Results 1  10
of
10
A Guided Tour Across the Boundaries of Learning Recursive Languages
 Lecture Notes in Artificial Intelligence
, 1994
"... The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data as well as from both, positive and negative data. We consider the influence of various monotonicity constraints to the learning process, and provide a thorough study concerning the i ..."
Abstract

Cited by 57 (29 self)
 Add to MetaCart
The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data as well as from both, positive and negative data. We consider the influence of various monotonicity constraints to the learning process, and provide a thorough study concerning the influence of several parameters. In particular, we present examples pointing to typical problems and solutions in the field. Then we provide a unifying framework for learning. Furthermore, we survey results concerning learnability in dependence on the hypothesis space, and concerning order independence. Moreover, new results dealing with the efficiency of learning are provided. First, we investigate the power of iterative learning algorithms. The second measure of efficiency studied is the number of mind changes a learning algorithm is allowed to perform. In this setting we consider the problem whether or not the monotonicity constraints introduced do influence the efficiency of learning algo...
Learning via Queries in ...
, 1992
"... We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we ..."
Abstract

Cited by 35 (11 self)
 Add to MetaCart
We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+; !]. Additionally, we resolve an open question in [7] about passive versus active learning. 1) Introduction This paper presents new results in the area of query inductive inference (introduced in [7]); in addition, there are results of interest in mathematical logic. Inductive inference is the study of inductive machine learning in a theoretical framework. In query inductive inference, we study the ability of a Query Inference Machine 1 Supported, in part, by NSF grants CCR 8803641 and 9020079. 2 Also with IBM Corporation, Application Solutions...
Learning recursive languages with bounded mind changes
 International Journal of Foundations of Computer Science
, 1993
"... ..."
Language learning with bounded number of mind changes
 In Proceedings of the Tenth Annual Symposium on Theoretical Aspects of Computer Science
, 1993
"... ..."
A Survey of Inductive Inference with an Emphasis on Queries
 Complexity, Logic, and Recursion Theory, number 187 in Lecture notes in Pure and Applied Mathematics Series
, 1997
"... this paper M 0 ; M 1 ; : : : is a standard list of all Turing machines, M ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
this paper M 0 ; M 1 ; : : : is a standard list of all Turing machines, M
Trading Monotonicity Demands versus Efficiency
 Bull. Inf. Cybern
, 1995
"... The present paper deals with the learnability of indexed families L of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands and their dual counterparts to the efficiency of the learning process. The efficiency of learning is measured in depend ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
The present paper deals with the learnability of indexed families L of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands and their dual counterparts to the efficiency of the learning process. The efficiency of learning is measured in dependence on the number of mind changes a learning algorithm is allowed to perform. The three notions of (dual) monotonicity reflect different formalizations of the requirement that the learner has to produce better and better (specializations) generalizations when fed more and more data on the target concept.
Automata techniques for query inference machines. Annals of pure and applied logic
, 1995
"... ..."
(Show Context)
A Guided Tour Across the Boundaries of . . .
"... The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data as well as from both, positive and negative data. We consider the influence of various monotonicity constraints to the learning process, and provide a thorough study concerning the i ..."
Abstract
 Add to MetaCart
The present paper deals with the learnability of indexed families of uniformly recursive languages from positive data as well as from both, positive and negative data. We consider the influence of various monotonicity constraints to the learning process, and provide a thorough study concerning the influence of several parameters. In particular, we present examples pointing to typical problems and solutions in the field. Then we provide a unifying framework for learning. Furthermore, we survey results concerning learnability in dependence on the hypothesis space, and concerning order independence. Moreover, new results dealing with the efficiency of learning are provided. First, we investigate the power of iterative learning algorithms. The second measure of efficiency studied is the number of mind changes a learning algorithm is allowed to perform. In this setting we consider the problem whether or not the monotonicity constraints introduced do influence the efficiency of learning algorithms. The paper mainly emphasis to provide a comprehensive summary of results recently obtained, and of proof techniques developed. Finally, throughout our guided tour we discuss the question of what a natural language learning algorithm might look like.
Abstract
"... In prior papers the following question was considered: which classes of computable sets can be learned if queries about those sets can be asked by the learner? The answer depended on the query language chosen. In this paper we develop a framework (reductions) for studying this question. Essentially, ..."
Abstract
 Add to MetaCart
(Show Context)
In prior papers the following question was considered: which classes of computable sets can be learned if queries about those sets can be asked by the learner? The answer depended on the query language chosen. In this paper we develop a framework (reductions) for studying this question. Essentially, once we have a result for queries to [S, <] 2, we can obtain the same result for many different languages. We obtain easier proofs of old results and several new results. An earlier result we have an easier proof of: the set of computable sets cannot be learned with queries to the language [+, <] (in notation: COMP / ∈ QEX[+, <]). A new result: the set of computable sets cannot be learned with queries to the language [+, <, POWa] where
Trading Monotonicity Demands versus Mind Changes
, 1995
"... The present paper deals with with the learnability of indexed families L of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands to the efficiency of the learning process. The efficiency of learning is measured in dependence on the number of mind ..."
Abstract
 Add to MetaCart
The present paper deals with with the learnability of indexed families L of uniformly recursive languages from positive data. We consider the influence of three monotonicity demands to the efficiency of the learning process. The efficiency of learning is measured in dependence on the number of mind changes a learning algorithm is allowed to perform. The three notions of monotonicity reflect different formalizations of the requirement that the learner has to produce better and better generalizations when fed more and more data on the target concept. We distinguish between exact learnability (L has to be inferred with respect to L), class preserving learning (L has to be inferred with respect to some suitable chosen enumeration of all the languages from L), and class comprising inference (L has to be learned with respect to some suitable chosen enumeration of uniformly recursive languages containing at least all the languages from L). In particular, we prove that a relaxation of the re...