Study on Pattern Inference from Positive Data

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The aim of this research is in investigating realizability of machine learning, by studying inductive inferece as a theoretical model of learning from examples. In general, examples using in learning are categorized in positive ones and negative ones. In language (or grammar) learning, positive examples are corresponding to (grammatically) correct sentences. Data obtained from experiments can be considered as positive examples of a certain property, when they are concernd with the property. In this research, we have considered theoretical limits of inductive learning based on positive examples and investigated efficient learning algorithms from the viewpoint of practical applications.A pattern is a string consisting of constant symbols and variables. The language of a pattern is the set of constant strings obtained by. substituting nonempty constant strings for variables in the pattern. For any fixed k, the class of unions of at most k pattern languages is already shown to be inferable from positive data.We apply a learning algorithm for pattern languages to discover a motif from amino-acid sequences. From only positive examples with the help of an alphabet indexing, the algorithm successfully finds sets of patterns, that can be considered as motifs.We have also studied speed-up of language acceptors for elementary formal systems, where we employ fast string pattern matching machines. Finally, we propose a possible approach to extending leaning algorithms for multiple patterns.