Statistical Relational Learning With Unconventional String Models.

Mai H Vu,Ashkan Zehfroosh,Herbert G Tanner,Kristina Strother-Garcia,Jeffrey Heinz,Michael Sebok

doi:10.3389/frobt.2018.00076

Mai H Vu, Ashkan Zehfroosh + Show 4 more

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https://doi.org/10.3389/frobt.2018.00076

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Abstract

This paper shows how methods from statistical relational learning can be used to address problems in grammatical inference using model-theoretic representations of strings. These model-theoretic representations are the basis of representing formal languages logically. Conventional representations include a binary relation for order and unary relations describing mutually exclusive properties of each position in the string. This paper presents experiments on the learning of formal languages, and their stochastic counterparts, with unconventional models, which relax the mutual exclusivity condition. Unconventional models are motivated by domain-specific knowledge. Comparison of conventional and unconventional word models shows that in the domains of phonology and robotic planning and control, Markov Logic Networks With unconventional models achieve better performance and less runtime with smaller networks than Markov Logic Networks With conventional models.

Highlights

This article shows that statistical relational learning (Getoor and Taskar, 2007; Domingos and Lowd, 2009; Natarajan et al, 2015) provides a natural solution to the problem of inferring formal languages when the alphabetic symbols underlying the formal languages share properties.Formal languages are sets of strings or probability distributions over strings (Hopcroft and Ullman, 1979; Kracht, 2003; Kornai, 2007)
As we will see we found that this range of sizes in the training data was sufficient to show that maximum likelihood estimate (MLE) and trained Markov logic networks (MLNs) behave especially with 100 strings in the training data set
The allowed bi-grams are shaded in the table. These results indicate that both models meet this benchmark of success with 20 training strings

Summary

Introduction

This article shows that statistical relational learning (Getoor and Taskar, 2007; Domingos and Lowd, 2009; Natarajan et al, 2015) provides a natural solution to the problem of inferring formal languages when the alphabetic symbols underlying the formal languages share properties.Formal languages are sets of strings or probability distributions over strings (Hopcroft and Ullman, 1979; Kracht, 2003; Kornai, 2007). We use the word word synonymously with string. They have found application in many domains, including natural language processing, robotic planning and control (Fu et al, 2015), and human-robot interaction (Zehfroosh et al, 2017). In each of these domains there are instances where formal languages have to be inferred from observations. Grammatical inference algorithms (de la Higuera, 2010; Heinz and Sempere, 2016) address the problem of learning formal languages in theory and practice and have found success in the aforementioned domains (Fu et al, 2015; Heinz et al, 2015)

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