: Scaled conjugate gradient [Lowd & Domingos, 2008] Use Hessian to choose step size Compute quadratic form inside MC-SAT Use inverse diagonal Hessian as preconditioner 81 Structure Learning Standard inductive logic programming optimizes the wrong thing But can be used to overgenerate for L1 pruning Our approach: ILP + Pseudo-likelihood + Structure priors [Kok & Domingos 2005, 2008, 2009] For each candidate structure change: Start from current weights & relax convergence Use subsampling to compute sufficient statistics 82 Structure Learning Initial state: Unit clauses or prototype KB Operators: Add/remove literal, flip sign Evaluation function: Pseudo-likelihood + Structure prior Search: Beam search, shortest-first search 83 Alchemy Open-source software including: Full first-order logic syntax Generative & discriminative weight learning Structure learning Weighted satisfiability, MCMC, lifted BP Programming language features alchemy.cs.washington.edu 84 Alchemy Prolog BUGS Represent- F.O. Logic + Horn Bayes ation Markov nets clauses nets Inference Model check- Theorem MCMC ing, MCMC, proving lifted BP Learning Parameters No Params. & structure Uncertainty Yes No Yes Relational Yes Yes No 85 Running Alchemy Programs MLN file Infer Types (optional) Learnwts Predicates Learnstruct Formulas Options Database files 86 Overview Motivation Foundational areas Markov logic NLP applications Basics Supervised learning Unsupervised learning 87 Uniform Distribn.: Empty MLN Example: Unbiased coin flips Type: flip = { 1, … , 20 } Predicate: Heads(flip) 1 e0 1 P(Heads( f )) 1 Z Z e Ze 1 0 0 2 88 Binomial Distribn.: Unit Clause Example: Biased coin flips Type: flip = { 1, … , 20 } Predicate: Heads(flip) Formula: Heads(f) p Weight: Log odds of heads: 1 p w log 1 ew 1 P(Heads(f )) 1 Z w p Z e Z e 1 e w1 0 By default, MLN includes unit clauses for all predicates (captures marginal distributions, etc.) 89 Multinomial Distribution Example: Throwing die Types: throw = { 1, … , 20 } face = { 1, … , 6 } Predicate: Outcome(throw,face) Formulas: Outcome(t,f) ^ f != f’ => !Outcome(t,f’). Exist f Outcome(t,f). Too cumbersome! 90 Multinomial Distrib.: ! Notation Example: Throwing die Types: throw = { 1, … , 20 } face = { 1, … , 6 } Predicate: Outcome(throw,face!) Formulas: Semantics: Arguments without “!” determine arguments with “!”. Also makes inference more efficient (triggers blocking). 91 Multinomial Distrib.: + Notation Example: Throwing biased die Types: throw = { 1, … , 20 } face = { 1, … , 6 } Predicate: Outcome(throw,face!) Formulas: Outcome(t,+f) Semantics: Learn weight for each grounding of args with “+”. 92 Logistic Regression (MaxEnt) P(C 1 | F f ) P(C 0 | F f ) a bi f i Logistic regression: log Type: obj = { 1, ... , n } Query predicate: C(obj) Evidence predicates: Fi(obj) Formulas: a C(x) bi Fi(x) ^ C(x) 1 Resulting distribution: P(C c, F f ) exp ac bi f i c Z i P(C 1 | F f ) expa bi f i Therefore: log a bi f i P(C 0 | F f ) log exp(0) Alternative form: Fi(x) => C(x) 93 Hidden Markov Models obs = { Red, Green, Yellow } state = { Stop, Drive, Slow } time = { 0, ..., 100 } State(state!,time) Obs(obs!,time) State(+s,0) State(+s,t) ^ State(+s',t+1) Obs(+o,t) ^ State(+s,t) Sparse HMM: State(s,t) => State(s1,t+1) v State(s2, t+1) v ... . 94 Bayesian Networks Use all binary predicates with same first argument (the object x). One predicate for each variable A: A(x,v!) One clause for each line in the CPT and value of the variable Context-specific independence: One clause for each path in the decision tree Logistic regression: As before Noisy OR: Deterministic OR + Pairwise clauses 95 Relational Models Knowledge-based model construction Allow only Horn clauses Same as Bayes nets, except arbitrary relations Combin. function: Logistic regression, noisy-OR or external Stochastic logic programs Allow only Horn clauses Weight of clause = log(p) Add formulas: Head holds Exactly one body holds Probabilistic relational models Allow only binary relations Same as Bayes nets, except first argument can vary 96 Relational Models Relational Markov networks SQL → Datalog → First-order logic One clause for each state of a clique + syntax in Alchemy facilitates this Bayesian logic Object = Cluster of similar/related observations Observation constants + Object constants Predicate InstanceOf(Obs,Obj) and clauses using it Unknown relations: Second-order Markov logic S. Kok & P. Domingos, “Statistical Predicate Invention”, in Proc. ICML-2007. 97 Overview Motivation Foundational areas Markov logic NLP applications Basics Supervised learning Unsupervised learning 98 Text Classification The 56th quadrennial United States presidential election was held on November 4, 2008. Outgoing Republican President George W. Bush's policies and Topic = politics actions and the American public's desire for change were key issues throughout the campaign. …… The Chicago Bulls are an American professional basketball team based in Chicago, Illinois, playing in the Central Division of the Eastern Conference in the Topic = sports National Basketball Association (NBA). …… …… 99 Text Classification page = {1, ..., max} word = { ... } topic = { ... } Topic(page,topic) HasWord(page,word) Topic(p,t) HasWord(p,+w) => Topic(p,+t) If topics mutually exclusive: Topic(page,topic!) 100 Text Classification page = {1, ..., max} word = { ... } topic = { ... } Topic(page,topic) HasWord(page,word) Links(page,page) Topic(p,t) HasWord(p,+w) => Topic(p,+t) Topic(p,t) ^ Links(p,p') => Topic(p',t) Cf. S. Chakrabarti, B. Dom & P. Indyk, “Hypertext Classification Using Hyperlinks,” in Proc. SIGMOD-1998. 101 Entity Resolution AUTHOR: H. POON & P. DOMINGOS TITLE: UNSUPERVISED SEMANTIC PARSING VENUE: EMNLP-09 SAME? AUTHOR: Hoifung Poon and Pedro Domings TITLE: Unsupervised semantic parsing VENUE: Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing AUTHOR: Poon, Hoifung and Domings, Pedro TITLE: Unsupervised ontology induction from text VENUE: Proceedings of the Forty-Eighth Annual Meeting of the Association for Computational Linguistics SAME? AUTHOR: H. Poon, P. Domings TITLE: Unsupervised ontology induction VENUE: ACL-10 102 Entity Resolution Problem: Given database, find duplicate records HasToken(token,field,record) SameField(field,record,record) SameRecord(record,record) HasToken(+t,+f,r) ^ HasToken(+t,+f,r’) => SameField(f,r,r’) SameField(f,r,r’) => SameRecord(r,r’) 103 Entity Resolution Problem: Given database, find duplicate records HasToken(token,field,record) SameField(field,record,record) SameRecord(record,record) HasToken(+t,+f,r) ^ HasToken(+t,+f,r’) => SameField(f,r,r’) SameField(f,r,r’) => SameRecord(r,r’) SameRecord(r,r’) ^ SameRecord(r’,r”) => SameRecord(r,r”) Cf. A. McCallum & B. Wellner, “Conditional Models of Identity Uncertainty with Application to Noun Coreference,” in Adv. NIPS 17, 2005. 104 Entity Resolution Can also resolve fields: HasToken(token,field,record) SameField(field,record,record) SameRecord(record,record) HasToken(+t,+f,r) ^ HasToken(+t,+f,r’) => SameField(f,r,r’) SameField(f,r,r’) <=> SameRecord(r,r’) SameRecord(r,r’) ^ SameRecord(r’,r”) => SameRecord(r,r”) SameField(f,r,r’) ^ SameField(f,r’,r”) => SameField(f,r,r”) More: P. Singla & P. Domingos, “Entity Resolution with Markov Logic”, in Proc. ICDM-2006. 105 Information Extraction Unsupervised Semantic Parsing, Hoifung Poon and Pedro Domingos. Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing. Singapore: ACL. UNSUPERVISED SEMANTIC PARSING. H. POON & P. DOMINGOS. EMNLP-2009. 106 Information Extraction Author Title Venue Unsupervised Semantic Parsing, Hoifung Poon and Pedro Domingos. Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing. Singapore: ACL. SAME? UNSUPERVISED SEMANTIC PARSING. H. POON & P. DOMINGOS. EMNLP-2009. 107 Information Extraction Problem: Extract database from text or semi-structured sources Example: Extract database of publications from citation list(s) (the “CiteSeer problem”) Two steps: Segmentation: Use HMM to assign tokens to fields Entity resolution: Use logistic regression and transitivity 108 Information Extraction Token(token, position, citation) InField(position, field!, citation) SameField(field, citation, citation) SameCit(citation, citation) Token(+t,i,c) => InField(i,+f,c) InField(i,+f,c) ^ InField(i+1,+f,c) Token(+t,i,c) ^ InField(i,+f,c) ^ Token(+t,i’,c’) ^ InField(i’,+f,c’) => SameField(+f,c,c’) SameField(+f,c,c’) <=> SameCit(c,c’) SameField(f,c,c’) ^ SameField(f,c’,c”) => SameField(f,c,c”) SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”) 109 Information Extraction Token(token, position, citation) InField(position, field!, citation) SameField(field, citation, citation) SameCit(citation, citation) Token(+t,i,c) => InField(i,+f,c) InField(i,+f,c) ^ !Token(“.”,i,c) ^ InField(i+1,+f,c) Token(+t,i,c) ^ InField(i,+f,c) ^ Token(+t,i’,c’) ^ InField(i’,+f,c’) => SameField(+f,c,c’) SameField(+f,c,c’) <=> SameCit(c,c’) SameField(f,c,c’) ^ SameField(f,c’,c”) => SameField(f,c,c”) SameCit(c,c’) ^ SameCit(c’,c”) => SameCit(c,c”) More: H. Poon & P. Domingos, “Joint Inference in Information Extraction”, in Proc. AAAI-2007. 110 Biomedical Text Mining Traditionally, name entity recognition or information extraction E.g., protein recognition, protein-protein identification BioNLP-09 shared task: Nested bio-events Much harder than traditional IE Top F1 around 50% Naturally calls for joint inference 111 Bio-Event Extraction Involvement of p70(S6)-kinase activation in IL-10 up-regulation in human monocytes by gp41 envelope protein of human immunodeficiency virus type 1 ... involvement Theme Cause up-regulation activation Theme Cause Site Theme human IL-10 gp41 p70(S6)-kinase monocyte 112 Bio-Event Extraction Token(position, token) DepEdge(position, position, dependency) IsProtein(position) EvtType(position, evtType) Logistic InArgPath(position, position, argType!) regression Token(i,+w) => EvtType(i,+t) Token(j,w) ^ DepEdge(i,j,+d) => EvtType(i,+t) DepEdge(i,j,+d) => InArgPath(i,j,+a) Token(i,+w) ^ DepEdge(i,j,+d) => InArgPath(i,j,+a) … 113 Bio-Event Extraction Token(position, token) DepEdge(position, position, dependency) IsProtein(position) EvtType(position, evtType) InArgPath(position, position, argType!) Token(i,+w) => EvtType(i,+t) Token(j,w) ^ DepEdge(i,j,+d) => EvtType(i,+t) DepEdge(i,j,+d) => InArgPath(i,j,+a) Adding a few joint inference Token(i,+w) ^ DepEdge(i,j,+d) => InArgPath(i,j,+a) … rules doubles the F1 InArgPath(i,j,Theme) => IsProtein(j) v (Exist k k!=i ^ InArgPath(j, k, Theme)). … More: H. Poon and L. Vanderwende, “Joint Inference for Knowledge Extraction from Biomedical Literature”, NAACL-2010. 114 Temporal Information Extraction Identify event times and temporal relations (BEFORE, AFTER, OVERLAP) E.g., who is the President of U.S.A.? Obama: 1/20/2009 present G. W. Bush: 1/20/2001 1/19/2009 Etc. 115 Temporal Information Extraction DepEdge(position, position, dependency) Event(position, event) After(event, event) DepEdge(i,j,+d) ^ Event(i,p) ^ Event(j,q) => After(p,q) After(p,q) ^ After(q,r) => After(p,r) 116 Temporal Information Extraction DepEdge(position, position, dependency) Event(position, event) After(event, event) Role(position, position, role) DepEdge(I,j,+d) ^ Event(i,p) ^ Event(j,q) => After(p,q) Role(i,j,ROLE-AFTER) ^ Event(i,p) ^ Event(j,q) => After(p,q) After(p,q) ^ After(q,r) => After(p,r) More: K. Yoshikawa, S. Riedel, M. Asahara and Y. Matsumoto, “Jointly Identifying Temporal Relations with Markov Logic”, in Proc. ACL-2009. X. Ling & D. Weld, “Temporal Information Extraction”, in Proc. AAAI-2010. 117 Semantic Role Labeling Problem: Identify arguments for a predicate Two steps: Argument identification: Determine whether a phrase is an argument Role classification: Determine the type of an argument (agent, theme, temporal, adjunct, etc.) 118 Semantic Role Labeling Token(position, token) DepPath(position, position, path) IsPredicate(position) Role(position, position, role!) HasRole(position, position) Token(i,+t) => IsPredicate(i) DepPath(i,j,+p) => Role(i,j,+r) HasRole(i,j) => IsPredicate(i) IsPredicate(i) => Exist j HasRole(i,j) HasRole(i,j) => Exist r Role(i,j,r) Role(i,j,r) => HasRole(i,j) Cf. K. Toutanova, A. Haghighi, C. Manning, “A global joint model for semantic role labeling”, in Computational Linguistics 2008. 119 Joint Semantic Role Labeling and Word Sense Disambiguation Token(position, token) DepPath(position, position, path) IsPredicate(position) Role(position, position, role!) HasRole(position, position) Sense(position, sense!) Token(i,+t) => IsPredicate(i) DepPath(i,j,+p) => Role(i,j,+r) Sense(I,s) => IsPredicate(i) HasRole(i,j) => IsPredicate(i) IsPredicate(i) => Exist j HasRole(i,j) HasRole(i,j) => Exist r Role(i,j,r) Role(i,j,r) => HasRole(i,j) Token(i,+t) ^ Role(i,j,+r) => Sense(i,+s) More: I. Meza-Ruiz & S. Riedel, “Jointly Identifying Predicates, Arguments and Senses using Markov Logic”, in Proc. NAACL-2009. 120 Practical Tips: Modeling Add all unit clauses (the default) How to handle uncertain data: R(x,y) ^ R’(x,y) (the “HMM trick”) Implications vs. conjunctions For soft correlation, conjunctions often better Implication: A => B is equivalent to !(A ^ !B) Share cases with others like A => C Make learning unnecessarily harder 121 Practical Tips: Efficiency Open/closed world assumptions Low clause arities Low numbers of constants Short inference chains 122 Practical Tips: Development Start with easy components Gradually expand to full task Use the simplest MLN that works Cycle: Add/delete formulas, learn and test 123 Overview Motivation Foundational areas Markov logic NLP applications Basics Supervised learning Unsupervised learning 124 Unsupervised Learning: Why? Virtually unlimited supply of unlabeled text Labeling is expensive (Cf. Penn-Treebank) Often difficult to label with consistency and high quality (e.g., semantic parses) Emerging field: Machine reading Extract knowledge from unstructured text with high precision/recall and minimal human effort (More in tomorrow’s talk at 4PM) 125 Unsupervised Learning: How? I.i.d. learning: Sophisticated model requires more labeled data Statistical relational learning: Sophisticated model may require less labeled data Relational dependencies constrain problem space One formula is worth a thousand labels Small amount of domain knowledge large-scale joint inference 126 Unsupervised Learning: How? Ambiguities vary among objects Joint inference Propagate information from unambiguous objects to ambiguous ones E.g.: Are they G. W. Bush … coreferent? He … … Mrs. Bush … 127 Unsupervised Learning: How Ambiguities vary among objects Joint inference Propagate information from unambiguous objects to ambiguous ones E.g.: Should be G. W. Bush … coreferent He … … Mrs. Bush … 128 Unsupervised Learning: How Ambiguities vary among objects Joint inference Propagate information from unambiguous objects to ambiguous ones E.g.: So must be G. W. Bush … singular male! He … … Mrs. Bush … 129 Unsupervised Learning: How Ambiguities vary among objects Joint inference Propagate information from unambiguous objects to ambiguous ones E.g.: Must be G. W. Bush … singular female! He … … Mrs. Bush … 130 Unsupervised Learning: How Ambiguities vary among objects Joint inference Propagate information from unambiguous objects to ambiguous ones E.g.: Verdict: G. W. Bush … Not coreferent! He … … Mrs. Bush … 131 Parameter Learning Marginalize out hidden variables log P ( x) Ez| x ni ( x, z ) Ex , z ni ( x, z ) wi Sum over z, conditioned on observed x Summed over both x and z Use MC-SAT to approximate both expectations May also combine with contrastive estimation [Poon & Cherry & Toutanova, NAACL-2009] 132 Unsupervised Coreference Resolution Head(mention, string) Type(mention, type) MentionOf(mention, entity) Mixture model MentionOf(+m,+e) Type(+m,+t) Joint inference formulas: Head(+m,+h) ^ MentionOf(+m,+e) Enforce agreement MentionOf(a,e) ^ MentionOf(b,e) => (Type(a,t) <=> Type(b,t)) … (similarly for Number, Gender etc.) 133 Unsupervised Coreference Resolution Head(mention, string) Type(mention, type) MentionOf(mention, entity) Apposition(mention, mention) MentionOf(+m,+e) Type(+m,+t) Head(+m,+h) ^ MentionOf(+m,+e) MentionOf(a,e) ^ MentionOf(b,e) => (Type(a,t) <=> Type(b,t)) Joint inference formulas: … (similarly for Number, Gender etc.) Leverage apposition Apposition(a,b) => (MentionOf(a,e) <=> MentionOf(b,e)) More: H. Poon and P. Domingos, “Joint Unsupervised Coreference Resolution with Markov Logic”, in Proc. EMNLP-2008. 134 USP: End-to-End Machine Reading [Poon & Domingos, EMNLP-2009, ACL-2010] Read text, extract knowledge, answer questions, all without any training examples Recursively clusters expressions composed with or by similar expressions Compared to state of the art like TextRunner, five-fold increase in recall, precision from below 60% to 91% (More in tomorrow’s talk at 4PM) 135 End of The Beginning … Let’s not forget our grand goal: Computers understand natural languages Time to think about a new synthesis Integrate previously fragmented subfields Adopt 80/20 rule End-to-end evaluations Statistical relational learning offers a promising new tool for this Growth area of machine learning and NLP 136 Future Work: Inference Scale up joint inference Cutting-planes methods (e.g., [Riedel, 2008]) Unify lifted inference with sampling Coarse-to-fine inference [Kiddon & Domingos, 2010] Alternative technology E.g., linear programming, lagrangian relaxation 137 Future Work: Supervised Learning Alternative optimization objectives E.g., max-margin learning [Huynh & Mooney, 2009] Learning for efficient inference E.g., learning arithmetic circuits [Lowd & Domingos, 2008] Structure learning: Improve accuracy and scalability E.g., [Kok & Domingos, 2009] 138 Future Work: Unsupervised Learning Model: Learning objective, formalism, etc. Learning: Local optima, intractability, etc. Hyperparameter tuning Leverage available resources Semi-supervised learning Multi-task learning Transfer learning (e.g., domain adaptation) Human in the loop E.g., interative ML, active learning, crowdsourcing 139 Future Work: NLP Applications Existing application areas: More joint inference opportunities Additional domain knowledge Combine multiple pipeline stages A “killer app”: Machine reading Many, many more awaiting YOU to discover 140 Summary We need to unify logical and statistical NLP Markov logic provides a language for this Syntax: Weighted first-order formulas Semantics: Feature templates of Markov nets Inference: Satisfiability, MCMC, lifted BP, etc. Learning: Pseudo-likelihood, VP, PSCG, ILP, etc. Growing set of NLP applications Open-source software: Alchemy alchemy.cs.washington.edu Book: Domingos & Lowd, Markov Logic, Morgan & Claypool, 2009. 141 References [Banko et al., 2007] Michele Banko, Michael J. Cafarella, Stephen Soderland, Matt Broadhead, Oren Etzioni, "Open Information Extraction From the Web", In Proc. IJCAI-2007. [Chakrabarti et al., 1998] Soumen Chakrabarti, Byron Dom, Piotr Indyk, "Hypertext Classification Using Hyperlinks", in Proc. SIGMOD-1998. [Damien et al., 1999] Paul Damien, Jon Wakefield, Stephen Walker, "Gibbs sampling for Bayesian non-conjugate and hierarchical models by auxiliary variables", Journal of the Royal Statistical Society B, 61:2. [Domingos & Lowd, 2009] Pedro Domingos and Daniel Lowd, Markov Logic, Morgan & Claypool. [Friedman et al., 1999] Nir Friedman, Lise Getoor, Daphne Koller, Avi Pfeffer, "Learning probabilistic relational models", in Proc. IJCAI- 142 1999. References [Halpern, 1990] Joe Halpern, "An analysis of first-order logics of probability", Artificial Intelligence 46. [Huynh & Mooney, 2009] Tuyen Huynh and Raymond Mooney, "Max- Margin Weight Learning for Markov Logic Networks", In Proc. ECML-2009. [Kautz et al., 1997] Henry Kautz, Bart Selman, Yuejun Jiang, "A general stochastic approach to solving problems with hard and soft constraints", In The Satisfiability Problem: Theory and Applications. AMS. [Kok & Domingos, 2007] Stanley Kok and Pedro Domingos, "Statistical Predicate Invention", In Proc. ICML-2007. [Kok & Domingos, 2008] Stanley Kok and Pedro Domingos, "Extracting Semantic Networks from Text via Relational Clustering", In Proc. 143 ECML-2008. References [Kok & Domingos, 2009] Stanley Kok and Pedro Domingos, "Learning Markov Logic Network Structure via Hypergraph Lifting", In Proc. ICML-2009. [Ling & Weld, 2010] Xiao Ling and Daniel S. Weld, "Temporal Information Extraction", In Proc. AAAI-2010. [Lowd & Domingos, 2007] Daniel Lowd and Pedro Domingos, "Efficient Weight Learning for Markov Logic Networks", In Proc. PKDD-2007. [Lowd & Domingos, 2008] Daniel Lowd and Pedro Domingos, "Learning Arithmetic Circuits", In Proc. UAI-2008. [Meza-Ruiz & Riedel, 2009] Ivan Meza-Ruiz and Sebastian Riedel, "Jointly Identifying Predicates, Arguments and Senses using Markov Logic", In Proc. NAACL-2009. 144 References [Muggleton, 1996] Stephen Muggleton, "Stochastic logic programs", in Proc. ILP-1996. [Nilsson, 1986] Nil Nilsson, "Probabilistic logic", Artificial Intelligence 28. [Page et al., 1998] Lawrence Page, Sergey Brin, Rajeev Motwani, Terry Winograd, "The PageRank Citation Ranking: Bringing Order to the Web", Tech. Rept., Stanford University, 1998. [Poon & Domingos, 2006] Hoifung Poon and Pedro Domingos, "Sound and Efficient Inference with Probabilistic and Deterministic Dependencies", In Proc. AAAI-06. [Poon & Domingos, 2007] Hoifung Poon and Pedro Domingo, "Joint Inference in Information Extraction", In Proc. AAAI-07. 145 References [Poon & Domingos, 2008a] Hoifung Poon, Pedro Domingos, Marc Sumner, "A General Method for Reducing the Complexity of Relational Inference and its Application to MCMC", In Proc. AAAI- 08. [Poon & Domingos, 2008b] Hoifung Poon and Pedro Domingos, "Joint Unsupervised Coreference Resolution with Markov Logic", In Proc. EMNLP-08. [Poon & Domingos, 2009] Hoifung and Pedro Domingos, "Unsupervised Semantic Parsing", In Proc. EMNLP-09. [Poon & Cherry & Toutanova, 2009] Hoifung Poon, Colin Cherry, Kristina Toutanova, "Unsupervised Morphological Segmentation with Log-Linear Models", In Proc. NAACL-2009. 146 References [Poon & Vanderwende, 2010] Hoifung Poon and Lucy Vanderwende, "Joint Inference for Knowledge Extraction from Biomedical Literature", In Proc. NAACL-10. [Poon & Domingos, 2010] Hoifung and Pedro Domingos, "Unsupervised Ontology Induction From Text", In Proc. ACL-10. [Riedel 2008] Sebatian Riedel, "Improving the Accuracy and Efficiency of MAP Inference for Markov Logic", In Proc. UAI-2008. [Riedel et al., 2009] Sebastian Riedel, Hong-Woo Chun, Toshihisa Takagi and Jun'ichi Tsujii, "A Markov Logic Approach to Bio- Molecular Event Extraction", In Proc. BioNLP 2009 Shared Task. [Selman et al., 1996] Bart Selman, Henry Kautz, Bram Cohen, "Local search strategies for satisfiability testing", In Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge. AMS. 147 References [Singla & Domingos, 2006a] Parag Singla and Pedro Domingos, "Memory-Efficient Inference in Relational Domains", In Proc. AAAI- 2006. [Singla & Domingos, 2006b] Parag Singla and Pedro Domingos, "Entity Resolution with Markov Logic", In Proc. ICDM-2006. [Singla & Domingos, 2007] Parag Singla and Pedro Domingos, "Markov Logic in Infinite Domains", In Proc. UAI-2007. [Singla & Domingos, 2008] Parag Singla and Pedro Domingos, "Lifted First-Order Belief Propagation", In Proc. AAAI-2008. [Taskar et al., 2002] Ben Taskar, Pieter Abbeel, Daphne Koller, "Discriminative probabilistic models for relational data", in Proc. UAI- 2002. 148 References [Toutanova & Haghighi & Manning, 2008] Kristina Toutanova, Aria Haghighi, Chris Manning, "A global joint model for semantic role labeling", Computational Linguistics. [Wang & Domingos, 2008] Jue Wang and Pedro Domingos, "Hybrid Markov Logic Networks", In Proc. AAAI-2008. [Wellman et al., 1992] Michael Wellman, John S. Breese, Robert P. Goldman, "From knowledge bases to decision models", Knowledge Engineering Review 7. [Yoshikawa et al., 2009] Katsumasa Yoshikawa, Sebastian Riedel, Masayuki Asahara and Yuji Matsumoto, "Jointly Identifying Temporal Relations with Markov Logic", In Proc. ACL-2009. 149

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