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Automatic learning of morphology

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Automatic learning of morphology

John Goldsmith

July 2003

University of Chicago

- Not “theoretical” – but based on a theory with solid foundations.
- Practical, real data.
- Don’t wait till your grammars are written to start worrying about language learning. You don’t know what language learning is till you’ve tried it. (Like waiting till your French pronunciation is perfect before you start writing a phonology of the language.)

- What you need (to write a language learning device) does not look like the stuff you codified in your grammar. Segmentation and classification.

- This leads to Minimum Description Length theory, which says:
- Minimize the sum of:
- Positive log probability of the data +
- Length of the grammar

- Minimize the sum of:
- It thus leads to a non-cognitive foundation for a science of linguistics – if you happen to be interested in that. You do not need to be. I am.

- Discovery of structure in the data is always equivalent to an increase in the probability that the model assigns to that data.
- The devil is in the details.

- Tuesday: the basics of probability theory, and the treatment and learning of phonotactics, and their role in nativization and alternations
- Thursday: MDL and the discovery of “chunks” in an unbroken string of data.

- Probability involves a set of numbers (not negative) that sum to 1.
- Logarithm of numbers between 0 and 1 are negative. So we shift our attention to -1 times the log (the positiv log: plog).

- 23 = 8, so log2 (8) is 3.
- 24 = 16, so log2 (16) is 4.
- 210 = 1024, so log2 (1024) is 10
- 2-1 = ½ , so log2 (1/2) is -1.
- 2-2 = 1/4 , so log2 (1/4) is -2.
- 2-10 = 1/1024 , so log2 (1/1024) is -10

- These numbers get bigger when the fraction gets smaller (closer to zero).
- They get smaller when the fraction gets bigger (close to 1). Since we want big fractions (high probability), we want small plogs.
- The plog is also the length of the compressed form a word. When you use WinZip, the length of the file is the sum of a lot of plogs for all the words (not exactly words, really, but close).

- The relationship between data and grammar.
- The goal is to create a device that learns aspects of language, given data: a little linguist in a tin box.
- Today: morphological structure.

- A C++ program that runs under Windows that is available at my homepage
http://humanities.uchicago.edu/ faculty/goldsmith/

There are explanations and other downloads available there.

Technical description in

Computational Linguistics (June 2001)

“Unsupervised Learning of the Morphology of a Natural Language”

- Look at Linguistica in action:
English, French

- Why do this?
- What is the theory behind it?
- What are the heuristics that make it work?
- Where do we go from here?

- A program that takes in a text in an “unknown” language…
- and produces a morphological analysis:
- a list of stems, prefixes, suffixes;
- more deeply embedded morphological structure;
- regular allomorphy

raw data

Linguistica

Analyzed data

Here: lists of stems, affixes,

signatures, etc.

Here: some messages

from the analyst to the

user.

Actions and outlines of information

- Brown corpus: 1,200,000 words of typical English
- French Encarta
- or anything else you like, in a text file.
- First set the number of words you want read, then select the file.

List of stems

A stem’s signature is the list of suffixes it appears with in the corpus,

in alphabetical order.

abilit ies.yabilities, ability

abolitionabolition

absence-tabsence, absent

absolute NULL-lyabsolute, absolutely

List of signatures

Signature: NULL ed ing s

for example,

account accounted accounting accounts

add added adding adds

More sophisticated signature…

Signature <e>ion . NULL

composite concentratecorporate détente

discriminateevacuateinflateopposite

participateprobateprosecutetense

What is this?

compositeand composition

composite composit composit + ion

It infers that iondeletes a stem-final ‘e’ before attaching.

In French, we find that the outermost layer of morphology is

not so interesting: it’s mostly é, e, and s. But we can get inside

the morphology of the resulting stems, and get the roots:

- (It is a lot of fun.)
- It can be of practical use: stemming for information retrieval, analysis for statistically-based machine translation.
- This clarifies what the task of language-acquisition is.

- It’s been suggested that (since language acquisition seems to be dauntingly, impossibly hard) it must require prior (innate) knowledge.
- Let’s choose a task where innate knowledge cannot plausibly be appealed to, and see
(i) if the task is still extremely difficult, and

(ii) what kind of language acquisition device could be capable of dealing with the problem.

- The nature of morphology-acquisition does not become clearer by reducing the number of possible analyses of the data, but rather by
- Better understanding the formal character of knowledge and learning.

- The selection of a grammar, given the data, is an optimization problem.
(this has nothing to do with Optimality theory, which does not optimize any function! Optimization means finding a maximum or minimum – remember calculus?)

Minimum Description Length provides us with a means for understanding grammar selection as minimizing a function. (We’ll get to MDL in a moment)

- Number of letters, for one:
- compare:

Naive Minimum Description Length

Corpus:

jump, jumps, jumping

laugh, laughed, laughing

sing, sang, singing

the, dog, dogs

total: 62 letters

Analysis:

Stems: jump laugh sing sang dog (20 letters)

Suffixes: s ing ed (6 letters)

Unanalyzed: the (3 letters)

total: 29 letters.

Notice that the description length

goes UP if we analyze sing into s+ing

- Jorma Rissanen 1989
- The best “theory” of a set of data is the one which is simultaneously:
- 1 most compact or concise, and
- 2 provides the best modeling of the data

- “Most compact” can be measured in bits, using information theory
- “Best modeling” can also be measured in bits…

- Conciseness: Length of the morphology. It’s almost as if you count up the number of symbols in the morphology (in the stems, the affixes, and the rules).
- Length of the modeling of the data. We want a measure which gets bigger as the morphology is a worse description of the data.
- Add these two lengths together = Description Length

Sum all the letters, plus all the structure inherent in the description, using information theory.

The essence of what you need to know from information theory is this:

that mentioning an object can be modeled by a pointer to that object,

whose length (complexity) is equal to -1 times the log of its frequency.

But why you should care about -log (freq(x)) =

is much less obvious.

Number of letters in suffix

l = number of bits/letter < 5

cost of setting up

this entity: length

of pointer in bits

Number of letters in stem

list of pointers to signatures

<X> indicates the number

of distinct elements in X

Probabilistic morphology: the measure:

- -1 * log probability ( data )
where the morphology assigns a probability to any data set.

This is known in information theory as the optimal compressed length of the data (given the model).

A grammar can be used not (just) to specify what is grammatical and what is not, but to assign a probability to each string (or structure).

If we have two grammars that assign different probabilities, then the one that assigns a higher probability to the observed data is the better one.

This follows from the basic principle of rationality in the Universe:

Maximize the probability of the observed data.

There is an objective answer to the question: which of two analyses of a given set of data is better? (modulo the differences between different universal Turing machines)

However, there is no general, practical guarantee of being able to find the best analysis of a given set of data.

Hence, we need to think of (this sort of) linguistics as being divided into two parts:

- An evaluator (which computes the Description Length); and
- A set of heuristics, which create grammars from data, and which propose modifications of grammars, in the hopes of improving the grammar.
(Remember, these “things” are mathematical things: algorithms.)

- Why is this problem so hard at first?
- Because figuring out the best analysis of any given word generally requires having figured out the rough outlines of the whole overall morphology. (Same is true for other parts of the grammar!).
How do we start?

- We’ll modify a suggestion made by Zellig Harris (1955, 1967, 1979[1968]). Harris always believed this would work.
- It doesn’t, but it’s clever and it’s a good start – but only that.

Successor frequency of jum: 2

jum p (jump, jumping, jumps, jumped, jumpy)

b (jumble)

Successor frequency of jump:5

e (jumped)

i (jumping)

jumps (jumps)

y (jumpy)

# (jump)

Zellig Harris:Successor Frequency

predicted break

19 9 6 3 1 3 1 1

a c c e p t i n g

able

ing

lerate (“accelerate”)

nted (“accented”)

ident (“accident”)

laim (“acclaim”)

omodate (“accomodate”)

reditated (“accredited”)

used (“accused”)

Zellig Harris: Successor frequency

ddead

fdeaf

ldeal

ndean

tdeath

Bad

predictions

a

18

a

e

5

d

b debate, debuting

c decade, december, decide

d dedicate, deduce, deduct

e deep

f

9

i

edefeat, defend, defer

ideficit, deficiency

rdefraud

3

Good

predictions

o

Zellig Harris:Successor frequencies

9 18 11 6 4 1 2 1 1 2 1 1

c o n s e r v a t i v e s

wrong

right

wrong

it cannot distinguish between

- phonological freedom due to phonological patterns (C after V, V after C)
- phonological freedom due to morphological pattern (...any morpheme after a +...)
But that’s the problem it’s supposed to solve.

- It can’t deal with cases where several suffixes begin with the same letter(s).
- E.g.

is

ais

donn

donna

it

ait

NULL

a

Analysis based on successor frequency

Correct analysis

- Harris’ method is pretty good.
- We accept only stems of 5 letters or more;
- Only cuts where the SuccFreq is > 1, and where the neighboring SuccFreq is 1.

Corpus

Pick a large corpus from a language --

5,000 to 1,000,000 words.

Corpus

Feed it into the

“bootstrapping” heuristic...

Bootstrap heuristic

Corpus

Bootstrap heuristic

Out of which comes a

preliminary morphology,

which need not be superb.

Morphology

Corpus

Bootstrap heuristic

Feed it to the incremental

heuristics...

Morphology

incremental

heuristics

Corpus

Out comes a modified

morphology.

Bootstrap heuristic

Morphology

modified

morphology

incremental

heuristics

Corpus

Is the modification

an improvement?

Ask MDL!

Bootstrap heuristic

Morphology

modified

morphology

incremental

heuristics

Corpus

If it is an improvement,

replace the morphology...

Bootstrap heuristic

modified

morphology

Morphology

Garbage

Corpus

Send it back to the

incremental

heuristics again...

Bootstrap heuristic

modified

morphology

incremental

heuristics

Continue until there

are no improvements

to try.

Morphology

modified

morphology

incremental

heuristics

- There is nothing sacred about the particular choice of heuristic steps I have chosen…

- Successor Frequency: strict
- Extend signatures to cases where a word is composed of a known stem and a known suffix.
- Loose fit: using 1st order MDL for new signatures
- Check signatures: Using MDL to find best stem/suffix cut. (More on this…)
- Smooth stems

- on/ve → ion/ive
- an/en → man/men
- l/tion → al/ation
- m/t → alism/alist, etc.
How?

- Signature l/tion with stems:
federainauguraorientasubstantia

We need to compute the Description Length of the analysis

as it stands versus

as it would be if we shifted varying parts of the stems to the suffixes.

Current description length is roughly:

The total length of the letters in the stems, converted to bits (by a factor of how many bits per letter) PLUS

The sum of the pointer-lengths to the suffixes – each pointer-length is of length -log( frequency ).

- Find relations among stems: find principles of allomorphy, like
“delete stem-final e before –ing” on the grounds that this simplifies the collection of Signatures:

Compare the signatures

- NULL.ing, and
- e.ing.

- NULL.ing: its stems do not end in –e
- ing almost never appears after stem-final e.
- So e.ing and NULL.ing can both be subsumed under:
- <e>ing.NULL, where <e>ing means a suffix ing which deletes a preceding e.

- Find a signature of the form L.X, where L is a letter. Check that no stems end with L.
- See if another signature NULL.X exists, none of whose stems end in L.
- Clean up and extend.

- Find roots (from among the Stem collection)

- Identifying suffixes through syntactic behavior ( syntax)
- Better allomorphy ( phonology)
- Languages with more morphemes/ word (“rich” morphology)

- “Using eigenvectors of the bigram graph to infer grammatical features and categories” (Belkin & Goldsmith 2002)

- Build a graph in which “similar” words are adjacent;
- Compute the normalized laplacian of that graph;
- Compute the eigenvectors with the lowest non-zero eigenvalues;
- Plot them.

?: and, to, in that, for, he, as, with,

on, by, at, or, from…

finite verbs: was, had,

has, would, said,

could, did, might,

went, thought,

told, knew, took,

asked…

world, way, same, united,

right, system, city, case,

church, problem, company,

past, field, cost, department,

university, rate, door,

non-finite verbs: be, do, go, make,

see, get, take, go, say, put,

find, give, provide, keep, run…

Prepositions: of in for on by at from

into after through under since

during against among within along

across including near

adjectives

social national white local political

personal private strong medical final

black French technical nuclear british

The End