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Automatic learning of morphology

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### The End grammatical features and categories” (Belkin & Goldsmith 2002)

Language learning: unsupervised learning

- 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.

Maximize the probability of the data. look like the stuff you codified in your grammar.

- 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.

!! look like the stuff you codified in your grammar.

- 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.

Classes to come: look like the stuff you codified in your grammar.

- 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.

Looking ahead look like the stuff you codified in your grammar.

- 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).

- 2 look like the stuff you codified in your grammar. 3 = 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

Plog (positive logs) look like the stuff you codified in your grammar.

- 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).

Evolution of computational applications involving language look like the stuff you codified in your grammar.

Learning look like the stuff you codified in your grammar.

- 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.

Linguistica look like the stuff you codified in your grammar.

- 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 look like the stuff you codified in your grammar.

Computational Linguistics (June 2001)

“Unsupervised Learning of the Morphology of a Natural Language”

Overview look like the stuff you codified in your grammar.

- 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?

Linguistica look like the stuff you codified in your grammar.

- 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

Here: lists of stems, affixes, look like the stuff you codified in your grammar.

signatures, etc.

Here: some messages

from the analyst to the

user.

Actions and outlines of information

Read a corpus look like the stuff you codified in your grammar.

- 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 look like the stuff you codified in your grammar.

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

in alphabetical order.

abilit ies.y abilities, ability

aboli tion abolition

absen ce-t absence, absent

absolute NULL-ly absolute, absolutely

List of signatures look like the stuff you codified in your grammar.

Signature look like the stuff you codified in your grammar. : NULL ed ing s

for example,

account accounted accounting accounts

add added adding adds

More sophisticated signature… look like the stuff you codified in your grammar.

Signature <e>ion . NULL

composite concentrate corporate détente

discriminate evacuate inflate opposite

participate probate prosecute tense

What is this?

composite and composition

composite composit composit + ion

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

Top signatures in English look like the stuff you codified in your grammar.

Top signatures in French look like the stuff you codified in your grammar.

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:

French roots look like the stuff you codified in your grammar.

Let’s look at the program. look like the stuff you codified in your grammar.

Why do this? look like the stuff you codified in your grammar.

- (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.

Language acquisition look like the stuff you codified in your grammar.

- 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.

Learning of morphology look like the stuff you codified in your grammar.

- 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.

Over-arching theory look like the stuff you codified in your grammar.

- 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)

What’s being minimized by look like the stuff you codified in your grammar. writing a good morphology?

- Number of letters, for one:
- compare:

Naive Minimum Description Length look like the stuff you codified in your grammar.

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

Minimum Description Length (MDL) look like the stuff you codified in your grammar.

- 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…

Essence of MDL look like the stuff you codified in your grammar.

Description Length = look like the stuff you codified in your grammar.

- 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

Conciseness of the morphology look like the stuff you codified in your grammar.

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.

Conciseness of stem list and suffix list look like the stuff you codified in your grammar.

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

Signature list length look like the stuff you codified in your grammar.

list of pointers to signatures

<X> indicates the number

of distinct elements in X

Length of the modeling of the data look like the stuff you codified in your grammar.

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).

Probability of a data set? look like the stuff you codified in your grammar.

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.

From all this, it follows: Universe:

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 Universe:
- 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.)

Let’s get back down to Earth Universe:

- 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 Universe:(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.

Zellig Harris: Universe:successor frequency

Successor frequency of jum: 2

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

b (jumble)

Successor frequency of jump:5

e (jumped)

i (jumping)

jump s (jumps)

y (jumpy)

# (jump)

Zellig Harris:Successor Frequency Universe:

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 Universe:

d dead

f deaf

l deal

n dean

t death

Bad

predictions

a

18

a

e

5

d

b debate, debuting

c decade, december, decide

d dedicate, deduce, deduct

e deep

f

9

i

e defeat, defend, defer

i deficit, deficiency

r defraud

3

Good

predictions

o

Zellig Harris: Universe: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

The problem with Harris’ approach Universe:

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.

(problems…) Universe:

- 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

But as a boot-strapping method Universe:to construct a first approximation of the signatures:

- 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 by step...

Bootstrap heuristic

Out of which comes a

preliminary morphology,

which need not be superb.

Morphology

Corpus by step...

Bootstrap heuristic

Feed it to the incremental

heuristics...

Morphology

incremental

heuristics

Corpus by step...

Out comes a modified

morphology.

Bootstrap heuristic

Morphology

modified

morphology

incremental

heuristics

Corpus by step...

Is the modification

an improvement?

Ask MDL!

Bootstrap heuristic

Morphology

modified

morphology

incremental

heuristics

Corpus by step...

If it is an improvement,

replace the morphology...

Bootstrap heuristic

modified

morphology

Morphology

Garbage

Corpus by step...

Send it back to the

incremental

heuristics again...

Bootstrap heuristic

modified

morphology

incremental

heuristics

Continue until there by step...

are no improvements

to try.

Morphology

modified

morphology

incremental

heuristics

The details of learning morphology by step...

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

Steps by step...

- 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

100,000 tokens, 12,208 types by step...

Check signatures by step...

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

Check signatures by step...

- Signature l/tion with stems:
federa inaugura orienta substantia

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: by step...

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 ).

Allomorphy by step...

- 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 and e.ing by step...

- 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.

More precisely: by step...

- 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 layers of affixation by step...

- Find roots (from among the Stem collection)

Where do we go from here? by step...

- 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)

Method 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.

Map 1,000 English words by left-hand neighbors grammatical features and categories” (Belkin & Goldsmith 2002)

?: 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…

Map 1,000 English words by right-hand neighbors grammatical features and categories” (Belkin & Goldsmith 2002)

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

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