LSA 352: Speech Recognition and Synthesis

1LSA 352 Summer 2007

LSA 352: Speech Recognition and Synthesis

Dan Jurafsky

Lecture 1: 1) Overview of Course2) Refresher: Intro to Probability 3) Language Modeling

IP notice: some slides for today from: Josh Goodman, Dan Klein, Bonnie Dorr, Julia Hirschberg,Sandiway Fong


Outline

Overview of CourseProbabilityLanguage Modeling

Language Modeling means “probabilistic grammar”


Definitions

Speech RecognitionSpeech-to-Text

– Input: a wavefile,– Output: string of words

Speech SynthesisText-to-Speech

– Input: a string of words– Output: a wavefile


Automatic Speech Recognition (ASR)Automatic Speech Understanding (ASU)

ApplicationsDictationTelephone-based Information (directions, air travel, banking, etc)Hands-free (in car)Second language ('L2') (accent reduction)Audio archive searchingLinguistic research– Automatically computing word durations, etc


Applications of Speech Synthesis/Text-to-Speech (TTS)

GamesTelephone-based Information (directions, air travel, banking, etc)Eyes-free (in car)Reading/speaking for disabledEducation: Reading tutorsEducation: L2 learning


Applications of Speaker/Lg Recognition

Language recognition for call routingSpeaker Recognition:

Speaker verification (binary decision)– Voice password, telephone assistant

Speaker identification (one of N)– Criminal investigation


History: foundational insights 1900s-1950s

Automaton:Markov 1911Turing 1936McCulloch-Pitts neuron (1943)

– http://marr.bsee.swin.edu.au/~dtl/het704/lecture10/ann/node1.html

– http://diwww.epfl.ch/mantra/tutorial/english/mcpits/html/Shannon (1948) link between automata and Markov models

Human speech processingFletcher at Bell Labs (1920’s)

Probabilistic/Information-theoretic modelsShannon (1948)

http://marr.bsee.swin.edu.au/~dtl/het704/lecture10/ann/node1.html

http://marr.bsee.swin.edu.au/~dtl/het704/lecture10/ann/node1.html

http://diwww.epfl.ch/mantra/tutorial/english/mcpits/html/


Synthesis precursors

Von Kempelen mechanical (bellows, reeds) speech production simulacrum1929 Channel vocoder (Dudley)


History: Early Recognition

• 1920’s Radio RexCelluloid dog with iron base held within house by electromagnet against force of springCurrent to magnet flowed through bridge which was sensitive to energy at 500 Hz500 Hz energy caused bridge to vibrate, interrupting current, making dog spring forwardThe sound “e” (ARPAbet [eh]) in Rex has 500 Hz component

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.


History: early ASR systems• 1950’s: Early Speech recognizers

1952: Bell Labs single-speaker digit recognizer – Measured energy from two bands (formants)– Built with analog electrical components– 2% error rate for single speaker, isolated digits

1958: Dudley built classifier that used continuous spectrum rather than just formants1959: Denes ASR combining grammar and acoustic probability

1960’sFFT - Fast Fourier transform (Cooley and Tukey 1965)LPC - linear prediction (1968)1969 John Pierce letter “Whither Speech Recognition?”

– Random tuning of parameters,– Lack of scientific rigor, no evaluation metrics– Need to rely on higher level knowledge


ASR: 1970’s and 1980’sHidden Markov Model 1972

Independent application of Baker (CMU) and Jelinek/Bahl/Mercer lab (IBM) following work of Baum and colleagues at IDA

ARPA project 1971-19765-year speech understanding project: 1000 word vocab, continous speech, multi-speakerSDC, CMU, BBNOnly 1 CMU system achieved goal

1980’s+Annual ARPA “Bakeoffs”Large corpus collection

– TIMIT– Resource Management– Wall Street Journal


State of the Art

ASRspeaker-independent, continuous, no noise, world’s best research systems:

– Human-human speech: ~13-20% Word Error Rate (WER)

– Human-machine speech: ~3-5% WERTTS (demo next week)


LVCSR Overview

Large Vocabulary Continuous (Speaker-Independent) Speech Recognition

Build a statistical model of the speech-to-words processCollect lots of speech and transcribe all the wordsTrain the model on the labeled speechParadigm: Supervised Machine Learning + Search


Unit Selection TTS Overview

Collect lots of speech (5-50 hours) from one speaker, transcribe very carefully, all the syllables and phones and whatnotTo synthesize a sentence, patch together syllables and phones from the training data.Paradigm: search


Requirements and Grading

Readings:Required Text:Selected chapters on web from

– Jurafsky & Martin, 2000. Speech and Language Processing.– Taylor, Paul. 2007. Text-to-Speech Synthesis.

GradingHomework: 75% (3 homeworks, 25% each)Participation: 25%You may work in groups


Overview of the course

http://nlp.stanford.edu/courses/lsa352/

http://nlp.stanford.edu/courses/lsa352/


6. Introduction to ProbabilityExperiment (trial)

Repeatable procedure with well-defined possible outcomesSample Space (S)

– the set of all possible outcomes – finite or infinite

Example– coin toss experiment– possible outcomes: S = {heads, tails}

Example– die toss experiment– possible outcomes: S = {1,2,3,4,5,6}





Slides from Sandiway Fong


Introduction to ProbabilityDefinition of sample space depends on what we are asking

Sample Space (S): the set of all possible outcomesExample

– die toss experiment for whether the number is even or odd– possible outcomes: {even,odd} – not {1,2,3,4,5,6}




More definitionsEvents

an event is any subset of outcomes from the sample spaceExample

die toss experiment let A represent the event such that the outcome of the die toss experiment is divisible by 3A = {3,6} A is a subset of the sample space S= {1,2,3,4,5,6}

ExampleDraw a card from a deck

– suppose sample space S = {heart,spade,club,diamond} (four suits)

let A represent the event of drawing a heartlet B represent the event of drawing a red cardA = {heart} B = {heart,diamond}




Introduction to Probability

Some definitionsCounting

– suppose operation oi can be performed in ni ways, then– a sequence of k operations o1o2...ok – can be performed in n1 n2 ... nk ways

Example– die toss experiment, 6 possible outcomes– two dice are thrown at the same time– number of sample points in sample space = 6 6 = 36




Definition of Probability

The probability law assigns to an event a nonnegative numberCalled P(A)Also called the probability AThat encodes our knowledge or belief about the collective likelihood of all the elements of AProbability law must satisfy certain properties


Probability Axioms

NonnegativityP(A) >= 0, for every event A

Additivity If A and B are two disjoint events, then the probability of their union satisfies:P(A U B) = P(A) + P(B)

Normalization The probability of the entire sample space S is equal to 1, I.e. P(S) = 1.


An example

An experiment involving a single coin tossThere are two possible outcomes, H and TSample space S is {H,T}If coin is fair, should assign equal probabilities to 2 outcomesSince they have to sum to 1P({H}) = 0.5P({T}) = 0.5P({H,T}) = P({H})+P({T}) = 1.0


Another exampleExperiment involving 3 coin tossesOutcome is a 3-long string of H or TS ={HHH,HHT,HTH,HTT,THH,THT,TTH,TTTT}Assume each outcome is equiprobable

“Uniform distribution”What is probability of the event that exactly 2 heads occur?A = {HHT,HTH,THH}P(A) = P({HHT})+P({HTH})+P({THH})= 1/8 + 1/8 + 1/8=3/8


Probability definitions

In summary:

Probability of drawing a spade from 52 well-shuffled playing cards:


Probabilities of two events

If two events A and B are independentThen

P(A and B) = P(A) x P(B)

If flip a fair coin twiceWhat is the probability that they are both heads?

If draw a card from a deck, then put it back, draw a card from the deck again

What is the probability that both drawn cards are hearts?A coin is flipped twice

What is the probability that it comes up heads both times?


How about non-uniform probabilities? An example

A biased coin,twice as likely to come up tails as heads, is tossed twice

What is the probability that at least one head occurs?Sample space = {hh, ht, th, tt} (h = heads, t = tails)Sample points/probability for the event:

ht 1/3 x 2/3 = 2/9 hh 1/3 x 1/3= 1/9th 2/3 x 1/3 = 2/9 tt 2/3 x 2/3 = 4/9

Answer: 5/9 = 0.56 (sum of weights in red)


Moving toward languageWhat’s the probability of drawing a 2 from a deck of 52 cards with four 2s?

What’s the probability of a random word (from a random dictionary page) being a verb?

P(drawing a two) 4

52

113

.077

P(drawing a verb) # of ways to get a verb

all words


Probability and part of speech tags• What’s the probability of a random word (from

a random dictionary page) being a verb?

• How to compute each of these• All words = just count all the words in the

dictionary• # of ways to get a verb: number of words

which are verbs!• If a dictionary has 50,000 entries, and 10,000

are verbs…. P(V) is 10000/50000 = 1/5 = .20

P(drawing a verb) # of ways to get a verb

all words


Conditional Probability

A way to reason about the outcome of an experiment based on partial information

In a word guessing game the first letter for the word is a “t”. What is the likelihood that the second letter is an “h”?How likely is it that a person has a disease given that a medical test was negative?A spot shows up on a radar screen. How likely is it that it corresponds to an aircraft?


More precisely

Given an experiment, a corresponding sample space S, and a probability lawSuppose we know that the outcome is within some given event BWe want to quantify the likelihood that the outcome also belongs to some other given event A.We need a new probability law that gives us the conditional probability of A given BP(A|B)


An intuition• A is “it’s raining now”.• P(A) in dry California is .01• B is “it was raining ten minutes ago”

• P(A|B) means “what is the probability of it raining now if it was raining 10 minutes ago”

• P(A|B) is probably way higher than P(A)• Perhaps P(A|B) is .10

• Intuition: The knowledge about B should change our estimate of the probability of A.


Conditional probability

One of the following 30 items is chosen at randomWhat is P(X), the probability that it is an X? What is P(X|red), the probability that it is an X given that it is red?




S

Conditional Probabilitylet A and B be eventsp(B|A) = the probability of event B occurring given event A occursdefinition: p(B|A) = p(A B) / p(A)


Conditional probability

P(A|B) = P(A B)/P(B)Or

)(),()|(

BPBAPBAP

A BA,B

Note: P(A,B)=P(A|B) · P(B)Also: P(A,B) = P(B,A)


Independence

What is P(A,B) if A and B are independent?

P(A,B)=P(A) · P(B) iff A,B independent.

P(heads,tails) = P(heads) · P(tails) = .5 · .5 = .25

Note: P(A|B)=P(A) iff A,B independentAlso: P(B|A)=P(B) iff A,B independent


Bayes Theorem

)()()|()|(

APBPBAPABP

•Swap the conditioning•Sometimes easier to estimate one

kind of dependence than the other


Deriving Bayes Rule

P(B | A) P(A B)P(A)

P(A | B) P(A B)P(B)

P(B | A)P(A) P(A B)

P(A | B)P(B) P(A B)

P(A | B)P(B) P(B | A)P(A)

P(A | B) P(B | A)P(A)

P(B)


Summary

ProbabilityConditional ProbabilityIndependenceBayes Rule


How many words?

I do uh main- mainly business data processingFragmentsFilled pauses

Are cat and cats the same word?Some terminology

Lemma: a set of lexical forms having the same stem, major part of speech, and rough word sense

– Cat and cats = same lemmaWordform: the full inflected surface form.

– Cat and cats = different wordforms


How many words?they picnicked by the pool then lay back on the grass and looked at the stars

16 tokens14 types

SWBD: ~20,000 wordform types, 2.4 million wordform tokens

Brown et al (1992) large corpus583 million wordform tokens293,181 wordform types

Let N = number of tokens, V = vocabulary = number of typesGeneral wisdom: V > O(sqrt(N))


Language Modeling

We want to compute P(w1,w2,w3,w4,w5…wn), the probability of a sequenceAlternatively we want to compute P(w5|w1,w2,w3,w4,w5): the probability of a word given some previous wordsThe model that computes P(W) or P(wn|w1,w2…wn-1) is called the language model.A better term for this would be “The Grammar”But “Language model” or LM is standard


Computing P(W)

How to compute this joint probability:

P(“the”,”other”,”day”,”I”,”was”,”walking”,”along”,”and”,”saw”,”a”,”lizard”)

Intuition: let’s rely on the Chain Rule of Probability


The Chain Rule of Probability

Recall the definition of conditional probabilities

Rewriting:

More generallyP(A,B,C,D) = P(A)P(B|A)P(C|A,B)P(D|A,B,C)In general P(x1,x2,x3,…xn) = P(x1)P(x2|x1)P(x3|x1,x2)…P(xn|x1…xn-1)

)()^()|(

BPBAPBAP

)()|()^( BPBAPBAP


The Chain Rule Applied to joint probability of words in sentence

P(“the big red dog was”)=

P(the)*P(big|the)*P(red|the big)*P(dog|the big red)*P(was|the big red dog)


Very easy estimate:

How to estimate?P(the|its water is so transparent that)

P(the|its water is so transparent that)=C(its water is so transparent that the)_______________________________C(its water is so transparent that)


Unfortunately

There are a lot of possible sentences

We’ll never be able to get enough data to compute the statistics for those long prefixes

P(lizard|the,other,day,I,was,walking,along,and,saw,a)OrP(the|its water is so transparent that)


Markov Assumption

Make the simplifying assumptionP(lizard|the,other,day,I,was,walking,along,and,saw,a) = P(lizard|a)

Or maybeP(lizard|the,other,day,I,was,walking,along,and,saw,a) = P(lizard|saw,a)


So for each component in the product replace with the approximation (assuming a prefix of N)

Bigram version

P(wn | w1n 1) P(wn | wn N 1

n 1 )

Markov Assumption

P(wn | w1n 1) P(wn | wn 1)


Estimating bigram probabilities

The Maximum Likelihood Estimate

P(wi | wi 1) count(wi 1,wi)

count(wi 1)

P(wi | wi 1) c(wi 1,wi)

c(wi 1)


An example<s> I am Sam </s><s> Sam I am </s><s> I do not like green eggs and ham </s>

This is the Maximum Likelihood Estimate, because it is the one which maximizes P(Training set|Model)


Maximum Likelihood Estimates

The maximum likelihood estimate of some parameter of a model M from a training set T

Is the estimatethat maximizes the likelihood of the training set T given the model M

Suppose the word Chinese occurs 400 times in a corpus of a million words (Brown corpus)What is the probability that a random word from some other text will be “Chinese”MLE estimate is 400/1000000 = .004

This may be a bad estimate for some other corpusBut it is the estimate that makes it most likely that “Chinese” will occur 400 times in a million word corpus.


More examples: Berkeley Restaurant Project sentences

can you tell me about any good cantonese restaurants close bymid priced thai food is what i’m looking fortell me about chez panissecan you give me a listing of the kinds of food that are availablei’m looking for a good place to eat breakfastwhen is caffe venezia open during the day


Raw bigram counts

Out of 9222 sentences


Raw bigram probabilities

Normalize by unigrams:

Result:


Bigram estimates of sentence probabilities

P(<s> I want english food </s>) =p(i|<s>) x p(want|I) x p(english|want)

x p(food|english) x p(</s>|food) = .24 x .33 x .0011 x 0.5 x 0.68 =.000031


What kinds of knowledge?

P(english|want) = .0011P(chinese|want) = .0065P(to|want) = .66P(eat | to) = .28P(food | to) = 0P(want | spend) = 0P (i | <s>) = .25


The Shannon Visualization Method

Generate random sentences:Choose a random bigram <s>, w according to its probabilityNow choose a random bigram (w, x) according to its probabilityAnd so on until we choose </s>Then string the words together<s> I

I want want to to eat eat Chinese

Chinese food food </s>



Shakespeare as corpus

N=884,647 tokens, V=29,066Shakespeare produced 300,000 bigram types out of V2= 844 million possible bigrams: so, 99.96% of the possible bigrams were never seen (have zero entries in the table)Quadrigrams worse: What's coming out looks like Shakespeare because it is Shakespeare


The wall street journal is not shakespeare (no offense)


Evaluation

We train parameters of our model on a training set.How do we evaluate how well our model works?We look at the models performance on some new dataThis is what happens in the real world; we want to know how our model performs on data we haven’t seenSo a test set. A dataset which is different than our training setThen we need an evaluation metric to tell us how well our model is doing on the test set.One such metric is perplexity (to be introduced below)


Unknown words: Open versus closed vocabulary tasks

If we know all the words in advancedVocabulary V is fixedClosed vocabulary task

Often we don’t know thisOut Of Vocabulary = OOV wordsOpen vocabulary task

Instead: create an unknown word token <UNK>Training of <UNK> probabilities

– Create a fixed lexicon L of size V– At text normalization phase, any training word not in L changed to

<UNK>– Now we train its probabilities like a normal word

At decoding time– If text input: Use UNK probabilities for any word not in training


Evaluating N-gram models

Best evaluation for an N-gramPut model A in a speech recognizerRun recognition, get word error rate (WER) for APut model B in speech recognition, get word error rate for BCompare WER for A and BIn-vivo evaluation


Difficulty of in-vivo evaluation of N-gram models

In-vivo evaluationThis is really time-consumingCan take days to run an experiment

SoAs a temporary solution, in order to run experimentsTo evaluate N-grams we often use an approximation called perplexityBut perplexity is a poor approximation unless the test data looks just like the training dataSo is generally only useful in pilot experiments (generally is not sufficient to publish)But is helpful to think about.


PerplexityPerplexity is the probability of the test set (assigned by the language model), normalized by the number of words:

Chain rule:

For bigrams:

Minimizing perplexity is the same as maximizing probabilityThe best language model is one that best predicts an unseen test set


A totally different perplexity Intuition

How hard is the task of recognizing digits ‘0,1,2,3,4,5,6,7,8,9,oh’: easy, perplexity 11 (or if we ignore ‘oh’, perplexity 10)How hard is recognizing (30,000) names at Microsoft. Hard: perplexity = 30,000If a system has to recognize

Operator (1 in 4)Sales (1 in 4)Technical Support (1 in 4)30,000 names (1 in 120,000 each)Perplexity is 54

Perplexity is weighted equivalent branching factor

Slide from Josh Goodman


Perplexity as branching factor


Lower perplexity = better model

Training 38 million words, test 1.5 million words, WSJ


Lesson 1: the perils of overfitting

N-grams only work well for word prediction if the test corpus looks like the training corpus

In real life, it often doesn’tWe need to train robust models, adapt to test set, etc


Lesson 2: zeros or not?

Zipf’s Law:A small number of events occur with high frequencyA large number of events occur with low frequencyYou can quickly collect statistics on the high frequency eventsYou might have to wait an arbitrarily long time to get valid statistics on low frequency events

Result:Our estimates are sparse! no counts at all for the vast bulk of things we want to estimate!Some of the zeroes in the table are really zeros But others are simply low frequency events you haven't seen yet. After all, ANYTHING CAN HAPPEN!How to address?

Answer:Estimate the likelihood of unseen N-grams!

Slide adapted from Bonnie Dorr and Julia Hirschberg


Smoothing is like Robin Hood:Steal from the rich and give to the poor (in probability mass)

Slide from Dan Klein


Laplace smoothing

Also called add-one smoothingJust add one to all the counts!Very simple

MLE estimate:

Laplace estimate:

Reconstructed counts:


Laplace smoothed bigram counts


Laplace-smoothed bigrams


Reconstituted counts


Note big change to counts

C(count to) went from 608 to 238!P(to|want) from .66 to .26!Discount d= c*/c

d for “chinese food” =.10!!! A 10x reductionSo in general, Laplace is a blunt instrumentCould use more fine-grained method (add-k)

But Laplace smoothing not used for N-grams, as we have much better methodsDespite its flaws Laplace (add-k) is however still used to smooth other probabilistic models in NLP, especially

For pilot studiesin domains where the number of zeros isn’t so huge.


Better discounting algorithms

Intuition used by many smoothing algorithmsGood-TuringKneser-NeyWitten-Bell

Is to use the count of things we’ve seen once to help estimate the count of things we’ve never seen


Good-Turing: Josh Goodman intuition

Imagine you are fishingThere are 8 species: carp, perch, whitefish, trout, salmon, eel, catfish, bass

You have caught 10 carp, 3 perch, 2 whitefish, 1 trout, 1 salmon, 1 eel = 18 fish

How likely is it that next species is new (i.e. catfish or bass)

3/18Assuming so, how likely is it that next species is trout?

Must be less than 1/18

Slide adapted from Josh Goodman


Good-Turing Intuition

Notation: Nx is the frequency-of-frequency-xSo N10=1, N1=3, etc

To estimate total number of unseen speciesUse number of species (words) we’ve seen oncec0

* =c1 p0 = N1/NAll other estimates are adjusted (down) to give probabilities for unseen



Good-Turing Intuition

Notation: Nx is the frequency-of-frequency-xSo N10=1, N1=3, etc

To estimate total number of unseen speciesUse number of species (words) we’ve seen oncec0

* =c1 p0 = N1/N p0=N1/N=3/18

All other estimates are adjusted (down) to give probabilities for unseen P(eel) = c*(1) = (1+1) 1/ 3 = 2/3




Bigram frequencies of frequencies and GT re-estimates


ComplicationsIn practice, assume large counts (c>k for some k) are reliable:

That complicates c*, making it:

Also: we assume singleton counts c=1 are unreliable, so treat N-grams with count of 1 as if they were count=0Also, need the Nk to be non-zero, so we need to smooth (interpolate) the Nk counts before computing c* from them


Backoff and Interpolation

Another really useful source of knowledgeIf we are estimating:

trigram p(z|xy) but c(xyz) is zero

Use info from:Bigram p(z|y)

Or even:Unigram p(z)

How to combine the trigram/bigram/unigram info?


Backoff versus interpolation

Backoff: use trigram if you have it, otherwise bigram, otherwise unigramInterpolation: mix all three


Interpolation

Simple interpolation

Lambdas conditional on context:


How to set the lambdas?

Use a held-out corpusChoose lambdas which maximize the probability of some held-out data

I.e. fix the N-gram probabilitiesThen search for lambda valuesThat when plugged into previous equationGive largest probability for held-out setCan use EM to do this search


Katz Backoff


Why discounts P* and alpha?

MLE probabilities sum to 1

So if we used MLE probabilities but backed off to lower order model when MLE prob is zeroWe would be adding extra probability massAnd total probability would be greater than 1


GT smoothed bigram probs


Intuition of backoff+discounting

How much probability to assign to all the zero trigrams?

Use GT or other discounting algorithm to tell usHow to divide that probability mass among different contexts?

Use the N-1 gram estimates to tell usWhat do we do for the unigram words not seen in training?

Out Of Vocabulary = OOV words


OOV words: <UNK> wordOut Of Vocabulary = OOV wordsWe don’t use GT smoothing for these

Because GT assumes we know the number of unseen eventsInstead: create an unknown word token <UNK>

Training of <UNK> probabilities– Create a fixed lexicon L of size V– At text normalization phase, any training word not in L changed to

<UNK>– Now we train its probabilities like a normal word

At decoding time– If text input: Use UNK probabilities for any word not in training


Practical Issues

We do everything in log spaceAvoid underflow(also adding is faster than multiplying)


ARPA format



Language Modeling Toolkits

SRILMCMU-Cambridge LM Toolkit


Google N-Gram Release


Google N-Gram Releaseserve as the incoming 92serve as the incubator 99serve as the independent 794serve as the index 223serve as the indication 72serve as the indicator 120serve as the indicators 45serve as the indispensable 111serve as the indispensible 40serve as the individual 234


Advanced LM stuffCurrent best smoothing algorithm

Kneser-Ney smoothingOther stuff

Variable-length n-gramsClass-based n-grams

– Clustering– Hand-built classes

Cache LMsTopic-based LMsSentence mixture modelsSkipping LMsParser-based LMs


Summary

LMN-gramsDiscounting: Good-TuringKatz backoff with Good-Turing discountingInterpolationUnknown wordsEvaluation:

– Entropy, Entropy Rate, Cross Entropy– Perplexity

Advanced LM algorithms

Documents

LSA 352: Speech Recognition and Synthesis