Language learning in dependence on the space of hypotheses

Language and Automata Theory and Applications

2009

Section: Definition 2 [20] Fix a Hypothesis Spacementioning

confidence: 99%

“…Additionally, one often considers the following requirements on the hypothesis space H = (H i ) i∈N (see [29,31]):…”

Section: Learning Indexed Familiesmentioning

confidence: 99%

Hypothesis Spaces for Learning

Language and Automata Theory and Applications

2009

“…hypothesis space H and an IIM M identifying C in the limit from text with respect to H. A quite natural and often studied modification of LimTxt r.e. is defined by the model of conservative inference, see [2,13] for this concept in the context of learning recursive languages. M is a conservative IIM for C with respect to H = (A i ) i∈N , if M performs only justified mind changes, i.e., if M , on some text t for some L ∈ C, outputs hypotheses i and later j, then M must have seen some element w / ∈ A i before returning j.…”

Section: Gold-style Language Learningmentioning

confidence: 99%

“…4 Recently, the combination of these two approaches [11,12] as well as the common features of learners in either model [14,15] have gained interest in the learning theory community. [14,15] contributes a systematic analysis of common features of both approaches, thereby focussing on the identification of formal languages, ranging over indexable classes of recursive languages, as target concepts, see [2,13,19]. Characterising different types of Gold-style language learning in terms of query learning has pointed out correspondences between the two models.…”

Section: Introductionmentioning

confidence: 99%

Gold-Style and Query Learning Under Various Constraints on the Target Class

Lecture Notes in Computer Science

Lange

Zilles

2005

Self Cite

Abstract. In language learning, strong relationships between Gold-style models and query models have recently been observed: in some quite general setting Gold-style learners can be replaced by query learners and vice versa, without loss of learning capabilities. These 'equalities' hold in the context of learning indexable classes of recursive languages. Former studies on Gold-style learning of such indexable classes have shown that, in many settings, the enumerability of the target class and the recursiveness of its languages are crucial for learnability. Moreover, studying query learning, non-indexable classes have been mainly neglected up to now. So it is conceivable that the recently observed relations between Gold-style and query learning are not due to common structures in the learning processes in both models, but rather to the enumerability of the target classes or the recursiveness of their languages. In this paper, the analysis is lifted onto the context of learning arbitrary classes of r.e. languages. Still, strong relationships between the approaches of Gold-style and query learning are proven, but there are significant changes to the former results. Though in many cases learners of one type can still be replaced by learners of the other type, in general this does not remain valid vice versa. All results hold even for learning classes of recursive languages, which indicates that the recursiveness of the languages is not crucial for the former 'equality' results. Thus we analyse how constraints on the algorithmic structure of the target class affect the relations between two approaches to language learning.

“…An advantage of an automatic family over general indexed families [1,24,26] is that the first-order theory of automatic families, as well as of automatic structures in general, is decidable [15,16,22]. Here in the first-order theory, the predicates (relations) and functions (mappings) allowed are automatic.…”

Section: Introductionmentioning

confidence: 99%

Automatic learners with feedback queries

Case

Journal of Computer and System Sciences

Ong

et al. 2014

Abstract. Automatic classes are classes of languages for which a finite automaton can decide whether a given element is in a set given by its index. The present work studies the learnability of automatic families by automatic learners which, in each round, output a hypothesis and update a long term memory, depending on the input datum, via an automatic function, that is, via a function whose graph is recognised by a finite automaton. Many variants of automatic learners are investigated: where the long term memory is restricted to be the just prior hypothesis whenever this exists, cannot be of size larger than the size of the longest example or has to consist of a constant number of examples seen so far. Furthermore, learnability is also studied with respect to queries which reveal information about past data or past computation history; the number of queries per round is bounded by a constant. These models are generalisations of the model of feedback queries, given by Lange, Wiehagen and Zeugmann.