A BAYESIAN APPROACH TO SPELLING CORRECTION Noisy

A BAYESIAN APPROACH TO SPELLING CORRECTION

‘Noisy channels’ l In a number of tasks involving natural language, the problem can be viewed as recovering an ‘original signal’ distorted by a `noisy channel’: – – l 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 l 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 l 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: l Apple Newton: 2 -3%

Types of spelling errors l Damerau (1964): 80% of all misspelled words (nonword errors) caused by SINGLE-ERROR MISSPELLINGS: – – INSERTION: ther DELETION: the th SUBSTITUTION: the thw TRANSPOSITION: the hte

Dealing with spelling errors (Kukich, 1992) l 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 l Peterson, 1986: large dictionaries may do more damage than good – – l wont veery Damerau and Mays (1989): no evidence this was the case

The Noisy Channel model

Bayesian inference l l `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 l l l (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’:

Bayesian equations, 2 l l l 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.

Applying the Bayesian Method to Spelling: Kernigham et al, 1990 l l correct takes words rejected by spell and generates a list of potential correct words Two steps: 1. 2. l Proposing candidate corrections Scoring the candidates An example of isolated word-error correction

Proposing candidate corrections l l The noisy channel assumption: misspelled word the result of a `noisy channel’ – the typist performing a single MISTYPING OPERATION Four possible operations: – – l 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 - a 0 ins acress ca ac 0 transp acress access c r 2 sub acress across o e 3 sub acress acres - s 5 ins

Scoring the candidates l Choose the correction with the highest probability: l P(c): MLE estimation in a 44 M words corpus, with smoothing (Good-Turing) c freq(c) p(c) actress 1343 . 0000315 cress 0 . 000000014 caress 4 . 0000001 access 2280 . 000058

A simplification THE TRAINING CORPUS: acress actress 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 l l l 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

Resulting likelihoods c Freq(c) P(t|c)p(c) % 37% actress 1343 . 0000315 . 000117 3. 69 x 10 -9 cress 0 . 000000014 . 00000144 2. 02 x 10 -12 0% caress 4 . 0000001 . 00000164 1. 64 x 10 -13 0% access 2280 . 000058 . 000000209 1. 21 x 10 -11 0% across 8436 . 00019 . 0000093 1. 77 x 10 -9 18% acres 2879 . 000065 . 0000321 2. 09 x 10 -9 21% acres 2879 . 000065 . 0000342 2. 09 x 10 -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 l l MINIMUM EDIT DISTANCE: allow for the possibility of more than one problem N-GRAM models: use context (detect ‘real words’)

References l l 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