constrained conditional models tutorial

CONSTRAINED CONDITIONAL MODELS TUTORIALJingyu Chen, Xiao Cheng

INTRODUCTION

Main ideas:• Idea 1: Modeling Separate modeling and problem formulation from algorithms

• Similar to the philosophy of probabilistic modeling

• Idea 2: Inference Keep model simple, make expressive decisions (via constraints)

• Unlike probabilistic modeling, where models become more expressive • Inject background knowledge

• Idea 3: Learning Expressive structured decisions can be supported by simply learned models

• Global Inference can be used to amplify the simple models (and even minimal supervision).

Task of interest: Structured Prediction• Common formulation

• e.g. HMM, CRF, Structured Perceptron etc.

• Covers a lot of NLP problems:• Parsing; Semantic Parsing; Summarization; Transliteration; Co-

reference resolution, Textual Entailment…• IE problems:

• Entities, relations, attributes…• How to improve without incurring performance issues?

Pipeline?• Very crude approximation to the real problem, propagates

error.• Ignores dependency :

• e.g. In relation extraction, the label of the entity depends on the relation it is involved and the relation label depends on the label of its arguments.

Model Formulation• Typical models

• With CCM we choose

Penalty Violation measure

Regularization

Local dependencye.g. HMM, CRF

Constraint expressivity

Multiclass Problem:

One v. All approximation:

Ideal classification, can be expressed through constraints

Implementations

Modeling Objective function

Constrained Optimization Solver

Integer Linear Programming

Inference Exact ILP, Heurisitic Search, Relaxation, Dynamic Programming

Learning Learn and , can be learnt jointly or separately, semi-supervised learning etc.

arg max𝑦𝑤𝑇 𝑓 (𝑥 , 𝑦 ) −𝜌𝑇 𝑑 (𝑥 , 𝑦 )

How do we use CCM to learn?

EXAMPLE 1: JOINT INFERENCE-BASED LEARNINGConstrained HMM in Information Extraction

Typical work flow• Define basic classifiers• Define constraints as linear inequalities• Combine the two into an objective function

HMMCCM Example• Information extraction without prior knowledge• Use HMM

HMMCCM Example

AUTHOR Lars Ole Andersen . Program analysis and

TITLE specialization for the

EDITOR C

BOOKTITLE Programming language

TECH-REPORT . PhD thesis .

INSTITUTION DIKU , University of Copenhagen , May

DATE 1994 .

Violates a lot of natural constraints

HMMCCM Example• Each field must be a consecutive list of words and can

appear at most once in a citation.

• State transitions must occur on punctuation marks.

• The citation can only start with AUTHOR or EDITOR.

• The words pp., pages correspond to PAGE.• Four digits starting with 20xx and 19xx are DATE.• Quotations can appear only in TITLE

HMMCCM Example• How do we use constraints with HMM?• Standard HMM:

• Learn the probability of the sequence of labels and input :

• Inference, taking the most likely label sequence:

HMMCCM Example• New objective function involving constraints• Penalize the probability of sequence if it violates

constraint

Penalty for each time the constraint is violated

HMMCCM Example• Transform to linear model

HMMCCM Example• We need to learn the new parameters maximizes the

scoring function

• Despite the fact that the scoring function is no longer a log likelihood of the dataset, it is still a smooth concave function with a unique global maximum with zero gradient.

HMMCCM Example

Simply counting the probabilityof the constraints being violated

HMMCCM Example

Are there other ways to learn?

Can this paradigm be generalized?

TRAINING PARADIGMS

Training paradigms

DecomposeLearn Inference

Prior knowledge: Features vs. ConstraintsFeature Constraint

Data dependent Yes No (if not learnt)

Learnable Yes Yes

Size Large Small

Improvement Approach Higher order model Post-processing for I+L

Domain

Penalty type Soft Hard & Soft

Common usage Local Global

Formulation Propositional/ FOL/

Comparison with MLN• MLN models constraints are formulated as an explicit

probability jointly with the overall distributions:• e.g.

• Constraints in CCM are formulated as linear inequalities• e.g.

• Theoretically the same, very different in practice

Training paradigms• Learning + Inference: Train with some constraints, apply

all constraints only in inference• No need to retrain an existing system• Fast and modular

• Inference-Based Training: Train jointly with constraints and dependencies (e.g. Graphical Models)• Better for strong interactions between

• Other training paradigm:• Pipe-line like sequential model [Roth, Small, Titov: AI&Stat’09]• Constraints Driven Learning (CODL) [Chang et. al’07,12]

Which paradigm is better?

For each iterationFor each in the training data

If

endifendfor

endfor

Algorithmic view of the differences

IBT−𝜌𝑇𝑑 (𝑥 , 𝑦)

𝒀 𝑷𝑹𝑬𝑫=arg max𝑦𝑤𝑇 𝑓 (𝑥 , 𝑦 ) −𝜌𝑇𝑑 (𝑥 , 𝑦 ) I+L

L+I vs. IBT tradeoffs

# of Features

In some cases problems are hard due to lack of training data.

Semi-supervised learning

Choice of paradigm• IBT:

• Better when the interaction between output label is strong

• L+I:• Faster computationally• Modular, no need to retrain existing classifier and works with

simple models such as

PARADIGM 2:LEARNING + INFERENCEAn example with Entity-Relation Extraction

Entity-Relation Extraction [RothYi07]

Dole ’s wife, Elizabeth , is a native of N.C. E1 E2 E3

R12 R2

3

1: 32Decision time inference


• Formulation 1: Joint Global Model

Intractable to learn Need to decomposition


• Formulation 2: Local learning + global inference


Cost function:

c{E1 = per}· x{E1 = per} + c{E1 = loc}· x{E1 = loc} + … + c{R12 = spouse_of}· x{R12 = spouse_of} + … + c{R12 = }· x{R12 = } + …

R12 R21 R23 R32 R13 R31

E1

DoleE2

ElizabethE3

N.C.


Exactly one label for each relation and entity

Relation and entity type constraints

Integral constraints, in effect boolean


• Each entity is either a person, organization or location:x{E1 = per}+ x{E1 = loc}+ x{E1 = org} + x{E1 = }=1

• (R12 = spouse_of) (E1 = person) (E2 = person)x{R12 = spouse_of} x{E1 = per}

x{R12 = spouse_of} x{E2 = per}


• Entity classification results


• Relation identification results

INNER WORKINGS OF INFERENCE

Constraints Encoding• Atoms

• Existential quantification

• Negation

• Conjunction• Disjunction

Integer Linear Programming (ILP)• Powerful tool, very general

• NP-hard even in binary case, but efficient for most NLP problems

• If ILP can not solve the problem efficiently, we can fall back to approximate solutions using heuristic search

Integer Linear Programming (ILP)

SENTENCE COMPRESSION

Sentence Compression Example Modelling Compression with Discourse Constraints, James Clarke and Mirella Lapata, COLING/SCL 2006

• 1. What is sentence compression? • Sentence compression is commonly expressed as a word deletion

problem: given an input sentence of words W = w1,w2, . . . ,wn, the aim is to produce a compression by removing any subset of these words (Knight and Marcu 2002).

A trigram language model: maximize a scoring function by ILP:

p i: word i starts the compressionq i,j : sequence wi,wj ends the compressionX i,j,k : trigram wi , wj ,wk in the compressionY i : word i in the compressionEach p ,q,x,y is either 0 or 1,

Sentential Constrains:• 1. disallows the inclusion of modifiers without their head

words:

• 2. presence of modifiers when the head is retained in the compression:

• 3. constrains that if a verb is present in the compression then so are its arguments:

Modifier Constraint Example

Sentential Constrains:• 4. preserve personal pronouns in the compressed output:

Discourse Constrains:• 1. Center of a sentence is retained in the compression,

and the entity realised as the center in the following sentence is also retained.

• Center of the sentences is the entity with the highest rank.• Entity may ranked by many features.• EX:• grammatical role• (subjects > objects > others).

Discourse Constrains:• 2. Lexical Chain Constrains:•

• Lexical chain is a sequences of semantically related words.

• Often the longest lexical chain is the most important chain.

SEMANTIC ROLE LABELING

Semantic Role labeling Example:

• What is SRL?• SRL identifies all

constituents that fill a semantic role, and determines their roles.

General information:• Both models(argument identifier and argument

classifiers) are trained by SNoW.

• Idea: maximization the scoring function

SRL: Argument Identification• use a learning scheme that utilizes two classifiers, one to• predict the beginnings of possible arguments, and the

other the ends. The predictions are combined to form argument candidates.

• Why:• When only shallow parsing is available, the system does

not have constituents to begin with. Therefore, conceptually, the system has to consider all possible subsequences.

SRL: List of features• POS tags• Length• Verb class• Head word and POS tag of the head word• Position• Path• Chunk pattern• Clause relative position• Clause coverage• NEG• MOD

SRL: Constraints• 1. Arguments cannot overlap with the predicate.

• 2. Arguments cannot exclusively overlap with the clauses.

• 3. If a predicate is outside a clause, its arguments cannot be embedded in that clause.

• 4. No overlapping or embedding arguments.

• 5. No duplicate argument classes for core arguments.• Note: conjunction is an exception.• [A0 I] [V left ] [A1 my pearls] [A2 to my daughter] and [A1 my

gold] [A2 to my son].

SRL: Constraints• 6. if an argument is a reference to some other argument

arg, then this referenced argument must exist in the sentence.

• 7. If there is a C-arg argument, then there has to be an arg argument; in addition,the C-arg argument must occur after arg.

• the label C-arg is then used to specify the continuity of the arguments.

• 8. Given a specific verb, some argument types should• never occur.

SRL Results:

QA• Questions?

constrained conditional models tutorial

Documents

inferencean example

models global inference

simple models

modeling separate modeling

model simple

joint global model intractable

expressive decisions

machine learning journal