Centering theory and
its direct applications
Lecture 2
Some definitions
Discourse = coherent sequence of
utterances
 Several sentences following one
another do not make a readable text
 Defining specific computable
measures of coherence is the goal of
this seminar

Centering theory ingredients

Deals with local coherence
What happens to the flow from
sentence to sentence
 Does not deal with global structuring
of the text (paragraphs/segments)


Defines coherence as an estimate of
the processing load required to
“understand” the text
Processing load

Upon hearing a sentence a person
Cognitive effort to interpret the
expressions in the utterance
 Integrates the meaning of the
utterance with that of the previous
sentence
 Creates some expectations on what
might come next

Example
(3)
John met his friend Mary today.
He was surprised to see her.
He thought she is still in Italy.

Form of referring expressions
(1)
(2)



Anaphora needs to be resolved
“Create” a discourse entity at first mention
with full noun phrase
Creating expectations
Creating and meeting
expectations
(1) a. John went to his favorite music store to buy a piano.
b. He had frequented the store for many years.
c. He was excited that he could finally buy a piano.
d. He arrived just as the store was closing for the day.
(2) a. John went to his favorite music store to buy a piano.
b. It was a store John had frequented for many years.
c. He was excited that he could finally buy a piano.
d. It was closing just as John arrived.
Interpreting pronouns
a.
b.
c.
d.
e.
Terry really goofs sometimes.
Yesterday was a beautiful day and he was
excited about trying out his new sailboat.
He wanted Tony to join him on a sailing
expedition.
He called him at 6am.
He was sick and furious at being woken
up so early.
Basic center definitions

Centers of an utterance
Set of entities serving to link that
utterance to the other utterances in
the discourse segment that contains it
 Not words or phrases themselves
 Semantic interpretations of noun
phraes

Types of centers



Forward looking centers
 An ordered set of entities
 What could we expect to hear about next
 Ordered by salience as determined by grammatical
function
 Subject > Indirect object > Object > Others
John gave the textbook to Mary.
 Cf = {John, Mary, textbook}
Preferred center Cp
 The highest ranked forward looking center
 High expectation that the next utterance in the
segment will be about Cp
Backward looking center

Single backward looking center, Cb (U)

For each utterance other than the
segment-initial one
The backward looking center of
utterance Un+1 connects with one of the
forward looking centers of Un
 Cb (U+1) is the most highly ranked
element from Cf (Un) that is also
realized in U+1

Centering transitions
ordering
Cb(Un+1)=Cb(Un) Cb(Un+1) !=
OR
Cb(Un)
Cb(Un)=[?]
Cb(Un+1) =
Cp (Un+1)
continue
Cb(Un+1) !=
Cp (Un+1)
retain
smooth-shift
rough-shift
Centering constraints

There is precisely one backwardlooking center Cb(Un)

Cb(Un+1) is the highest-ranked element
of Cf(Un) that is realized in Un+1
Centering rules

If some element of Cf(Un) is realized
as a pronoun in Un+1 then so is
Cb(Un+1)

Transitions not equal

continue > retain > smooth-shift >
rough-shift
Centering analysis

Terry really goofs sometimes.
 Cf={Terry}, Cb=?, undef

Yesterday was a beautiful day and he was excited
about trying out his new sailboat.
 Cf={Terry,sailboat}, Cb=Terry, continue

He wanted Tony to join him in a sailing expedition.
 Cf={Terry, Tony, expedition}, Cb=Terry, continue

He called him at 6am.
 Cf={Terry,Tony}, Cb=Terry, continue

He called him at 6am.
 Cf={Terry,Tony}, Cb=Terry, continue

Tony was sick and furious at being woken up so early.
 Cf={Tony}, Cb=Tony, smooth shift

He told Terry to get lost and hung up.
 Cf={Tony,Terry}, Cb=Tony, continue

Of course, Terry hadn’t intended to upset Tony.
 Cf={Terry,Tony}, Cb = Tony, retain
Rough shifts in evaluation of
writing skills

One of the graders of student essays in standardized tests is an
automatic program

ETS researchers have developed a number of applications that use
natural language processing technologies to evaluate and score
the writing abilities of test takers:

The CriterionSM Online Essay Evaluation Service automatically
evaluates essay responses using e-rater and the Critique writing
analysis tools.

E-rater® gives holistic scores for essays.

CritiqueTM provides real-time feedback about grammar, usage,
mechanics and style, and organization and development.

C-raterTM offers automated analysis of conceptual information in
short-answer, free responses.
E-rater features

Syntactic variety


Clear transitions




Represented by features that quantify the
occurrence of clause types
Cue phrases in certain syntactic
constructions
Existence of main and supporting points
Appropriateness of the vocabulary content
of the essay
What about local coherence?
Ranking forward looking
centers
Subject >
 Indirect object >
 Object >
 Others >
 Quantified indefinite subjects (people,
everyone) >
 Arbitrary plural pronominals

Essay score model
Human score available
 E-rater prediction available
 Percentage of rough-shifts in each
essay: analysis done manually


Negative correlation between the
human score and the percentage of
rough-shifts
Karamanis’07

Why are we reading this paper?

Gives quite complete list of references on
later work on centering
• Centering variants

Reminds that entity coherence is not the
only factor in text flow
• We’ll be discussing rhetorical structure theory
during the next class

Applications---can some aspects of the work
be done differently/improved upon?
Information ordering task

Given a set of sentences/clauses, what is
the best presentation?


Criteria for deciding which of two orderings
is better


Take a newspaper article and jumble the
sentences---the result will be much more
difficult to read than the original
Centering would definitely be applicable
Summarization, question answering,
generation

Linear multi-factor regression


Adding rough shifts significantly improves
the model of the score


Approximate the human score as a linear
function of the e-rater prediction and the
percentage of rough-shifts
0.5 improvement on 1—6 scale
How easy/difficult would it be to fully
automate the rough-shift variable
Centering variations

Continuity (NOCB=lack of continuity)


Coherence



Cb(Un) = Cb(Un+1)
Salience


Cf(Un) and Cf(Un+1) share at least one
element
The Cb(U) = Cp(U)
Coherence is more important than salience
Cheapness (fulfilled expectations)

Cb (Un+1) = Cp(Un)
GNOME corpus

20 descriptions of museum artifacts



Split into finite unites (clauses)
Semi-automatic centering annotation
Item 144 is a torc. Its present arrangement,
twisted into three rings, may be a modern
alteration; it should probably be a single
ring, worn around the neck. The terminals
are in the form of goats’ heads.
Rhetorical coherence


Each text can be seen as a hierarchical tree
structure
Different spans are related by some
rhetorical relation





Elaboration (adding more information)
Contrast
Sequence
Purpose
Summary etc
Local rhetorical coherence

Applies only locally rather than on the text as a whole
 Signaled by cue phrases
 Contrast: but, however, on the other hand
 Continuation: and, then, later
 Consequence: because, in order to, so

These local rhetorical relations structure the text

When missing, entity coherence determines the flow
 8 out of the 20 texts do not have any explicitly marked
rhetorical relations
Joint centering and local
rhetorical coherence

In clauses directly marked for a rhetorical
relation

Merge the Cf lists of the two clauses

Apply centering transitions on the resulting
Cf list rather than the original

GNOME-RR contains 1.58 fewer CF lists
compared to the original average number
(8.35)
Metrics of coherence
M.NOCB (no continuity)
 M.CHEAP (expectations not met)
 M.KP sum of the violations of
continuity, cheapness, coherence and
salience
 M. BFP seeks to maximize transitions
according to Rule 2

Experimental methodology

Gold-standard ordering



The original order of the text (object
description, news article)
Assume that other orderings are inferior
Classification error rate

Percentage orderings that score better than
the gold-standard
+ 0.5*percentage of the orderings that score
the same
Results

NOCB gives best results

Significantly better than the other
metrics

M.BFP is the second best metric

Adding the local rhetorical relations
hurts performance---is this surprising?
Reminders

Select topics you would like to present



Should schedule next week now
The second time you present one of the
goals will be to relate the papers with
previous topics we have covered
Start thinking about the topic of your
literature overview



About 15 papers
5/6 pages
Due Nov 12