We have approached the cross-lingual word sense disambiguation task by means of a probabilistic system which considers the probability of a word sense (in a target language), given a sentence (in a source language) containing the ambiguous word. In particular, we used the Naive Bayes classifier in two different ways. First, we calculated the probability of each word in the source language of being associated/translated to the corresponding word (in the target language). The probabilities were estimated by means of a bilingual statistical dictionary which is calculated using the Giza++ system over the EUROPARL parallel corpus. We filtered this corpus by selecting only those sentences which included some senses of the ambigu­ous word which were obtained by translating this ambiguous word on the Google search engine.

In Figure 1 we may see the complete process for approaching the problem of cross-lingual WSD.

The second approach considered a weighted probability for each word in the source sentence. The closer a word of the sentence to the ambigu­ous word, the higher the weight given to it.

In other words, given an English sentence S = {w\,w2,--- ,Wk,--- ,Wk+i,---} with the am­biguous word Wk in position k. Let us consider N candidate translations of Wk, {i^, t%, • • • , t^} obtained somehow (we will further discuss about this issue in this section). We are insterested on finding the most probable candidate translations for the polysemous word Wk- Therefore, we may use a Naïve Bayes classifier which considers the probability of t\ given wu- A formal description of the classifier is given as follows.

We are interested on finding the argument that maximizes p(tk\S), therefore, we may to calculate the denominator. Moreover, if we assume that all the different translations are equally distributed, then Eq. (2) may be approximated by Eq. (3).

The complete calculation of Eq. (3) requires to apply the chain rule. However, if we assumed that the words of the sentence are independent, then we may rewrite Eq. (3) as Eq. (4).

The best translation is obtained as shown in Eq. (5). Nevertheless the position of the ambiguous word, we are only considering a product of the probabilités of translation. Thus, we named this approach, the unweighted version. Algorithm 1 provides details about the implementation.

withi = !,••• ,N.

Algorithm 1 : An unweighted naïve Bayes ap­proach to cross-lingual WSD Input: A set Q of sentences:

Output: The best word/sense for each ambiguous word Wj G Si i for 1 = 1 to \Q\ do for i = 1 to N do

for j = 1 to I Si I do foreach Wj G Si do

if Wj G Dictionary then I Pi,i = Pi,i*p(wj\tï);

is return arg maxtfc If/JiP(wj\ti)

A second approach (weighted version) is also proposed as shown in Eq. (6). Algorithm 2 pro-|t^)des details about its implementation.

BestSensew(wk) =

With respect to the N candidate translations of the polysemous word wk, {ti,t2, ■ ■ ■ , i^}, we have used of the Google translator. Google pro­vides all the possible translations for wk with the corresponding grammatical category. There­fore, we are able to use those translations that match with the same grammatical category of the Algorithm 2: A weighted naïve Bayes ap­proach to cross-lingual WSD Input: A set Q of sentences:

Output: The best word/sense for each ambiguous word Wj G Si i for 1 = 1 to \Q\ do for i = 1 to N do

Naïve Bayes classifier

EUROPARLparallel corpus

Filtering

Figure 1 : An overview of the presented approach for cross-lingual word sense disambiguation ambiguous word. Even if we attempted other approaches such as selecting the most probable translations from the statistical dictionary, we con­firmed that by using the Google online transla­tor we obtain the best results. We consider that this result is derived from the fact that Google has a better language model than we have, because our bilingual statistical dictionary was trained only with the EUROPARL parallel corpus.

The experimental results of both, the un­weighted and the weighted versions of the pre­sented approach for cross-lingual word sense dis­ambiguation are given in Section 3.

This module is based on the cross-lingual word sense disambiguation system. Once we knew the best word/sense (Spanish) for the ambigu­ous word(English), we lemmatized the Spanish word. Thereafter, we searched, at WordNet, the synonyms of this word (sense) that agree with the grammatical category (noun, verb, etc) of the query (source polysemous word), and we return those synonyms as possible lexical substitutes. Notice again that this task is complemented by the WSD solver.

In Figure 2 we may see the complete process of approaching the problem of cross-lingual lexical substitution.

dictionary;

for j = 1 to \Si\ do foreach Wj G Si do if Wj G Dictionary then

is return arg maxtfc nUiK^jl^

C-WSD system

Figure 2: An overview of the presented approach for cross-lingual lexical substitution

In Table 2 we may see the results we have ob­tained with the different versions of the presented approach. In the same Table we can find a com­parison of our runs with others presented at the SemEval-2 competition. In particular, we have tested four different runs which correspond to two evaluations for each different version of the prob­abilistic classifier. The description of each run is given in Table 1.

We obtained a better performance with those runs that were evaluated with the five best trans­lations (oof) than with those that were evaluated with only the best ones. This fact lead us to con­sider in further work to improve the ranking of the translations found by our system. On other hand, the unweighted version of the proposed classifier improved the weighted one. This behavior was un­expected, because in the development dataset, the results were opposite. We consider that the prob­lem comes from taking into account the entire sen­tence instead of a neighborhood (windows) around the ambiguous word. We will further investigate about this issue. We got a better performance than other systems, and those runs that outperformed our system runs did it by around 3% of precision and recall in the case of the oof evaluation.

In Table 3 we may see the obtained results for the cross-lingual lexical substitution task. The ob­tained results are low in comparison with the best one. Since this task relies on the C-WSD task, then a lower performance on the C-WSD task will con­duct to a even lower performance in C-LS. Firstly, we need to improve the C-WSD solver. In partic­ular, we need to improve the ranking procedure in order to obtain a better translation of the source ambiguous word. Moreover, we consider that the use of language modeling would be of high ben­efit, since we could test whether or not a given translation together with the terms in its context would have high probability in the target language.