Unigram tagger

apertium-tagger from “m5w/apertium” supports all the unigram models from “A set of open-source tools for Turkish natural language processing.”

Installation

First, install all prerequisites. See “If you want to add language data / do more advanced stuff.”

Then, replace <directory> with the directory you’d like to clone “m5w/apertium” into and clone the repository.

git clone https://github.com/m5w/apertium.git <directory>

Then, configure your environment and finally configure, build, and install “m5w/apertium.”

Usage

See apertium-tagger -h .

Training a Model on a Hand-Tagged Corpus

First, get a hand-tagged corpus as you would for any non-unigram model.

$ cat handtagged.txt
^a/a<a>$
^a/a<b>$
^a/a<b>$
^aa/a<a>+a<a>$
^aa/a<a>+a<b>$
^aa/a<a>+a<b>$
^aa/a<b>+a<a>$
^aa/a<b>+a<a>$
^aa/a<b>+a<a>$
^aa/a<b>+a<b>$
^aa/a<b>+a<b>$
^aa/a<b>+a<b>$
^aa/a<b>+a<b>$

Example 2.1.1: handtagged.txt : a Hand-Tagged Corpus for apertium-tagger

Then, replace MODEL with the unigram model from “A set of open-source tools for Turkish natural language processing” you’d like to use, replace SERIALISED_BASIC_TAGGER with the filename to which you’d like to write the model, and train the tagger.

$ apertium-tagger -s 0 -u MODEL SERIALISED_BASIC_TAGGER handtagged.txt

Disambiguation

Either write your input to a file or pipe it to the tagger.

$ cat raw.txt
^a/a<a>/a<b>/a<c>$
^aa/a<a>+a<a>/a<a>+a<b>/a<b>+a<a>/a<b>+a<b>/a<a>+a<c>/a<c>+a<a>/a<c>+a<c>$

Example 2.2.1: raw.txt : Input for apertium-tagger

Replace MODEL with the unigram model from “A set of open-source tools for Turkish natural language processing” you’d like to use, replace SERIALISED_BASIC_TAGGER with the file to which you wrote the unigram model, and disambiguate the input.

$ apertium-tagger -gu MODEL SERIALISED_BASIC_TAGGER raw.txt
^a/a<b>$
^aa/a<b>+a<b>$
$ echo '^a/a<a>/a<b>/a<c>$
^aa/a<a>+a<a>/a<a>+a<b>/a<b>+a<a>/a<b>+a<b>/a<a>+a<c>/a<c>+a<a>/a<c>+a<c>$' | \
apertium-tagger -gu MODEL SERIALISED_BASIC_TAGGER
^a/a<b>$
^aa/a<b>+a<b>$

Unigram Models

See section 5.3 of “A set of open-source tools for Turkish natural language processing.”

Model 1

See section 5.3.1 of “A set of open-source tools for Turkish natural language processing.”

This model assigns each analysis string a score of

${\begin{aligned}\mathrm {score} &=f(T)~{\text{,}}\end{aligned}}$

${\begin{aligned}{\text{where}}~&T~{\text{is the analysis string}}\end{aligned}}$

with additive smoothing.

Consider the following corpus.

$ cat handtagged.txt
^a/a<a>$
^a/a<b>$
^a/a<b>$

Example 3.1.1: handtagged.txt : A Hand-Tagged Corpus for apertium-tagger

Given the lexical unit ^a/a<a>/a<b>/a<c>$ , the tagger assigns the analysis string a<a> a score of

${\begin{aligned}\mathrm {score} &=\mathrm {tokenCount\_T} +1\\&=1+1\\&=2~{\text{,}}\end{aligned}}$

${\begin{aligned}{\text{where}}~&\mathrm {tokenCount\_T} ~{\text{is the frequency of}}~T~{\text{in the corpus}}~{\text{.}}\end{aligned}}$

The tagger then assigns the analysis string a<b> a score of

${\begin{aligned}\mathrm {score} &=2+1\\&=3\end{aligned}}$

and the unknown analysis string a<c> a score of

${\begin{aligned}\mathrm {score} &=0+1\\&=1~{\text{.}}\end{aligned}}$

If ./autogen.sh is passed the option --enable-debug , the tagger prints such calculations to standard error.

$ ./autogen.sh --enable-debug
$ make
$ echo '^a/a<a>/a<b>/a<c>$' | apertium-tagger -gu 1 SERIALISED_BASIC_TAGGER


score("a<a>") ==
2 ==
  2.000000000000000000
  score("a<b>") ==
3 ==
  3.000000000000000000
  score("a<c>") ==
1 ==
  1.000000000000000000
  ^a<b>$

Training on Corpora with Ambiguous Lexical Units

Consider the following corpus.

$ cat handtagged.txt
^a/a<a>$
^a/a<a>/a<b>$
^a/a<b>$
^a/a<b>$

Example 3.1.1.1: handtagged.txt : a Hand-Tagged Corpus for apertium-tagger

The tagger expects lexical units of 1 analysis string, or lexical units of size 1. However, the size of the lexical unit ^a/a<a>/a<b>$ is 2. For this lexical unit,

$P({\texttt {a<a>}})=P({\texttt {a<b>}})={\frac {1}{2}}~{\text{;}}$

the tagger must effectively increment the frequency of both analysis strings by 0.500000000000000000 . However, the tagger can’t increment the analysis strings’ frequencies by a non-integral number because model 1 represents analysis strings’ frequencies as std::size_t .

Instead, the tagger multiplies all the stored analysis strings’ frequencies by this lexical unit’s size and increments the frequency of each of this lexical unit’s analysis strings by 1.

${\begin{aligned}f({\texttt {a<a>}})&=(1)(2)&f({\texttt {a<b>}})&=(0)(1)\\&+1=2+1=3&&+1=0+1=1\end{aligned}}$

The tagger could then increment the analysis strings’ frequencies of another lexical unit of size 2 without multiplying any of the stored analysis strings’ frequencies. To account for this, the tagger stores the least common multiple of all lexical units’ sizes; only if the LCM isn’t divisible by a lexical unit’s size does the tagger multiply all the analysis strings’ frequencies.

After incrementing the analysis strings’ frequencies of the lexical unit ^a/a<a>/a<b>$, the tagger increments the analysis string a<b> of the lexical unit ^a/a<b>$ by

${\begin{aligned}{\frac {\mathrm {LCM} }{\mathrm {TheLexicalUnit.size} }}={\frac {2}{1}}=2~{\text{.}}\end{aligned}}$

If the tagger gets another lexical unit of size 2, it would increment the frequency of each of the lexical unit’s analysis strings by

${\begin{aligned}{\frac {\mathrm {LCM} }{\mathrm {TheLexicalUnit.size} }}={\frac {2}{2}}=1~{\text{,}}\end{aligned}}$

and if it gets a lexical unit of size 3, it would multiply all the analysis strings’ frequencies by 3 and then increment the frequency of each of the lexical unit’s analysis strings by

${\begin{aligned}{\frac {\mathrm {LCM} }{\mathrm {TheLexicalUnit.size} }}={\frac {6}{3}}=2~{\text{.}}\end{aligned}}$

Each model supports functions to increment all their stored analysis strings’ frequencies, so models 2 and 3 support this algorithm as well.

TODO: If one passes the -d option to apertium-tagger , the tagger prints warnings about ambiguous analyses in corpora to stderr.

$ apertium-tagger -ds 0 -u 1 handtagged.txt
apertium-tagger: handtagged.txt: 2:13: unexpected analysis "a<b>" following anal
ysis "a<a>"
^a/a<a>/a<b>$
^

File Format

The tagger represents this model as std::map<Analysis, std::size_t> Model; .

The tagger first serialises Model.size() , the number of unique analysis strings in the corpus. To reduce file size, the tagger only puts a number’s non-zero bytes, preceded by the number of non-zero bytes in the number, henceforth known as the number’s size.

[. . . .]

([. . .]).serialise(0x00000000, [. . .]); // 00
([. . .]).serialise(0x000000ff, [. . .]); // 01ff
([. . .]).serialise(0x0000ffff, [. . .]); // 02ffff
([. . .]).serialise(0x00ffffff, [. . .]); // 03ffffff
([. . .]).serialise(0xffffffff, [. . .]); // 04ffffffff

[. . . .]

Model 2

See section 5.3.2 of “A set of open-source tools for Turkish natural language processing.”

Consider Example 3.1.1: handtagged.txt .

The tag string <b> is twice as frequent as <a>. However, model 1 scores b<a> and b<b> equally because neither analysis string appears in the corpus.

This model splits each analysis string into a root, $r$ , and the part of the analysis string that isn’t the root, $a$ . An analysis string’s root is its first lemma. The $r$ of a<b>+c<d> is a , and its $a$ is <b>+c<d> . The tagger assigns each analysis string a score of $P(r|a)f(a)$ with add-one smoothing. (Without additive smoothing, this model would be the same as model 1.) The tagger assigns higher scores to unknown analysis strings with frequent $a$ than to unknown analysis strings with infrequent $a$ .

Given the lexical unit ^b/b<a>/b<b>$, the tagger assigns the analysis string b<a> a score of

${\begin{aligned}\mathrm {score} &={\frac {(\mathrm {tokenCount\_r\_a} +1)(\mathrm {tokenCount\_a} +1)}{\mathrm {tokenCount\_a} +1+\mathrm {typeCount\_a} }}\\&={\frac {(0+1)(1+1)}{1+1+2}}\\&={\frac {(1)(2)}{4}}\\&={\frac {1}{2}}~{\text{,}}\end{aligned}}$

${\begin{aligned}{\text{where}}~&\mathrm {tokenCount\_r\_a} ~{\text{is the frequency of the}}~r,a~{\text{in the corpus ,}}\\&\mathrm {tokenCount\_a} ~{\text{is the frequency of the}}~a~{\text{in the corpus ,}}\\{\text{and}}~&\mathrm {typeCount\_a} ~{\text{is the size of the parameter vector of all}}~r~{\text{preceding the}}~a~{\text{.}}\end{aligned}}$

Note that $\mathrm {typeCount\_a}$ counts the analysis string being scored. For example, the tagger would assign the known analysis string a<a> a score of

${\begin{aligned}\mathrm {score} &={\frac {(1+1)(1+1)}{1+1+1}}\\&={\frac {(2)(2)}{3}}\\&={\frac {4}{3}}~{\text{.}}\end{aligned}}$

The tagger assigns the analysis string b<b> a score of

${\begin{aligned}\mathrm {score} &={\frac {(0+1)(2+1)}{2+1+2}}\\&={\frac {(1)(3)}{5}}\\&={\frac {3}{5}}~{\text{.}}\end{aligned}}$

Model 3

See section 5.3.3 of “A set of open-source tools for Turkish natural language processing.”

Consider Example 3.1.1: handtagged.txt .

The morpheme a<b> is twice as frequent as the morpheme a<a> . However, model 2 scores the analysis strings a<a>+a<a> and a<b>+a<a> equally because the $a$ of neither appears in the corpus.

This model splits each analysis string into an $r~{\text{,}}$ a first inflection, $i_{0}~{\text{,}}$ and a sequence of derivation-inflection pairs, $(d_{1},i_{1})...(d_{n},i_{n})~{\text{.}}$ The $r$ of the analysis string a<b>+c<d> is a , its $i_{0}$ is <b> , and its $(d_{1},i_{1})...(d_{n},i_{n})$ is c<d> , where its $d_{1}$ is c , and its $i_{1}$ is <d> . The tagger assigns each analysis string a score of $P(r|i_{0})f(i_{0})\prod _{i=1}^{n}P(d_{i}|i_{i-1})P(i_{i}|d_{i})$ with add-one smoothing. The tagger assigns higher scores to unknown analysis strings with frequent $r,i_{0}$ than to unknown analysis strings with infrequent $r,i_{0}~{\text{.}}$

Given the lexical unit ^aa/a<a>+a<a>/a<b>+a<a>$ , the tagger assigns the analysis string a<a>+a<a> a score of

${\begin{aligned}\mathrm {score} =\;&{\frac {(\mathrm {tokenCount\_r\_i\_0} +1)(\mathrm {tokenCount\_i\_0} +1)}{\mathrm {tokenCount\_i\_0} +1+\mathrm {typeCount\_i\_0} }}\\&{\begin{aligned}\prod _{i=1}^{n}\,&{\frac {\mathrm {tokenCount\_d\_i} (d_{n},i_{n-1})+1}{\mathrm {tokenCount\_i} (i_{n-1})+1+\mathrm {typeCount\_i} (i_{n-1},d_{n})}}\\&{\frac {\mathrm {tokenCount\_i\_d} (i_{n},d_{n})+1}{\mathrm {tokenCount\_d} (d_{n})+1+\mathrm {typeCount\_d} (d_{n},i_{n})}}\end{aligned}}\\=\;&{\frac {(1+1)(1+1)}{1+1+1}}{\frac {0+1}{0+1+1}}{\frac {0+1}{0+1+1}}\\=\;&{\frac {(2)(2)}{3}}{\frac {1}{2}}{\frac {1}{2}}\\=\;&{\frac {4}{3}}{\frac {1}{4}}\\=\;&{\frac {1}{3}}~{\text{,}}\end{aligned}}$

${\begin{aligned}{\text{where}}~&\mathrm {tokenCount\_r\_i\_0} ~{\text{is the frequency of the}}~r,i_{0}~{\text{in the corpus}}~{\text{,}}\\&\mathrm {tokenCount\_i\_0} ~{\text{is the frequency of the}}~i_{0}~{\text{in the corpus}}~{\text{,}}\\&\mathrm {typeCount\_i\_0} ~{\text{is the size of the parameter vector of}}~r~{\text{preceding the}}~i_{0}~{\text{,}}\\&\mathrm {tokenCount\_d\_i} (d_{n},i_{n-1})~{\text{is the frequency of the}}~d_{n}~{\text{following the}}~i_{n-1}~{\text{in the corpus}}~{\text{,}}\\&\mathrm {tokenCount\_i} (i_{n-1})~{\text{is the frequency of non-final}}~i_{n-1}~{\text{in the corpus}}~{\text{,}}\\&\mathrm {typeCount\_i} (i_{n-1},d_{n})~{\text{is the size of the parameter vector of}}~d~{\text{following the}}~i_{n-1}~{\text{,}}\\&\mathrm {tokenCount\_i\_d} (i_{n},d_{n})~{\text{is the frequency of the}}~i_{n}~{\text{following the}}~d_{n}~{\text{in the corpus}}~{\text{,}}\\&\mathrm {tokenCount\_d} (d_{n})~{\text{is the frequency of the}}~d_{n}~{\text{in the corpus}}~{\text{,}}\\{\text{and}}~&\mathrm {typeCount\_d} (d_{n},i_{n})~{\text{is the size of the parameter vector of}}~i~{\text{following the}}~d_{n}~{\text{.}}\end{aligned}}$

The tagger assigns the analysis string a<b>+a<a> a score of

${\begin{aligned}\mathrm {score} =\;&{\frac {(2+1)(2+1)}{2+1+1}}{\frac {0+1}{0+1+1}}{\frac {0+1}{0+1+1}}\\=\;&{\frac {(3)(3)}{4}}{\frac {1}{2}}{\frac {1}{2}}\\=\;&{\frac {9}{4}}{\frac {1}{4}}\\=\;&{\frac {9}{16}}~{\text{.}}\end{aligned}}$