User:Gang Chen/GSoC 2013 Summary

Project

A Sliding-Window Drop-in Replacement for the HMM Part-of-Speech Tagger in Apertium

Summary

Although the title shows that the new tagger is a sliding-window drop-in replacement for the HMM tagger, actually we did three things further:

1) Besides the Sliding-Window (SW) tagger, we also implemented the Light Sliding-Window (LSW) tagger, and successfully incorporated rules into the LSW tagger.

2) Instead of replacing the original HMM, we implemented the LSW tagger as an extension, so that the functionalities of the original HMM are fully kept.

3) We wrote a paper about the implementation of the SW and LSW tagger, and conducted a series of experiments.

The SW tagger

Let $\Gamma =\{\gamma _{1},\gamma _{2},...\gamma _{|\Gamma |}\}$ be the tag set, and $W=\{w_{1},w_{2},...\}$ be the words to be tagged.

A partition of W is established so that $w_{i}\equiv w_{j}$ if and only if both are assigned the same subset of tags, where each class of the partition is called an ambiguity class.

Let $\Sigma =\{\sigma _{1},\sigma _{2},...,\sigma _{\Sigma }\}$be the collection of ambiguity classes, where each $\sigma _{i}$is an ambiguity class.

Let$T:\Sigma \rightarrow 2^{\Gamma }$ be the function returning the collection $T(\gamma )$ of PoS tags for an ambiguity class $\gamma$.

The PoS tagging problem may be formulated as follows: given a text $w[1]w[2]...w[L]\in W^{+}$, each word $w[t]$ is assigned (using a lexicon and a morphological analyzer) an ambiguity class $\sigma [t]\in \Sigma$ to obtain the ambiguously tagged text $\sigma [1]\sigma [2]...\sigma [t]\in \Sigma ^{+}$; the task of a PoS tagger is to get a tag sequence$\gamma [1]\gamma [2]...\gamma [t]\in \Gamma ^{+}$ as correct as possible, that is, the one that maximizes a the probability of that tag sequence given the word sequence:

$\gamma ^{*}[1]...\gamma ^{*}[L]=argmax_{\gamma [t]\in T(\gamma [t])}P(\gamma [1]...\gamma [L]|\sigma [1]...\sigma [L])$

The core of the SW tagger is to use neighboring ambiguity classes to approximate the dependencies:

$P(\gamma [1]...\gamma [L]|\sigma [1]...\sigma [L])=\prod _{t=1}^{t=L}p(\gamma [t]|C_{(-)}\gamma [t]C_{(+)})$

where $t=1..L$, $C_{(-)}$ is the left context of length $N_{(-)}$ (e.g. if $N_{(-)}=1$, then $C_{(-)}=\sigma [t-1]$), $C_{(+)}$ is the left context of length $N_{(+)}$. Usually, at the left most and right most of the ambiguity sequence, specific sentence marks “ # ” are added in order to make the formula work in general.

The LSW taggger

Core Difference from the SW tagger

The SW tagger tags a word by looking around the neighbouring ambiguity classes,and has therefore a number of parameters in $O(|\Sigma |^{N_{(-)}+N_{(+)}}|\Gamma |)$. The LSW tagger tags a word by looking around the neighbouring tags, and therefore it has a number of parameters in $O(|\Gamma |^{N_{(-)}+N_{(+)}+1})$. Usually the tag set size $|\Gamma |$ is significantly smaller than the combinational ambiguity class size $|\Sigma |$. In this way, the parameters could be effectively reduced.

The LSW approximates the best tag as follows:

$\gamma ^{*}=argmax_{\gamma \in T(\sigma [t])}{\sum _{E_{(-)}\in T'(C_{(-)}[t]) \atop E_{(+)}\in T'(C_{(+)}[t])}P(E_{(-)}\gamma E_{(+)}|C_{(-)}[t]\sigma [t]C_{(+)}[t])}$

where $T':\Sigma ^{*}\rightarrow \Gamma ^{*}$, returning the set of tag sequences for an ambiguity sequence; $E_{(-)}$ and $E\{(+)\}$ are the left and right tag sequence respectively.