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, allowing for 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,

\frac {\sum_{a_1^M} \exp H(T_1^M, a_1^M, s_1^N)}{b}

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

$b=1$