A BAYESIAN APPROACH TO SPELLING CORRECTION

‘Noisy channels’

In a number of tasks involving natural language, the problem can be viewed as recovering an ‘original signal’ distorted by a `noisy channel’:

– Speech recognition– Spelling correction– OCR / handwriting recognition– (less felicitously perhaps): pronunciation variation

This metaphor has provided the justification for the Bayesian approach to statistical NLP,which has found application also outside these application areas

Spelling Errors

They are leaving in about fifteen minuets to go to her house

The study was conducted mainly be John Black.

The design an construction of the system will take more than one year.

Hopefully, all with continue smoothly in my absence.

Can they lave him my messages?

I need to notified the bank of this problem.

He is trying to fine out.

Handwriting recognition

From Woody Allen’s Take the Money and Run (1969)– Allen (a bank robber), walks up to the teller and

hands her a note that reads. "I have a gun. Give me all your cash."

The teller, however, is puzzled, because he reads "I have a gub." "No, it's gun", Allen says. "Looks like 'gub' to me," the teller says, then asks another teller to help him read the note, then another, and finally everyone is arguing over what the note means.

Spelling errors

How common are spelling errors?– .005% in carefully edited newswire– 1-3% in `normal’ human written text– 20% of web queries are misspelled (Google

includes spelling correction algorithms)– 38% in applications like directory lookup– Handwriting recognition errors:

Apple Newton: 2-3%

Types of spelling errors

Damerau (1964): 80% of all misspelled words (non-word errors) caused by SINGLE-ERROR MISSPELLINGS:

– INSERTION: the ther– DELETION: the th– SUBSTITUTION: the thw– TRANSPOSITION: the hte

Dealing with spelling errors (Kukich, 1992)

3 increasingly broader problems:– NON-WORD ERROR DETECTION: ‘graffe’ instead

of ‘giraffe’– ISOLATED WORD-ERROR CORRECTION:

replacing ‘graffe’ with ‘giraffe’ without looking at context

– CONTEXT-DEPENDENT ERROR DETECTION / CORRECTION: detecting also spelling errors that result in a real world

Detecting non-word errors: Dictionaries

Peterson, 1986: large dictionaries may do more damage than good– wont– veery

Damerau and Mays (1989): no evidence this was the case

The Noisy Channel model

Bayesian inference

`Bayesian inference’ is the name given to techniques typically used in diagnostics to identify the CAUSE of certain OBSERVATIONS

The name ‘Bayesian’ comes from the fact that Bayes’ rule is used to ‘turn around’ a problem: from one of finding statistics about the posterior probability of the CAUSE to one of finding the posterior probability of the OBSERVATIONS

Bayesian inference: the equations

(These are equations that we will encounter again and again for different tasks)

The statistical formulation of the problem of finding the most likely `explanation’ for the observation:

Using Bayes’ Rule, this probability can be `turned around’:

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OwPw

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Vw OP

wPwOPw

Bayesian equations, 2

Some of these quantities are easy to compute, but others much less so – especially P(O)

Fortunately, we don’t really need to compute this term!! (It’s the same for ALL `explanations’)

This equation is a pattern that we will encounter again and again.

priorlikelihood

Vw)()|(argmaxˆ wPwOPw

Applying the Bayesian Method to Spelling: Kernigham et al, 1990

correct takes words rejected by spell and generates a list of potential correct words

Two steps:1. Proposing candidate corrections

2. Scoring the candidates

An example of isolated word-error correction

Proposing candidate corrections

The noisy channel assumption: misspelled word the result of a `noisy channel’ – the typist performing a single MISTYPING OPERATION

Four possible operations: – INSERTION: x xy– DELETION: xy x– SUBSTITUTION: y x– REVERSAL: xy yx

At most one operation involved (cfr. Damerau, 1964)

Example: acress

Error Correction Corr letter Error letter

Position Type

acress actress t - 2 del

acress cress - a 0 ins

acress caress ca ac 0 transp

acress access c r 2 sub

acress across o e 3 sub

acress acres - s 5 ins

Scoring the candidates

Choose the correction with the highest probability:

P(c): MLE estimation in a 44M words corpus, with smoothing (Good-Turing)

priorlikelihood

Cc)()|(argmaxˆ cPctPc

c freq(c) p(c)

actress 1343 .0000315

cress 0 .000000014

caress 4 .0000001

access 2280 .000058

A simplification

THE TRAINING CORPUS:

acress actress actressacress acres acres acres

WOULD WANT:

Likelihoods: P(acress|actress) = 1/3 P(acress|acress) = ¼

APPROXIMATE WITH:

P(acress|actress) = del[ct,c] / count[ct] = 1/3 (?)

Confusion matrices

Difficult to compute directly, but can be estimated by looking at LOCAL FACTORS only

Entry [m,n] in a CONFUSION MATRIX for SUBSTITUTION will tell us how often n is used instead of m

Kernighan et al used four confusion matrices:– del[x,y] (number of times x is typed instead of correct xy)– ins[x,y] (number of times xy is typed instead of correct x)– sub[x,y] (number of times y is typed instead of correct x)– trans[x,y] (number of times yx is typed instead of correct xy)

Estimating the likelihood of a typo

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Resulting likelihoods

c Freq(c) P(c) P(t|c) P(t|c)p(c) %

actress 1343 .0000315 .000117 3.69x10-9 37%

cress 0 .000000014 .00000144 2.02x10-12 0%

caress 4 .0000001 .00000164 1.64x10-13 0%

access 2280 .000058 .000000209 1.21x10-11 0%

across 8436 .00019 .0000093 1.77x10-9 18%

acres 2879 .000065 .0000321 2.09x10-9 21%

acres 2879 .000065 .0000342 2.09x10-9 23%

Evaluation (3 judges, 329 triples)

Method Results Perc. Correct

correct 286/329 87±1.9%

no prior 263/329 80 ±2.2%

no channel 247/329 75 ±2.4%

neither 172/329 52 ±2.8

Judge 1 271/273 99 ±0.5

Judge 2 271/275 99 ±0.7

Judge 3 271/281 96 ±1.1

More sophisticated methods

MINIMUM EDIT DISTANCE: allow for the possibility of more than one problem

N-GRAM models: use context (detect ‘real words’)

References

Jurafsky and Martin, chapter 5 Kernighan, M. D., Church, K. W., and Gale, W. A.

(1990). A spelling correction method based on a noisy channel model. COLING-90, 205-211.

Karen Kukich (1992). Techniques for automatically correcting words in text. ACM Computing Surveys, 24(4), 377-439.

More recent work:– Brill, E. and Moore, R. An improved error model for noisy

channel spelling correction Proc. ACL 2000