In recent years we have seen the development of efficient provably correct algorithms for learning Weighted Finite Automata (WFA). Most of these algorithms avoid the known hardness results by defining parameters beyond the number of states that can be used to quantify the complexity of learning automata under a particular distribution. One such class of methods are the so-called spectral algorithms that measure learning complexity in terms of the smallest singular value of some Hankel matrix. However, despite their simplicity and wide applicability to real problems, their impact in application domains remains marginal to this date. One of the goals of this paper is to remedy this situation by presenting a derivation of the spectral method for learning WFA that-without sacrificing rigor and mathematical elegance-puts emphasis on providing intuitions on the inner workings of the method and does not assume a strong background in formal algebraic methods. In addition, our algorithm overcomes some of the shortcomings of previous work and is able to learn from statistics of substrings. To illustrate the approach we present experiments on a real application of the method to natural language parsing.

In this article, we describe our participation in HatEval, a shared task aimed at the detection of hate speech against immigrants and women. We focused on Spanish subtasks, building from our previous experiences on sentiment analysis in this language. We trained linear classifiers and Recurrent Neural Networks, using classic features, such as bagof-words, bag-of-characters, and word embeddings, and also with recent techniques such as contextualized word representations. In particular, we trained robust task-oriented subwordaware embeddings and computed tweet representations using a weighted-averaging strategy. In the final evaluation, our systems showed competitive results for both Spanish subtasks ES-A and ES-B, achieving the first and fourth places respectively.

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