Generation of Referring Expressions (GRE)

The Incremental Algorithm (IA)

Dale & Reiter (1995)

The task: GRE

NLG can have different kinds of inputs: ‘Flat’ data (collections of atoms, e.g., in the

tables of a database) Logically complex data

In both cases, unfamiliar constants may be used, and this is sometimes unavoidable

No familiar constant available:

1. The referent has a familiar name, but it’s not unique, e.g., ‘John Smith’

2. The referent has no familiar name: trains, furniture, trees, atomic particles, …

( In such cases, databases use database keys,

e.g., ‘Smith$73527$’, ‘TRAIN-3821’ )

3. Similar: sets of objects.

Natural Languages are too economic to have a proper name for everything

Names may not even be most appropriate So, speakers/NLG systems have to invent

ways of referring to things. E.g., ‘the 7:38 Trenton express’

Older work on GRE

Winograd (1972) – the SHRDLU system,

and especially

Appelt (1985) – the KAMP system: trying to understand reference as part of speech acts: How can RE’s sometimes add information? Why can RE1 be more relevant than RE2?

Dale and Reiter isolate GRE as a separate task, and focus on simple cases

Dale & Reiter: best description fulfils Gricean maxims.

(Quality:) list properties truthfully (Quantity:) list sufficient properties to allow hearer to

identify referent – but not more (Relevance:) use properties that are of interest in

themselves * (Manner:) be brief

* Slightly different from D&R 1995

D&R’s expectation:

Violation of a maxim leads to implicatures. For example,

[Quantity] ‘the pitbull’ (when there is only one dog).

There’s just one problem: …

…people don’t speak this way

For example, [Quantity] ‘the red chair’ (when there is

only one red object in the domain). [Quantity] ‘I broke my arm’

(when I have two).

General: empirical work shows much redundancy

Similar for other maxims, e.g., [Quality] ‘the man with the martini’ (Donellan)

Consider the following formalization:

Full Brevity (FB): Never use more than the minimal number of properties required for identification (Dale 1989)

An algorithm:

Dale 1989:

1. Check whether 1 property is enough

2. Check whether 2 properties is enough

….

Etc., until

success {minimal description is generated} or

failure {no description is possible}

Problem: exponential complexity

Worst-case, this algorithm would have to inspect all combinations of properties. n properties combinations.

Some algorithms may be faster, but …

Theoretical result: any FB algorithm must be exponential in the number of properties.

n2

D&R conclude that Full Brevity cannot be achieved in practice.

They designed an algorithm that only approximates Full Brevity:

the Incremental Algorithm (IA).

Psycholinguistic inspiration behind IA (e.g. Pechmann 89; overview in Levelt 89)

Speakers often include “unnecessary modifiers” in their referring expressions

Speakers often start describing a referent before they have seen all distractors (as shown by eye-tracking experiments)

Some Attributes (e.g. Colour) seem more likely to be noticed and used than others

Some Attributes (e.g., Type) contribute strongly to a Gestalt. Gestalts help readers identify referents. (“The red thing” vs. “the red bird”)

Let’s start with a simplified version of IA, which uses properties rather than <Attribute:Value> pairs.Type and head nouns are ignored, for now.

Incremental Algorithm (informal):

Properties are considered in a fixed order:

P = A property is included if it is ‘useful’:

true of target; false of some distractors Stop when done; so earlier properties have

a greater chance of being included. (E.g., a perceptually salient property)

Therefore called preference order.

nPPPP ,...,,, 321

r = individual to be described P = list of properties, in preference order P is a property L= properties in generated description

(Recall: we’re not worried about realization today)

FailureReturn

LReturn then {r}C If

]][[C:C

}{L:L

do then ]][[ C &]][[r If

:do P allFor

Domain:C

Φ:L

P

P

PP

P

P = < desk (ab), chair (cde), Swedish (ac), Italian (bde), dark (ade), light (bc), grey (a), 100£ ({ac}), 150£(bd) , 250£ ({}), wooden ({}), metal (abcde), cotton ({d}) >

Domain = {a,b,c,d,e} . Now describe: a = <...>

d = <...>

e = <...>

P = < desk (ab), chair (cde), Swedish (ac), Italian (bde), dark (ade), light (bc), grey (a), 100£ (ac),150£ (bd),250£ ({}), wooden ({}), metal (abcde), cotton (d) >

Domain = {a,b,c,d,e} . Now describe: a = <desk {ab}, Swedish {ac}> d = <chair,Italian,150> (Nonminimal) e = <chair,Italian, ....> (Impossible)

Incremental Algorithm

It’s a hillclimbing algorithm: ever better approximations of a successful description.

‘Incremental’ implies no backtracking.

Not always the minimal number of properties.

Incremental Algorithm

Logical completeness: A unique description is found in finite time if there exists one Question: is IA logicaly complete?

Computational complexity: Assume thattesting for usefulness takes constant time.Then worst-case time complexity is O(np) where np is the number of properties in P.

Better approximation of Full Brevity(D&R 1995)

Attribute + Value model: Properties grouped together as in original example:

Origin: Sweden, Italy, ...

Colour: dark, grey, ... Optimization within the set of properties

based on the same Attribute

Incremental Algorithm, using Attributes and Values

r = individual to be described

A = list of Attributes, in preference order

Def: = Value j of Attribute i

L= properties in generated description

jiV ,

FailureReturn

LReturn then {r}C If

]][[VC:C

}{VL:L

do then ]]V[[ C &]]V[[r If

)A(r,estValueBFindV

:doA A allFor

Domain:C

Φ:L

ji,

ji,

ji,ji,

iji,

i

FindBestValue(r,A):

- Find Values of A that are true of r,

while removing some distractors

(If these don’t exist, go to next Attribute)

- Within this set, select the Value that

removes the largest number of distractors(NB: discriminatory power)

- If there’s a tie, select the most general one

- If there’s still a tie, select an arbitrary one

Example: D = {a,b,c,d,f,g}

Type: furniture (abcd), desk (ab), chair (cd) Origin: Europe (bdfg), USA (ac), Italy (bd)

Describe a: {desk, American}

(furniture removes fewer distractors than desk)

Describe b: {desk, European}

(European is more general than Italian)

N.B. This disregards relevance, etc.

This is a better approximation of Full Brevity

But is it a better algorithm?

Question 1: Is it true that all values of an attribute are (roughly) equally preferred? If the colour of a car is pink, this is more

notable than if it’s white Question 2: Doesn’t the new algorithm

sometimes fail unnecessarily?

About question 2

Exercise: Construct an example where no description is found, although one exists.

Hint: Let Attribute have Values whose extensions overlap.

Example: D = {a,b,c,d,e,f} Contains: wood (abe), plastic (acdf) Colour: grey (ab), yellow (cd)

Describe a: {wood, grey, ...} - Failure

(wood removes more distractors than plastic)

Compare:

Describe a: {plastic, grey} - Success

Conlusion

The version of IA that uses <Attribute,Value> format allows the use of simple ontological information (e.g., Italian European)⊂

But grouping properties into Attributes makes it difficult to model the “unusualness” of a property

And the idea of using discriminatory power leads to logical incompleteness.

IA is therefore (?) often used in its simpler form, without the <Attribute,Value> format

Complexity of the algorithm

nd = nr. of distractors

nl = nr. of properties in the description

nv = nr. of Values (for all Attributes)

According to D&R: O(nd nl )

(Typical running time)

Alternative assessment: O(nv)

(Worst-case running time)

Minor complication: Head nouns

Another way in which human descriptions are nonminimal

A description needs a Noun, but not all properties are expressed as Nouns

Example: Suppose Colour was the

most-preferred Attribute, and suppose target = a

Colours: dark (ade), light (bc), grey (a) Type: furniture (abcde), desk (ab), chair (cde) Origin: Sweden (ac), Italy (bde) Price: 100 (ac), 150 (bd) , 250 ({}) Contains: wood ({}), metal ({abcde}), cotton(d)

target = a Describe a: {grey} ‘The grey’ ? (Not in English)

D&R’s repair:

Assume that Values of the AttributeType can be expressed in a Noun.

After the core algorithm:

- check whether Type is represented.

- if not, then add the best Value of the Type Attribute to the description

Versions of Dale and Reiter’s Incremental Algorithm (IA) have often been implemented

Still the starting point for many new algorithms.

But how human-like is the output of the IA really? The paper does not contain an evaluation of the algorithms discussed

Comments on the algorithm

1. Redundancy exists, but not for principled reasons, e.g., for

- marking topic changes, etc. (Corpus work by Pam Jordan et. al.)

- making it easy to find the referent (Experimental work by Paraboni et al.)

Limitations of the algorithm

2. Targets are individual objects, never sets. What changes when target = {a,b,c} ?

3. Incremental algorithm uses only conjunctions of atomic properties. No negations, disjunctions, etc.

Limitations of D&R

4. No relations with other objects, e.g., ‘the orange on the table’.

5. Differences in salience are not taken into account.

• When we say “the dog”, does this mean that there is only one dog in the world?

6. Language realization is disregarded.

Limitations of D&R

7. Calculation of complexity is iffy

• Role of “Typical” run time and length of description is unclear

• Greedy Algorithm (GA) dismissed even though it has polynomial complexity

• GA: always choose the property that removes the maximum number of distractors

More fundamental features

Speaker and Hearer have shared knowledge This knowledge can be formalised using

atomic statements Foundations were left unformalised, e.g.

Closed-World Assumption Unique Name Assumption

The aim of GRE is to identify the target referent uniquely. (I.e., the aim is to construct a “distinguishing description” of the referent.)

Discussion: How bad is it for a GRE

algorithm to take exponential time choosing the best RE? How do human speakers cope? More complex types of referring expressions

problem becomes even harder Restrict to combinations whose length is

less than x problem not exponential. Example: descriptions containing at most n

properties (Full Brevity)

Linguist’s view

We don’t pretend to mirror psychologically correct processes. (It’s enough if GRE output is correct).

So why worry if our algorithms are slow?

Mathematicians’ view

structure of a problem becomes clear when no restrictions are put.

Practical addition:

What if the input does not conform with these restrictions? (GRE does not control its own input!)

A compromise view

Compare with Description Logic:- Increasingly complex algorithms …- that tackle larger and larger fragments of logic …- and whose complexity is ‘conservative’

When looking at more complex phenomena, take care not to slow down generation of simple cases too much

A note on the history of the IA

Appelt (1985) did not focus on distinguishing descriptions

did not describe an algorithm in detail suggested attempting properties one by one cited the Gricean maxims suggested that the shortest description may

not always be the best one