1. CRANDEM: Conditional Random Fields for ASR
Jeremy Morris
11/21/2008

2. Outline Background – Tandem HMMs & CRFs Crandem HMM Phone recognition
Word recognition

3. Background Conditional Random Fields (CRFs)
Discriminative probabilistic sequence model
Directly defines a posterior probability of a label sequence given a set of observations

4. Background
Problem: How do we make use of CRF classification for word recognition?
Attempt to use CRFs directly?
Attempt to fit CRFs into current state-of-the-art models for speech recognition?
Here we focus on the latter approach
How can we integrate what we learn from the CRF into a standard HMM-based ASR system?

5. 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

6. Background
Tandem HMM
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

7. Background
Tandem HMM
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 the softmax function to transform into probabilities
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

8. Idea: Crandem
Use a CRF classifier 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

9. 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

10. Forward-Backward Algorithm
The Forward-Backward algorithm is already used during CRF training
Similar to the forward-backward algorithm for HMMs
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

11. Forward Backward Algorithm

12. 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, decorelate with PCA

13. 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
Various CRF models examined (state feature functions only, state+transition functions), and various input feature spaces examined (phone classifier and phonological feature classifier)

14. Phone Recognition Phonological feature attributes
Detector outputs describe phonetic features of a speech signal
Place, Manner, Voicing, Vowel Height, Backness, etc.
A phone is described with a vector of feature values
Phone class attributes
Detector outputs describe the phone label associated with a portion of the speech signal
/t/, /d/, /aa/, etc.

15. Phone Recognition

16. Phone Recognition - Results
Phonological feature attributes
Detector outputs describe phonetic features of a speech signal
Place, Manner, Voicing, Vowel Height, Backness, etc.
A phone is described with a vector of feature values
Phone class attributes
Detector outputs describe the phone label associated with a portion of the speech signal
/t/, /d/, /aa/, etc.

17. Results (Fosler-Lussier & Morris 08)
Model
Phone Accuracy
PLP HMM reference
68.1%
Tandem (61 feas)
70.6%
Tandem (48 feas)
70.8%
CRF (state)
69.9%
CRF (state+trans)
70.7%
Crandem (state) – log
71.1%
Crandem (state+trans) – log
71.7%
Crandem (state) – unnorm
71.2%
Crandem (state+trans) – unnorm
71.8%
* Significantly (p<0.05) improvement at 0.6% difference between models

18. Results (Fosler-Lussier & Morris 08)
Model
Phone Accuracy
PLP HMM reference
68.1%
Tandem (105 feas)
70.9%
Tandem (48 feas)
71.2%
CRF (state)
71.4%
CRF (state+trans)
71.6%
Crandem (state) – log
71.7%
Crandem (state+trans) – log
72.4%
Crandem (state) – unnorm
Crandem (state+trans) – unnorm
* Significantly (p≤0.05) improvement at 0.6% difference between models

19. Word Recognition Second task – Word recognition
Dictionary for word recognition has 54 distinct phones instead of 48, so new CRFs and MLPs trained to provide input features
MLPs and CRFs again trained on TIMIT to provide both phone classifier output and phonological feature classifier output
Initial experiments – use MLPs and CRFs trained on TIMIT to generate features for WSJ recognition
Next pass – use MLPs and CRFs trained on TIMIT to align label files for WSJ, then train MLPs and CRFs for WSJ recognition

20. Initial Results Model Word Accuracy MFCC HMM reference 90.85%
Tandem MLP (54feas)
90.30%
Tandem MFCC+MLP (54feas)
90.90%
Crandem (54feas) (state)
90.95%
Crandem (54feas) (state+trans)
90.77%
Crandem MFCC+CRF (state)
92.29%
Crandem MFCC+CRF (state+tran)
92.40%
* Significant (p≤0.05) improvement at roughly 1% difference between models

21. Initial Results Model Word Accuracy MFCC HMM reference 90.85%
Tandem MLP (98feas)
91.26%
Tandem MFCC+MLP (98feas)
92.04%
Crandem (98feas) (state)
91.31%
Crandem (98feas) (state+trans)
90.49%
Crandem MFCC+CRF (state)
92.47%
Crandem MFCC+CRF (state+tran)
92.62%
* Significant (p≤0.05) improvement at roughly 1% difference between models

22. Initial Results Model Word Accuracy MFCC HMM reference 90.85%
Tandem MLP (WSJ 54)
90.41%
Tandem MFCC+MLP (WSJ 54)
92.21%
Crandem (WSJ 54) (state)
89.58%
* Significant (p≤0.05) improvement at roughly 1% difference between models

23. Word Recognition Problems
Some of the models show slight significant improvement over their Tandem counterpart
Unfortunately, what will cause an improvement is not yet predictable
Transition features give slight degredation when used on their own slight improvement when classifier is mixed with MFCCs
Retraining directly on WSJ data does not give improvement for CRF
Gains from CRF training are wiped away if we just retrain the MLPs on WSJ data

24. Word Recognition Problems (cont.)
The only model that gives improvement for the Crandem system is a CRF model trained on linear outputs from MLPs
Softmax outputs – much worse than baseline
Log softmax outputs – ditto
This doesn’t seem right, especially given the results from the Crandem phone recognition experiments
These were trained on softmax outputs
I suspect “implementor error” here, though I haven’t tracked down my mistake yet

25. Word Recognition Problems (cont.)
Because of the “linear inputs only” issue, certain features have yet to be examined fully
“Hifny”-style Gaussian scores have not provided any gain – scaling of these features may be preventing them from being useful

26. Current Work Sort out problems with CRF models
Why is it so sensitive to the input feature type? (linear vs. log vs. softmax)
If this sensitivity is “built in” to the model, how can I appropriately scale features to include them in the model that works?
Move on to next problem – direct decoding on CRF lattices