Markov Logic Networks for NLP CSCI-GA.2591 NYU Markov Logic Networks for NLP CSCI-GA.2591 Ralph Grishman

Markov Logic Networks There is strong interest in combining symbolic and statistical reasoning The general area is termed “Statistical Relational Learning” One of the most widely used representations is Markov Logic Networks early software support (Alchemy) continuing software development (Tuffy) lots of publications (Domingos)

Markov Logic In a traditional knowledge base, consisting of a set of formulas, all these formulas must be true in each possible world In Markov logic, each formula is assigned a weight a formula which is violated makes the world less likely but still possible

Markov Logic Network Consists of: a set of pairs {<Fi, wi>} of a formula and its weight a set of constants C = {c1, … , cn} assume that C is closed under all functions Network has a node for each possible grounding of each formula two nodes are connected if their formulas share a ground atom

Probability of a state x where F = number of formulas Fi ni(x) = number of true groundings of Fi in x

An Example (from last week) Four axioms: friends of friends are friends people without friends smoke people who smoke get cancer if two people are friends, either both smoke or neither does Predicates: are friends: F(x, y) smokes: S(x) gets cancer: C (x)

… adding weights Clearly these formulas are not always true: not everyone who smokes gets cancer Adding weights to these formulas allows us to capture formulas which are generally true the weights reflect the strength of the coupling of the two nodes, but are not probabilities (may be more than 1)

An Example … with weights Four axioms: friends of friends are friends 0.7 people without friends smoke 2.3 people who smoke get cancer 1.5 if two people are friends, either both smoke or neither does 1.1 Predicates: are friends: F(x, y) smokes: S(x) gets cancer: C (x)

Harnessing the Power This seems intuitively a more powerful representation than FOL or MRFs separately can it be made efficient enough? in view of the brute-force approach: we deal with quantified formulas by grounding them producing very large sets of formulas

Inference First task: finding most likely state (grounding) subproblem: SAT (satisfiability task for propositional logic): deciding whether a propositional logic formula can be satisfied, and give a state which satisfies it ex: x  y satisfied if x=false and y = true x & !x not satisfiable How about (a + b + c) (a’ + b’ + c) (a + b’ + c’) (a’ + b + c’)? intensively studied problem [Davis-Putnam procedure, 1962] NP hard

WalkSAT Random walk to search for satisfiability Repeat: select a clause not satisfied by current assignment to variables (if none, done) choose a variable at random and flip it Generally prefer flipping a variable which minimizes the number of clauses which become unsatisfied (but sometimes make a pure random choice c https://www.cs.rochester.edu/u/kautz/walksat/

MaxWalkSAT Generalization of WalkSAT to handle weighted propositions

Reducing memory requirements problem: a domain may be too large to fully instantiate address through lazy instantiation: LazyWalkSAT observe that most propositions are false most clauses are true so just keep true propositions and false clauses in memory

More SATs SampleSAT combines WalkSAT with simulated annealing MC-SAT in Alchemy extends SampleSAT

Learning Scaled conjugant gradient or similar Maximize likelihood of data base Can be quite slow – must do inference at cycle Use pseudo-likekihood (dependent only on Markov blanket) to speed up Optimizing more difficult because of very different constraints Deterministic and near-deterministic dependencies

Alchemy Implementation of Markov Logic Networks From Univ. of Washington

Installation / Access Distribution is for Linux systems General site: https://alchemy.cs.washington.edu I have been running Alchemy 2.0 Distribution is for Linux systems User’s manual https://alchemy.cs.washington.edu/user-manual/manual.html (section 2) Suggestions for building for Mac or Windows at: https://alchemy.cs.washington.edu/requirements (may not be sufficient) Installed on CIMS servers at ~grishman/alchemy/alchemy2

MLN Files (highlights) 3 components Declaration of types and constants Declaration of predicates List of formulas and their weights

Data Base File Typically large file of ground atoms Training and test sets

Basic operations Learn weights Infer learnwts -g –i f.mln –t f.train.db –o f.out.mln Infer infer –i f.out.mln –e f.test.db –q … -r results

Warm-Up Assignment The ACE event inventory includes Attack, Injure, and Die events, which are correlated … intuitively, attacks cause the attacked party both injury and death. Using Alchemy, Represent the predicates by attack(x,y), injured(y), and die(y) Write the formulas to expess the relations between these predicates Prepare small training and test data bases Learn weights for these formulas Infer the probability of the ground atoms Very briefly, explain the inferred results. Due: one week (Nov. 20)

Looking ahead Hopefully it is a small step from this to doing joint inference for trigger identification … combining these rules with P(event-type | trigger-word)