1 Conditional Random Fields for Automatic Speech Recognition Jeremy Morris 06/03/2010.

1

Conditional Random Fields for Automatic Speech

Recognition

Jeremy Morris

06/03/2010

Motivation

What is the purpose of Automatic Speech Recognition? Take an acoustic speech signal … … and extract higher level information (e.g.

words) from it

2

“speech”

Motivation

How do we extract this higher level information from the speech signal?

First extract lower level information Use it to build models of phones, words

3

“speech”/ s p iy ch/

Motivation

State-of-the-art ASR takes a top-down approach to this problem Extract acoustic features from the signal Model a process that generates these features Use these models to find the word sequence that

best fits the features

4


Motivation

A bottom-up approach Look for evidence of speech in the signal

Phones, phonological features Combine this evidence together to find the most

probable sequence of words in the signal

5


voicing?burst?frication?

Motivation

How can we combine this evidence? Conditional Random Fields (CRFs)

Discriminative, probabilistic sequence model Models the conditional probability of a sequence given

evidence

6


voicing?burst?frication?

7

Outline

Motivation CRF Models Phone Recognition HMM-CRF Word Recognition CRF Word Recognition Conclusions

8

CRF Models Conditional Random Fields (CRFs)

Discriminative probabilistic sequence model Directly defines a posterior probability P(Y|X) of a

label sequence Y given evidence X

9

CRF Models The structure of the evidence can be arbitrary

No assumptions of independence

10


No assumptions of independence States can be influenced by any evidence

11



12



13


No assumptions of independence States can be influenced by any evidence Evidence can influence transitions between states

14


No assumptions of independence States can be influenced by any evidence Evidence can influence transitions between states

15

CRF Models Evidence is incorporated via feature functions

state featurefunctions

16

CRF Models Evidence is incorporated via feature functions

state featurefunctions

transition featurefunctions

17

)(

)),,(),((exp

)|(1

xZ

yyxtyxs

XYP k i jkkjjkii

CRF Models

The form of the CRF is an exponential model of weighted feature functions Weights trained via gradient descent to maximize

the conditional likelihood

state featurefunctions transition feature

functions

18

Outline


19

Phone Recognition

What evidence do we have to combine? MLP ANN trained to estimate frame-level

posteriors for phonological features MLP ANN trained to estimate frame-level

posteriors for phone classes

P(voicing|X)P(burst|X)P(frication|X)…

P( /ah/ | X)P( /t/ | X)P( /n/ | X)…

20

Phone Recognition

Use these MLP outputs to build state feature functions

otherwise

tyifxMLPxys xtP

xtPt ,0

//),(),( )|/(/

)|/(//,/ {

21

Phone Recognition


otherwise

tyifxMLPxys xtP

xtPt ,0

//),(),( )|/(/

)|/(//,/ {

otherwise

tyifxMLPxys xdP

xdPt ,0

//),(),( )|/(/

)|/(//,/ {

22

Phone Recognition


otherwise

tyifxMLPxys xtP

xtPt ,0

//),(),( )|/(/

)|/(//,/ {

otherwise

tyifxMLPxys xstopP

xstopPt ,0

//),(),( )|(

)|(/,/ {

23

Phone Recognition Pilot task – phone recognition on TIMIT

ICSI Quicknet MLPs trained on TIMIT, used as inputs to the CRF models

Compared to Tandem and a standard PLP HMM baseline model

Output of ICSI Quicknet MLPs as inputs Phone class attributes (61 outputs) Phonological features attributes (44 outputs)

Phone Recognition

24

*Signficantly (p<0.05) better than comparable Tandem system (Morris & Fosler-Lussier 08)

Model Accuracy

HMM (PLP inputs) 68.1%

CRF (phone classes) 70.2%

HMM Tandem16mix (phone classes) 70.4%

CRF (phone classes +phonological features) 71.5%*

HMM Tandem16mix (phone classes+ phonological features)

70.2%

25

Phone Recognition Moving forward: How do we make use of

CRF classification for word recognition? Attempt to fit CRFs into current state-of-the-art

models for speech recognition? Attempt to use CRFs directly?

Each approach has its benefits Fitting CRFs into a standard framework lets us

reuse existing code and ideas A model that uses CRFs directly opens up new

directions for investigation Requires some rethinking of the standard model for ASR

26

Outline


HMM-CRF Word Recognition Inspired by Tandem HMM systems

Uses ANN outputs as input features to an HMM

27


PCA

HMM-CRF Word Recognition Inspired by Tandem HMM systems

Uses ANN outputs as input features to an HMM HMM-CRF system (Crandem)

Use a CRF to generate input features for HMM See if improved phone accuracy helps the system

Problem: CRFs estimate probability of the entire sequence, not individual frames

28


PCA

29

HMM-CRF Word Recognition One solution: Forward-Backward Algorithm

Used during CRF training to maximized conditional likelihood

Provides an estimate of the posterior probability of a phone label given the input

)()|( ,,

, xZXyP titi

ti

30

HMM-CRF Word Recognition Original Tandem system


PCA

31

HMM-CRF Word Recognition Modified Tandem system (Crandem)


PCA

LocalFeature

Calc.

32

HMM-CRF Word Recognition Pilot task – phone recognition on TIMIT

Same ICSI Quicknet MLP outputs used as inputs Crandem compared to Tandem, a standard PLP

HMM baseline model, and to the original CRF Evidence on transitions

This work also examines the effect of using the same MLP outputs as transition features for the CRF

33* Significant (p<0.05) improvement at 0.6% difference between models

HMM-CRF Word Recognition

Model Phone Accuracy

PLP HMM reference 68.1%

Tandem (phone class) 70.8%

CRF (phone class) 70.2%

Crandem (phone class, state only) 71.1%

CRF (phone class, state+trans) 70.7%

Crandem (phone class, state+trans) 71.7%

Pilot Results 1 (Fosler-Lussier & Morris 08)

34* Significant (p<0.05) improvement at 0.6% difference between models


Model Phone Accuracy


Tandem (phone+phono) 71.2%

CRF (phone+phono, state only) 71.4%

Crandem (phone+phono, state only) 71.7%

CRF (phone+phono, state+trans) 71.6%

Crandem (phone+phono, state+trans) 72.4%

Pilot Results 2 (Fosler-Lussier & Morris 08)

35

HMM-CRF Word Recognition Extension – Word recognition on WSJ0

New MLPs and CRFs trained on WSJ0 corpus of read speech No phone level assignments, only word transcripts Initial alignments from HMM forced alignment of MFCC

features Compare Crandem baseline to Tandem and original

MFCC baselines WJ0 5K Word Recognition task

Same bigram language model used for all systems

36* Significant (p≤0.05) improvement at roughly 0.9% difference between models


Model DevWER

EvalWER

MFCC HMM reference 9.3% 8.7%

Tandem MLP 9.1% 8.4%

Crandem (1 epoch) 8.9% 9.4%

Crandem (10 epochs) 10.2% 10.4%


Results (Morris & Fosler-Lussier 09)


HMM-CRF Word RecognitionModel Phone

Accuracy

MFCC HMM reference 70.1%

Tandem MLP 75.6%

Crandem (1 epoch) 72.8%

Crandem (10 epochs) 72.9%

Crandem (20 epochs) 72.3%

CRF (1 epoch) 69.5%

CRF (10 epochs) 70.6%

CRF (20 epochs) 71.0%

38


Comparison of MLP activation vs. CRF activation

39


Ranked average per-frame activation MLP vs. CRF

40

HMM-CRF Word Recognition Insights from these experiments

CRF posteriors very different in flavor from MLP posteriors Overconfident in local decision being made Higher phone accuracy did not translate to lower WER

Further experiment to test this idea Transform posteriors via taking a root and

renormalizing Bring classes closer together Achieved results insignificantly different from baseline,

no longer degraded with further epochs of training (though no improvement either)

41

Outline


CRF Word Recognition Instead of feeding CRF outputs into an HMM

4242


CRF Word Recognition Instead of feeding CRF outputs into an HMM Why not decode words directly off the CRF?

4343



CRF Word Recognition

The standard model of ASR uses likelihood based acoustic models

CRFs provide a conditional acoustic model P(Φ|X)

44

)()|()|(maxarg)|(maxarg,

WPWPXPXWPWW

AcousticModel

LexiconModel

LanguageModel


45

)()|()(

)|(maxarg)|(maxarg,

WPWPP

XPXWP

WW

CRFAcousticModel

LexiconModel

LanguageModel

PhonePenaltyModel

46

CRF Word Recognition Models implemented using OpenFST

Viterbi beam search to find best word sequence Word recognition on WSJ0

WJ0 5K Word Recognition task Same bigram language model used for all systems

Same MLPs used for CRF-HMM (Crandem) experiments

CRFs trained using 3-state phone model instead of 1-state model

Compare to Tandem and original MFCC baselines

47

CRF Word Recognition Results – Phone Classes only

Model DevWER

EvalWER


Tandem MLP 9.1% 8.4%

CRF (state only) 11.3% 11.5%

CRF (state+trans) 9.2% 8.6%

* Significant (p≤0.05) improvement at roughly 0.9% difference between models

48

CRF Word Recognition Results – Phone & Phonological features

Model DevWER

EvalWER


Tandem MLP (all) 9.1% 8.4%

Tandem MLP (best) 8.6% 8.1%

CRF (state+trans) 8.3% 8.0%

* Significant (p≤0.05) improvement at roughly 0.9% difference between models

49

Outline


50

Conclusions & Future Work Designed and developed software for CRF

training for ASR Developed a system for word-level ASR

using CRFs Meets baseline performance of an MLE trained

HMM system Platform for further exploration

51

Conclusions & Future Work Topics for further exploration:

Feature modeling What kinds of features can benefit these kinds of

models? Incorporating context

Segmental approaches Integration between higher level and lower level

models Language model and acoustic model separate models Combining low level evidence with higher-level evidence

52

53



Model DevWER

EvalWER


Tandem MLP (39) 9.1% 8.4%

Crandem (1 epoch) 8.9% 9.4%

Crandem* ( 1 epoch) 8.4% 8.5%


Crandem* (10 epochs) 8.5% 8.8%


Crandem* (20 epochs) 8.5% 8.5%

Transformed Results


55

)(

)()|(

P

XPXP)|( XP

)()|()(

)|(maxarg)|(maxarg,

WPWPP

XPXWP

WW

CRFAcousticModel

LexiconModel

LanguageModel

PhonePenaltyModel

Review - Word Recognition

Problem: For a given input signal X, find the word string W that maximizes P(W|X)

56

)|(maxarg XWPW



In an HMM, we would make this a generative problem

57

)(

)()|(maxarg)|(maxarg

XP

WPWXPXWP

WW



In an HMM, we would make this a generative problem

We can drop the P(X) because it does not affect the choice of W

58

)()|(maxarg)|(maxarg WPWXPXWPWW


We want to build phone models, not whole word models…

59




… so we marginalize over the phones

60


)()|()|(maxarg WPWPXPW



… so we marginalize over the phones and look for the best sequence that fits these

constraints61


)()|()|(maxarg WPWPXPW

)()|()|(maxarg,

WPWPXPW


62

)()|()|( WPWPXP

Acoustic Model

Lexicon

Language Model

Word Recognition

However - our CRFs model P(Φ|X) rather than P(X|Φ) This makes the formulation of the problem

somewhat different

63

)()|()|( WPWPXP

Acoustic Model

Word Recognition

We want a formulation that makes use of P(Φ|X)

64

)|(maxarg XWPW

Word Recognition

We want a formulation that makes use of P(Φ|X) We can get that by marginalizing over the phone

strings But the CRF as we formulate it doesn’t give P(Φ|

X) directly

65

)|,(maxarg)|(maxarg XWPXWPWW

)|(),|(maxarg XPXWPW

Word Recognition

Φ here is a phone level assignment of phone labels

CRF gives related quantity – P(Q|X) where Q is the frame level assignment of phone labels

66

)|(),|( XPXWP

Word Recognition

Frame level vs. Phone level Mapping from frame level to phone level may not

be deterministic Example: The word “OH” with pronunciation /ow/ Consider this sequence of frame labels:

ow ow ow ow ow ow ow This sequence can possibly be expanded many

different ways for the word “OH” (“OH”, “OH OH”, etc.)

67

Word Recognition

Frame level vs. Phone segment level This problem occurs because we’re using a single

state to represent the phone /ow/ Phone either transitions to itself or transitions out to

another phone We can change our model to a multi-state model

and make this decision deterministic This brings us closer to a standard ASR HMM topology

ow1 ow2 ow2 ow2 ow2 ow3 ow3 Now we can see a single “OH” in this utterance

68

Word Recognition

Multi-state model gives us a deterministic mapping of Q -> Φ Each frame-level assignment Q has exactly one

segment level assignment associated with it Potential pitfalls if the multi-state model is

inappropriate for the features we are using

69

)|( XP Q

XQP )|,(

Q

XQPXQP )|(),|(

Q

XQPQP )|()|(

Word Recognition

Replacing P(Φ|X) we now have a model with our CRF in it

What about P(W| Φ,X)? Conditional independence assumption gives P(W| Φ)

70

)|(maxarg XWPW

)|(),|(maxarg XPXWPW

QW

XQPQPXWP,

)|()|(),|(maxarg

QW

XQPQPWP,

)|()|()|(maxarg

Word Recognition

What about P(W|Φ)? Non-deterministic across sequences of words

Φ = / ah f eh r / W = ? “a fair”? “affair”? The more words in the string, the more possible

combinations can arise

71

)|( XWP

Q

XQPQPWP,

)|()|()|(

Word Recognition

Bayes Rule P(W) –language model P(Φ|W) – dictionary model P(Φ) – prior probability of phone sequences

72

)(

)()|(

P

WPWP)|( WP

Word Recognition What is P(Φ) ?

Prior probability over possible phone sequences Essentially acts as a “phone fertility/penalty” term –

lower probability sequences get a larger boost in weight than higher probability sequences

Approximate this with a standard n-gram model Seed it with phone-level statistics drawn from the same

corpus used for our language model

73

Word Recognition

Our final model incorporates all of these pieces together Benefit of this approach – reuse of standard models

Each element can be built as a finite state machine (FSM) Evaluation can be performed via FSM composition and best path

evaluation as for HMM-based systems (Mohri & Riley, 2002)

74

)|(maxarg XWPW

)|()|()(

)()|(maxarg,,

XQPQPP

WPWP

QW

Pilot Experiment: TIDIGITS

First word recognition experiment – TIDIGITS recognition Both isolated and strings of spoken digits, ZERO

(or OH) to NINE Male and female speakers

Training set – 112 speakers total Random selection of 11 speakers held out as

development set Remaining 101 speakers used for training as

needed

75


Important characteristics of the DIGITS problem: A given phone sequence maps to a single word sequence A uniform distribution over the words is assumed

P(W|Φ) easy to implement directly as FSM

76

)|(maxarg XWPW

)|()|()(

)()|(maxarg,,

XQPQPP

WPWP

QW


Implementation Created a composed dictionary and language

model FST No probabilistic weights applied to these FSTs –

assumption of uniform probability of any digit sequence Modified CRF code to allow composition of above

FST with phone lattice Results scored using standard HTK tools Compared to a baseline HMM system trained on the

same features

77


Labels Unlike TIMIT, TIDIGITS is only labeled at the word

level Phone labels were generated by force aligning the

word labels using an HMM-trained, MFCC based system

Features TIMIT-trained MLPs applied to TIDIGITS to create

features for CRF and HMM training

78

79

Pilot Experiment: ResultsModel WER

HMM (triphone, 1 Gaussinan, ~4500 parameters) 1.26%

HMM (triphone, 16 Gaussians ~120,000 paramters) 0.57%

CRF (monophone, ~4200 parameters) 1.11%

CRF (monophone, windowed, ~37000 parameters) 0.57%

HMM (triphone, 16 Gaussians, MFCCs) 0.25%

Basic CRF performance falls in line with HMM performance for a single Gaussian model

Adding more parameters to the CRF enables the CRF to perform as well as the HMM on the same features

Larger Vocabulary

Wall Street Journal 5K word vocabulary task Bigram language model MLPs trained on 75 speakers, 6488 utterances

Cross-validated on 8 speakers, 650 utterances Development set of 10 speakers, 368 utterances

for tuning purposes Results compared to HMM-Tandem baseline

and HMM-MFCC baseline

80

Larger Vocabulary

Phone penalty model P(Φ) Constructed using the transcripts and the lexicon Currently implemented as a phone pair (bigram)

model More complex model might lead to better

estimates

81

Larger Vocabulary

Direct finite-state composition not feasible for this task State space grows too large too quickly

Instead Viterbi decoding performed using the weighted finite-state models as constraints Time-synchronous beam pruning used to keep

time and space usage reasonable

82

Larger Vocabulary – Initial Results

83

Model WER

HMM MFCC Baseline 9.3%

HMM PLP Baseline 9.7%

HMM Tandem MLP 9.1%

CRF (phone) 11.3%

CRF (phone windowed) 11.7%

CRF (phone + phonological) 10.9%

CRF (3state phone inputs) 12.4%

CRF (3state phone + phono) 11.7%

HMM PLP (monophone labels) 17.5%

Preliminary numbers reported on development set only

Next Steps

Context Exploring ways to put more context into the CRF, either at the

label level or at the feature level Feature selection

Examine what features will help this model, especially features that may be useful for the CRF that are not useful for HMMs

Phone penalty model Results reported with just a bigram phone model A more interesting model leads to more complexity but may lead

to better results Currently examining trigram phone model to test the impact

84

Discussion

85

References J. Lafferty et al, “Conditional Random Fields:

Probabilistic models for segmenting and labeling sequence data”, Proc. ICML, 2001

A. Gunawardana et al, “Hidden Conditional Random Fields for phone classification”, Proc. Interspeech, 2005

J. Morris and E. Fosler-Lussier. “Conditional Random Fields for Integrating Local Discriminative Classifiers”, IEEE Transactions on Audio, Speech and Language Processing, 2008

M. Mohri et al, “Weighted finite-state transducers in speech recognition”, Computer Speech and Language, 2002

86

87

Background Tandem HMM

Generative probabilistic sequence model Uses outputs of a discriminative model (e.g. ANN

MLPs) as input feature vectors for a standard HMM

88


ANN MLP classifiers are trained on labeled speech data Classifiers can be phone classifiers, phonological

feature classifiers Classifiers output posterior probabilities for each

frame of data E.g. P(Q |X), where Q is the phone class label and X is

the input speech feature vector

89


Posterior feature vectors are used by an HMM as inputs

In practice, posteriors are not used directly Log posterior outputs or “linear” outputs are more

frequently used “linear” here means outputs of the MLP with no application

of a softmax function Since HMMs model phones as Gaussian mixtures, the

goal is to make these outputs look more “Gaussian” Additionally, Principle Components Analysis (PCA) is

applied to features to decorrelate features for diagonal covariance matrices

90

Idea: Crandem Use a CRF model to create inputs to a

Tandem-style HMM CRF labels provide a better per-frame accuracy

than input MLPs We’ve shown CRFs to provide better phone

recognition than a Tandem system with the same inputs

This suggests that we may get some gain from using CRF features in an HMM

91

Idea: Crandem Problem: CRF output doesn’t match MLP

output MLP output is a per-frame vector of posteriors CRF outputs a probability across the entire

sequence Solution: Use Forward-Backward algorithm to

generate a vector of posterior probabilities

92

Forward-Backward Algorithm Similar to HMM forward-backward algorithm Used during CRF training Forward pass collects feature functions for

the timesteps prior to the current timestep Backward pass collects feature functions for

the timesteps following the current timestep Information from both passes are combined

together to determine the probability of being in a given state at a particular timestep

93

Forward-Backward Algorithm

This form allows us to use the CRF to compute a vector of local posteriors y at any timestep t.

We use this to generate features for a Tandem-style system Take log features, decorrelate with PCA

)()|( ,,

, xZXyP titi

ti

94

Phone Recognition Pilot task – phone recognition on TIMIT

61 feature MLPs trained on TIMIT, mapped down to 39 features for evaluation

Crandem compared to Tandem and a standard PLP HMM baseline model

As with previous CRF work, we use the outputs of an ANN MLP as inputs to our CRF

Phone class attributes Detector outputs describe the phone label

associated with a portion of the speech signal /t/, /d/, /aa/, etc.

95* Significantly (p<0.05) improvement at 0.6% difference between models

Results (Fosler-Lussier & Morris 08)Model Phone

Accuracy


Tandem 70.8%

CRF 69.9%

Crandem – log 71.1%

96

Word Recognition Second task – Word recognition on WSJ0

Dictionary for word recognition has 54 distinct phones instead of 48 New CRFs and MLPs trained to provide input features

MLPs and CRFs trained on WSJ0 corpus of read speech No phone level assignments, only word transcripts Initial alignments from HMM forced alignment of MFCC

features Compare Crandem baseline to Tandem and original

MFCC baselines

97* Significant (p≤0.05) improvement at roughly 1% difference between models

Initial ResultsModel WER


Tandem MLP (39) 8.95%

Crandem (19) (1 epoch) 8.85%

Crandem (19) (10 epochs) 9.57%


98

Word Recognition CRF performs about the same as the

baseline systems But further training of the CRF tends to

degrade the result of the Crandem system Why? First thought – maybe the phone recognition

results are deteriorating (overtraining)


Initial ResultsModel Phone

Accuracy


Tandem MLP (39) 75.58%

Crandem (19) (1 epoch) 72.77%



100

Word Recognition Further training of the CRF tends to degrade

the result of the Crandem system Why? First thought – maybe the phone recognition

results are deteriorating (overtraining) Not the case

Next thought – examine the pattern of errors between iterations

101

* 29 deletions are substitutions in one model and deletions in the other**50 of these subs are different words between the epoch 1 and epoch 10 models

Initial ResultsModel Total

ErrorsInsertions Deletions Subs.

Crandem (1 epoch)

542 57 144 341

Crandem (10 epochs)

622 77 145 400

SharedErrors

429 37 131*(102)

261**(211)

NewErrors (1->10)

193 40 35 118

102

Word Recognition Training the CRF tends to degrade the result

of the Crandem system Why? First thought – maybe the phone recognition

results are deteriorating (overtraining) Not the case

Next thought – examine the pattern of errors between iterations There doesn’t seem to be much of a pattern here, other

than a jump in substitutions Word identity doesn’t give a clue – similar words wrong

in both lists

103

Word Recognition Further training of the CRF tends to degrade

the result of the Crandem system Why? Current thought – perhaps the reduction in scores

of the correct result is impacting the overall score This appears to be happening in at least some cases,

though it is not sufficient to explain everything

Word Recognition

MARCH vs. LARGE

Iteration 10 0 m 0.952271 l 0.00878177 en 0.00822043 em 0.00821897

0 1 m 0.978378 em 0.00631441 l 0.00500046 en 0.00180805

0 2 m 0.983655 em 0.00579973 l 0.00334182 hh 0.00128429

0 3 m 0.980379 em 0.00679143 l 0.00396782 w 0.00183199

0 4 m 0.935156 aa 0.0268882 em 0.00860147 l 0.00713632

0 5 m 0.710183 aa 0.224002 em 0.0111564 w 0.0104974 l 0.009005

Iteration 100 0 m 0.982478 em 0.00661739 en 0.00355534 n 0.00242626 l

0.001504

0 1 m 0.989681 em 0.00626308 l 0.00116445 en 0.0010961

0 2 m 0.991131 em 0.00610071 l 0.00111827 en 0.000643053

0 3 m 0.989432 em 0.00598472 l 0.00145113 aa 0.00127722

0 4 m 0.958312 aa 0.0292846 em 0.00523174 l 0.00233473

0 5 m 0.757673 aa 0.225989 em 0.0034254 l 0.00291158

104

Word Recognition

MARCH vs. LARGE - logspace

Iteration 10 0 m -0.0489053 l -4.73508 en -4.80113 em -4.80131

0 1 m -0.0218596 em -5.06492 l -5.29822 en -6.31551

0 2 m -0.01648 em -5.14994 l -5.70124 hh -6.65755

0 3 m -0.0198163 em -4.99209 l -5.52954 w -6.30235

0 4 m -0.0670421 aa -3.61607 em -4.75582 l -4.94256

0 5 m -0.342232 aa -1.4961 em -4.49574 w -4.55662 l -4.71001

Iteration 100 0 m -0.017677 em -5.01805 en -5.6393 n -6.02141 l -6.49953

0 1 m -0.0103729 em -5.07308 l -6.75551 en -6.816

0 2 m -0.0089087 em -5.09935 l -6.79597 en -7.34928

0 3 m -0.0106245 em -5.11855 l -6.53542 aa -6.66307

0 4 m -0.0425817 aa -3.53069 em -5.25301 l -6.05986

0 5 m -0.277504 aa -1.48727 em -5.67654 l -5.83906

105

106

Word Recognition Additional issues

Crandem results sensitive to format of input data Posterior probability inputs to the CRF give very poor

results on word recognition. I suspect is related to the same issues described

previously Crandem results also require a much smaller

vector after PCA MLP uses 39 features – Crandem only does well once

we reduce to 19 features However, phone recognition results improve if we use 39

features in the Crandem system (72.77% -> 74.22%)

Date post:	21-Jan-2016
Category:	Documents
Upload:	madeline-barnett
View:	219 times
Download:	0 times

1 Conditional Random Fields for Automatic Speech Recognition Jeremy Morris 06/03/2010.

Documents