Study on Inductive Learning Based on Positive Examples

本研究的目的是研究机器学习的可实现性，通过研究归纳推理作为示例学习的理论模型。一般来说，学习中使用的例子分为积极的例子和消极的例子。在语言(或语法)学习中，积极的例子对应于(语法上)正确的句子。从实验中获得的数据可以被认为是某一性质的积极例子，当它们与该性质有关时。在本研究中，我们考虑了基于正例的归纳学习的理论局限性，从实际应用的角度研究了高效的学习算法。模式是由常量符号和变量组成的字符串。语言或模式是通过用非空常量字符串替换模式中的变量而获得的常量字符串的集合。对于任何固定的k，已经证明了至多k个模式语言的并类可以从正数据中推断出来，我们应用模式语言的学习算法从氨基酸序列中发现一个基元。在字母索引的帮助下，该算法成功地从正例中找到了可以被认为是模式的集合或模式。基本形式系统是模式上的逻辑程序，因此是模式的自然扩展。我们使用初级形式系统作为语言学习的统一框架。在这个框架内，我们已经展示了各种结果，例如，模型推理风格的语言学习，以及从正数据中可推断的语言的存在或丰富类别。

The aim of this research is in investigating realizability of machine learning, by studying inductive inference 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 concerned 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 or 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 or patterns, that can be considered as motifs.Elementary formal systems are logic programs over patterns, and therefore natural extension of patterns. We employ elementary formal systems as a unifying framework for language learning. Within this framework, we have shown various results, such as, model inference style language learning, and the existence or rich classes of languages inferable from positive data.