Lehnen et al., ICASSP 2011. Incorporating Alignments into Conditional Random Fields for Grapheme to Phoneme Conversion

Citation

Patrick Lehnen, Stefan Hahn, Andreas Guta and Hermann Ney. 2011. Incorporating Alignments into Conditional Random Fields for Grapheme to Phoneme Conversion. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-2011.

Online Version

Incorporating Alignments into Conditional Random Fields for Grapheme to Phoneme Conversion

Summary

The authors present a novel approach for better grapheme to phoneme (g2p) conversion. They argue that alignments are crucial in g2p conversion and are usually added by external models. Thus, the authors introduce an approach by which the alignment generation step can be efficiently added into the CRF training process. This is achieved in two ways. One in which linear segmentation is considered and the other in which all possible alignments given some constraints are incorporated in the CRF model. Apart from the standard CRF training process, the authors also introduce alignment as a hidden variable in the model.

Method

A conditional random field is modeled as:

$p(t_{1}^{N}|s_{1}^{N})={\frac {\exp H(t_{1}^{N},s_{1}^{N})}{\sum _{{\tilde {t}}_{1}^{N}}\exp H({{\tilde {t}}_{1}^{N}},s_{1}^{N})}}$

${\text{where, }}H(t_{1}^{N},s_{1}^{N})=\left(\sum _{n=1}^{N}\sum _{l=1}^{L}\lambda _{l}h_{l}(t_{n-1},t_{n},s_{1}^{N})\right)$

Alignments

The authors add alignment by modeling it as a hidden variable, $a_{1}^{M}$ in CRFs as follows,

$p(t_{1}^{M}|s_{1}^{M})=\sum _{a_{1}^{M}}p(t_{1}^{M},a_{1}^{M}|s_{1}^{N})$

They model the tuple $(t_{1}^{M},a_{1}^{M})$ by a projection using the BIO labeling scheme, restricting it to a 1-to-1 or many-to-one monotonic alignment scheme.

Training

The CRF model incorporating alignment as a hidden variable can be trained in two ways,

• Maximization approach
• Summation approach

Maximization Approach

This approach assumes a linear segmentation at the beginning and trains the CRF using an Expectation-Maximization like algorithm. The maximization step of the training process is given by,

$p(t_{1}^{N}|s_{1}^{N})|_{t_{1}^{N}=t_{1}^{N}(T_{1}^{M},a_{1}^{M})}={\frac {\exp H(t_{1}^{N},s_{1}^{N})}{\sum _{{\tilde {t}}_{1}^{N}}\exp H({{\tilde {t}}_{1}^{N}},s_{1}^{N})}}$

The expectation step is given by,

${\hat {a}}_{1}^{M}={\underset {a_{1}^{M}}{\operatorname {argmax} }}\left\{p(t_{1}^{N}(T_{1}^{M},a_{1}^{M})|s_{1}^{N})\right\}$

This training continues in a CRF training/resegmentation loop until convergence.

Summation Approach

In this approach, alignments are summer over directly by modeling the CRF as,

$p(T_{1}^{M}|s_{1}^{M})={\frac {\sum _{a_{1}^{M}}\exp H(T_{1}^{M},a_{1}^{M},s_{1}^{N})}{\sum _{{\tilde {a}}_{1}^{M}}\sum _{{\tilde {T}}_{1}^{M}}\exp H({\tilde {T}}_{1}^{M},{\tilde {a}}_{1}^{M},s_{1}^{N})}}$

$={\frac {\sum _{t_{1}^{M}:a_{1}^{M}}\exp H(t_{1}^{N},s_{1}^{N})}{\sum _{{\tilde {t}}_{1}^{N}}\exp H({\tilde {t}}_{1}^{N},s_{1}^{N})}}$

The numerator term is similar to the denominator term and can be solved by the same posterior approach using Forward-Backward algorithm.

Experiments and Results

Dataset

Experiments are reported on two publicly available English g2p corpora:

• NETtalk corpus, consisting about 15k grapheme/phoneme word pairs. About 1000 g2p pairs are used as development set. Gold standard manual alignments are available in this corpus.
• The Celex corpus, containing about 40k g2p word pairs. Test set is about 15k words in size.

Evaluation Metric

The authors report error rates in terms of phoneme error rate (PER) and word error rate (WER).

Results =

Results of the paper are shown below in Table 1.