Masako Sato

Properties of Language Classes With Finite Elasticity

This paper considers properties of language classes with finite elasticity in the viewpoint of set theoretic operations. Finite elasticity was introduced by Wright as a sufficient condition for language classes to be inferable from positive data, and as a property preserved by (not usual) union operation for language classes. We show that the family of language classes with finite elasticity is closed under not only union but also various operations for language classes such as intersection, concatenation and so on.

Characteristic Sets for Unions of Regular Pattern Languages and Compactness

The paper deals with the class RPk of sets of at most k regular patterns. A semantics of a set P of regular patterns is a union L(P) of languages defined by patterns in P. A set Q of regular patterns is said to be a more general than P, denoted by P ⊆ Q, if for any p ∈ P, there is a more general pattern q in Q than p. It is known that the syntactic containment P ⊆ Q for sets of regular patterns is efficiently computable. We prove that for any sets P and Q in RPk, (i) S2(P) ⊆ L(Q), (ii) the syntactic containment P ⊆ Q and (iii) the semantic containment L(P) ⊆ L(Q) are equivalent mutually, provided #Σ ≥ 2k - 1, where Sn(P) is the set of strings obtained from P by substituting strings with length at most n for each variable. The result means that S2 (P) is a characteristic set of L(P) within the language class for RPk under the condition above. Arimura et al. showed that the class RPk has compactness with respect to containment, if #Σ ≥ 2k+1. By the equivalency above, we prove that RPk has compactness if and only if #Σ ≥ 2k - 1. The results obtained enable us to design efficient learning algorithms of unions of regular pattern languages such as already presented by Arimura et al. under the assumption of compactness.

Mining indirect association rules

A large database, such as POS data, could give us many insights about customer behavior. Many techniques and measures have been proposed to extract interesting rules. As the study of Association rule mining has proceeded, the rules about items that are not bought together at the same transaction have been regarded as important. Although this concept, Negative Association rule mining, is quite useful, it is difficult for the user to analyze the interestingness of Negative Association rules because we would get them too many. To settle this issue, Indirect Association rule mining has proposed. In this paper, we propose a new framework of Indirect Association rule via a mediator and a new measure μ based on measures PA and PD due to Zhang to mine Negative Association rules effectively without the domain knowledge. The μ measure has the advantage over the IS measure that is proposed with the first framework of Indirect Association rule mining, and satisfies all of the well-known properties for a good measure. Finally, we are going to analyze the retail data and present interpretations for derived Indirect Association rules.

Compactness and Learning of Classes of Unions of Erasing Regular Pattern Languages

A regular pattern is a string of constant symbols and distinct variables. A semantics of a set P of regular patterns is a union L(P) of erasing pattern languages generated by patterns in P. The paper deals with the class RPk of sets of at most k regular patterns, and an efficient learning from positive examples of the language class defined by RPk. In efficient learning languages, the complexity for the MINL problem to find one of minimal languages containing a given sample is one of very important keys. Arimura et al.[5] introduced a notion of compactness w.r.t. containment for more general framework, called generalization systems, than RPk of language description which guarantees the equivalency between the semantic containment L(P) ? L(Q) and the syntactic containment P ? Q, where ? is a syntactic subsumption over the generalization systems.Under the compactness, the MINL problem reduces to finding one of minimal sets in RPk for a given sample under the subsumption ?. They gave an efficient algorithm to find such minimal sets under the assumption of compactness and some conditions.We first show that for each k ? 1, the class RPk has compactness if and only if the number of constant symbols is greater than k+1. Moreover, we prove that for each P ? RPk, a finite subset S2(P) is a characteristic set of L(P) within the class, where S2(P) consists of strings obtained from P by substituting strings with length two for each variable. Then our class RPk is shown to be polynomial time inferable from positive examples using the efficient algorithm of the MINL problem due to Arimura et al.[5], provided the number of constant symbols is greater than k + 1.

Learning of erasing primitive formal systems from positive examples

The present paper considers the learning problem of erasing primitive formal systems, PFSs for short, in view of inductive inference in Gold framework from positive examples. A PFS is a kind of logic program over strings called regular patterns, and consists of exactly two axioms of the forms p(π) ← and p(τ) ← p(x1),..., p(xn), where p is a unary predicate symbol, π and τ are regular patterns, and xis are distinct variables. A PFS is erasing or nonerasing according to allowing the empty string substitution for some variables or not. We investigate the learnability of the class PFSL of languages generated by the erasing PFSs satisfying a certain condition. We first show that the class PFSL has M-finite thickness. Moriyama and Sato showed that a language class with M-finite thickness is learnable if and only if there is a finite tell tale set for each language in the class. We then introduce a particular type of finite set of strings for each erasing PFS, and show that the set is a finite tell tale set of the language. These imply that the class PFSL is learnable from positive examples.

Language Learning with a Neighbor System

We consider inductive language learning from positive examples, some of which may be incorrect. In the present paper, the error or incorrectness we consider is the one described uniformly in terms of a distance over strings. Firstly, we introduce a notion of a recursively generable distance over strings, and define a k-neighbor closure of a language L as the collection of strings each of which is at most k distant from some string in L. Then we define a k-neighbor system as the collection of original languages and their j-neighbor closures with j ≤ k, and adopt it as a hypothesis space. In ordinary learning paradigm, a target language, whose examples are fed to an inference machine, is assumed to belong to a hypothesis space without any guarantee. In this paper, we allow an inference machine to infer a neighbor closure instead of the original language as an admissible approximation. We formalize such kind of inference, and give some sufficient conditions for a hypothesis space.

Learning Languages Generated by Elementary Formal Systems and Its Application to SH Languages

The Elementary Formal Systems (EFSs, for short) are originally introduced by Smullyan to develop his recursion theory. In a word, EFSs are a kind of logic programs which use strings instead of terms in first order logic, and they are shown to be natural devices to define languages.

Refutable Language Learning with a Neighbor System

We consider inductive language learning and machine discovery from examples with some errors. In the present paper, the error or incorrectness we consider is the one described uniformly in terms of a distance over strings. Firstly, we introduce a notion of a recursively generable distance over strings, and for a language L, we define a k-neighbor language L? as a language obtained from L by (i) adding some strings not in L each of which is at most k distant from some string in L and by (ii) deleting some strings in L each of which is at most k distant from some string not in L. Then we define a k-neighbor system of a base language class as the collection of k-neighbor languages of languages in the class, and adopt it as a hypothesis space. We give formal definitions of k-neighbor (refutable) inferability, and discuss necessary and sufficient conditions on such kinds of inference.

Inferring a Rewriting System from Examples

In their previous paper, Mukouchi and Arikawa discussed both refutability and inferability of a hypothesis space from examples. If a target language is a member of the hypothesis space, then an inference machine should identify it in the limit, otherwise it should refute the hypothesis space itself in a finite time. They pointed out the necessity of refutability of a hypothesis space from a view point of machine discovery. Recently, Mukouchi focused sequences of examples successively generated by a certain kind of system. He call such a sequence an observation with time passage, and a sequence extended as long as possible a complete observation. Then the set of all possible complete observations is called a phenomenon of the system. In this paper, we introduce phenomena generated by rewriting systems known as 0L systems and pure grammars, and investigate their inferability in the limit from positive examples as well as refutable inferability from complete examples. First, we show that any phenomenon class generated by 0L systems is inferable in the limit from positive examples. We also show that the phenomenon class generated by pure grammars such that left hand side of each production is not longer than a fixed length is inferable in the limit from positive examples, while the phenomenon class of unrestricted pure grammars is shown not to be inferable. We also obtain the result that the phenomenon class of pure grammars such that the number of productions and that of axioms are not greater than a fixed number is inferable in the limit from positive examples as well as refutably inferable from complete examples.

Semantic analysis of association rules via item response theory

This paper aims to install Latent trait on Association Rule Mining for the semantic analysis of consumer behavior patterns. We adapt Item Response Theory, a famous educational testing model, in order to derive interesting insights from rules by Latent trait. The primary contributions of this paper are fourfold. (1) Latent trait as an unified measure can measure interestingness of derived rules and specify the features of derived rules. Although the interestingness of rules is swayed by which measure could be applied, Latent trait that combines descriptive and predictive property can represent the unified interestingness of the rules. (2) Negative Association rules can be derived without domain knowledge. (3) Causal rules can be derived and analyzed by the Graded Response Theory which is extended model of Item Response Theory. (4) The features of consumer choice that is based on the concept of multinomial logit mode in Marketing Science could be extracted. Especially the effect of promotions and product prices based on Causal rules can be generated. Our framework has many important advances for accomplishing in mining and analyzing consumer behavior patterns with diversity.