群論に基づく2次元パターンの帰納的推論

概要

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In this paper, we discuss inductive inference which is a kind of learning. We consider this problem through "a guessing task of a two-dimensional arrangement of cards". This task is summarized as follows. Four kinds of color cards are arranged regularly at a 4 × 8 two-dimensional domain. All cards are turned-off at an initial state. From the initial state, a subject (learner) tries to find a rule of the card arrangement under a constraint of minimum number of turning-up cards. Firstly, we describe regularity of patterns of the card arrangement by theory of groups. In this description method, regularity of patterns is defined by "unit structure" and "repetition structure". We indicate efficiency of the description method by theory of groups through analysis of regularity of patterns generated by human subjects. Secondly, we construct an algorithm which can solve the guessing task on the basis of the description method by theory of groups, and realize the algorithm on a computer. Results of computer simulations are summarized as follows. Inference by this algorithm prescribes the upper boundry of inference by human subjects. This algorithm could guess correctly 95% of patterns generated by human subjects.
社団法人人工知能学会の論文
1990-09-01