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Dependency Grammar Dependency Grammar Introduc)on Christopher Manning Dependency Grammar and Dependency Structure Dependency syntax postulates that syntac)c structure consists of relaons between lexical items, normally binary asymmetric relaons (“arrows”) called dependencies submitted Bills were by on Brownback ports Senator Republican and immigration of Kansas Christopher Manning Dependency Grammar and Dependency Structure Dependency syntax postulates that syntac)c structure consists of relaons between lexical items, normally binary asymmetric relaons (“arrows”) called dependencies submitted nsubjpass auxpass prep The arrows are Bills were by commonly typed prep pobj with the name of on Brownback pobj nn appos grammacal ports Senator Republican relaons (subject, cc conj prep preposi)onal object, and immigration of apposi)on, etc.) pobj Kansas Christopher Manning Dependency Grammar and Dependency Structure Dependency syntax postulates that syntac)c structure consists of relaons between lexical items, normally binary asymmetric relaons (“arrows”) called dependencies submitted The arrow connects a nsubjpass auxpass prep head (governor, Bills were by superior, regent) with a prep pobj dependent (modifier, on inferior, subordinate) Brownback pobj nn appos ports Senator Republican Usually, dependencies cc conj prep form a tree (connected, and immigration of acyclic, single-head) pobj Kansas Christopher Manning Dependency Grammar and Dependency Structure ROOT Discussion of the outstanding issues was completed . • Some people draw the arrows one way; some the other way! • Tesnière had them point from head to dependent… • Usually add a fake ROOT so every word is a dependent of precisely 1 other node Christopher Manning Dependency Grammar/Parsing History • The idea of dependency structure goes back a long way • To Pāṇini’s grammar (c. 5th century BCE) • Basic approach of 1st millennium Arabic grammarians • Cons)tuency is a new-fangled inven)on • 20th century inven)on (R.S. Wells, 1947) • Modern dependency work o^en linked to work of L. Tesnière (1959) • Was dominant approach in “East” (Russia, China, …) • Good for free-er word order languages • Among the earliest kinds of parsers in NLP, even in the US: • David Hays, one of the founders of U.S. computaonal linguis)cs, built early (first?) dependency parser (Hays 1962) Christopher Manning Rela9on between phrase structure and dependency structure • A dependency grammar has a no)on of a head. Officially, CFGs don’t. • But modern linguis)c theory and all modern stas)cal parsers (Charniak, Collins, Stanford, …) do, via hand-wrihen phrasal “head rules”: • The head of a Noun Phrase is a noun/number/adj/… • The head of a Verb Phrase is a verb/modal/…. • The head rules can be used to extract a dependency parse from a CFG parse • The closure of dependencies give cons)tuency from a dependency tree • But the dependents of a word must be at the same level (i.e., “flat”) – there can be no VP! Christopher Manning Dependency Condioning Preferences What are the sources of informaon for dependency parsing? 1. Bilexical affini)es [issues à the] is plausible 2. Dependency distance mostly with nearby words 3. Intervening material Dependencies rarely span intervening verbs or punctuaon 4. Valency of heads How many dependents on which side are usual for a head? ROOT Discussion of the outstanding issues was completed . Christopher Manning Dependency Parsing • A sentence is parsed by choosing for each word what other word (including ROOT) that it is a dependent of. • Usually some constraints: • Only one word is a dependent of ROOT • Don’t want cycles A → B, B → A • This makes the dependencies a tree • Final issue is whether arrows can cross (non-projecve) or not ROOT I ’ll give a talk tomorrow on bootstrapping 9 Christopher Manning Methods of Dependency Parsing 1. Dynamic programming (like in the CKY algorithm) You can do it similarly to lexicalized PCFG parsing: an O(n5) algorithm Eisner (1996) gives a clever algorithm that reduces the complexity to O(n3), by producing parse items with heads at the ends rather than in the middle 2. Graph algorithms You create a Minimum Spanning Tree for a sentence McDonald et al.’s (2005) MSTParser scores dependencies independently using a ML classifier (he uses MIRA, for online learning, but it can be something else) 3. Constraint Sasfac)on Edges are eliminated that don’t sasfy hard constraints. Karlsson (1990), etc. 4. “Determinis)c parsing” Greedy choice of aachments guided by good machine learning classifiers MaltParser (Nivre et al. 2008) DP for generave dependency grammars Christopher Manning Probabilistic dependency grammar: generative model $ λw ρw 1. Start with left wall $ 0 0 2. Generate root w0 w0 3. Generate left children w-1, w w w-2, ..., w-ℓ from the FSA λw0 -1 1 4. Generate right children w1, w-2 w w2, ..., wr from the FSA ρw0 2 ... 5. Recurse on each wi for i in {- ... ℓ, ..., -1, 1, ..., r}, sampling αi λw-ℓ (steps 2-4) w-ℓ 6. Return αℓ...α-1w0α1...αr wr w-ℓ.-1 These 5 slides are based on slides by Jason Eisner and Noah Smith Christopher Manning Naïve Recognition/Parsing goal O(n5) p combinations p c r i j k 0 n goal takes It takes takes to It takes two to tango It takes two to tango Christopher Manning Dependency Grammar Cubic Recognition/Parsing (Eisner & Satta, 1999) • Triangles: span over words, where tall side of triangle is the head, other } side is dependent, and no non-head words expecting more dependents • Trapezoids: span over words, where larger side is head, smaller side is } dependent, and smaller side is still looking for dependents on its side of the trapezoid Christopher Manning Dependency Grammar Cubic Recognition/Parsing (Eisner & Satta, 1999) A triangle is agoal head with some left (or right) subtrees. One trapezoid per dependency. It takes two to tango Christopher Manning Cubic Recognition/Parsing (Eisner & Satta, 1999) goal O(n) combinations 0 i n O(n3) combinations i j k i j k O(n3) combinations i j k i j k Gives O(n3) dependency grammar parsing Graph Algorithms: MSTs 17 Christopher Manning McDonald et al. (2005 ACL) Online Large-Margin Training of Dependency Parsers • One of two best-known recent dependency parsers • Score of a dependency tree = sum of scores of dependencies • Scores are independent of other dependencies • If scores are available, parsing can be solved as a minimum spanning tree problem • Chiu-Liu-Edmonds algorithm • One then needs a score for dependencies Christopher Manning McDonald et al. (2005 ACL): Online Large-Margin Training of Dependency Parsers • Edge scoring is via a discriminave classifier • Can condi)on on rich features in that context • Each dependency is a linear func)on of features )mes weights • Feature weights were learned by MIRA, an online large-margin algorithm • But you could use an SVM, maxent, or a perceptron • Features cover: • Head and dependent word and POS separately • Head and dependent word and POS bigram features • Words between head and dependent • Length and direc)on of dependency Greedy Transion-Based Parsing MaltParser Christopher Manning MaltParser [Nivre et al. 2008] • A simple form of greedy discriminave dependency parser • The parser does a sequence of bohom up ac)ons • Roughly like “shi^” or “reduce” in a shi^-reduce parser, but the “reduce” ac)ons are specialized to create dependencies with head on le^ or right • The parser has: • a stack σ, wrihen with top to the right • which starts with the ROOT symbol • a buffer β, wrihen with top to the le^ • which starts with the input sentence • a set of dependency arcs A • which starts off empty • a set of ac)ons Christopher Manning Basic transion-based dependency parser Start: σ = [ROOT], β = w1, …, wn , A = ∅ 1. Shi σ, wi|β, A è σ|wi, β, A 2. Le^-Arcr σ|wi, wj|β, A è σ, wj|β, A∪{r(wj,wi)} 3. Right-Arcr σ|wi, wj|β, A è σ, wi|β, A∪{r(wi,wj)} Finish: β = ∅ Notes: • Unlike the regular presentaon of the CFG reduce step, dependencies combine one thing from each of stack and buffer Christopher Manning Ac9ons (“arc-eager” dependency parser) Start: σ = [ROOT], β = w1, …, wn , A = ∅ 1. Le^-Arcr σ|wi, wj|β, A è σ, wj|β, A∪{r(wj,wi)} Precondi)on: r’ (wk, wi) ∉ A, wi ≠ ROOT 2. Right-Arcr σ|wi, wj|β, A è σ|wi|wj, β, A∪{r(wi,wj)} 3. Reduce σ|wi, β, A è σ, β, A Precondi)on: r’ (wk, wi) ∈ A 4. Shi σ, wi|β, A è σ|wi, β, A Finish: β = ∅ This is the common “arc-eager” variant: a head can immediately take a right dependent, before its dependents are found Christopher Manning 1. Le^-Arcr σ|wi, wj|β, A è σ, wj|β, A∪{r(wj,wi)} Precondi)on: (wk, r’, wi) ∉ A, wi ≠ ROOT 2. Right-Arcr σ|wi, wj|β, A è σ|wi|wj, β, A∪{r(wi,wj)} Example 3. Reduce σ|wi, β, A è σ, β, A Precondi)on: (wk, r’, wi) ∈ A 4. Shi σ, wi|β, A è σ|wi, β, A Happy children like to play with their friends . [ROOT] [Happy, children, …] ∅ Shi [ROOT, Happy] [children, like, …] ∅ LAamod [ROOT] [children, like, …] {amod(children, happy)} = A1 Shi [ROOT, children] [like, to, …] A1 LAnsubj [ROOT] [like, to, …] A1 ∪ {nsubj(like, children)} = A2 RAroot [ROOT, like] [to, play, …] A2 ∪{root(ROOT, like) = A3 Shi [ROOT, like, to] [play, with, …] A3 LAaux [ROOT, like] [play, with, …] A3∪{aux(play, to) = A4 RAxcomp [ROOT, like, play] [with their, …] A4∪{xcomp(like, play) = A5 Christopher Manning 1. Le^-Arcr σ|wi, wj|β, A è σ, wj|β, A∪{r(wj,wi)} Precondi)on: (wk, r’, wi) ∉ A, wi ≠ ROOT 2. Right-Arcr σ|wi, wj|β, A è σ|wi|wj, β, A∪{r(wi,wj)} Example 3.
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