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47
Incremental concept learning for bounded data mining
 Information and Computation
, 1999
"... Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning ma ..."
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Cited by 42 (32 self)
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Important re nements of concept learning in the limit from positive data considerably restricting the accessibility of input data are studied. Let c be any concept; every in nite sequence of elements exhausting c is called positive presentation of c. In all learning models considered the learning machine computes a sequence of hypotheses about the target concept from a positive presentation of it. With iterative learning, the learning machine, in making a conjecture, has access to its previous conjecture and the latest data item coming in. In kbounded examplememory inference (k is a priori xed) the learner is allowed to access, in making a conjecture, its previous hypothesis, its memory of up to k data items it has already seen, and the next element coming in. In the case of kfeedback identi cation, the learning machine, in making a conjecture, has access to its previous conjecture, the latest data item coming in, and, on the basis of this information, it can compute k items and query the database of previous data to nd out, for each of the k items, whether or not it is in the database (k is again a priori xed). In all cases, the sequence of conjectures has to converge to a hypothesis
Types of Monotonic Language Learning and their Characterization. COLT’92
 Proc. 5th Annual ACM Conf. on Computational Learning Theory
, 1992
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Ignoring Data May be the Only Way to Learn Efficiently
, 1994
"... In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to t ..."
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Cited by 23 (13 self)
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In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.
On the Impact of Forgetting on Learning Machines
 Journal of the ACM
, 1993
"... this paper contributes toward the goal of understanding how a computer can be programmed to learn by isolating features of incremental learning algorithms that theoretically enhance their learning potential. In particular, we examine the effects of imposing a limit on the amount of information that ..."
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Cited by 15 (5 self)
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this paper contributes toward the goal of understanding how a computer can be programmed to learn by isolating features of incremental learning algorithms that theoretically enhance their learning potential. In particular, we examine the effects of imposing a limit on the amount of information that learning algorithm can hold in its memory as it attempts to This work was facilitated by an international agreement under NSF Grant 9119540.
On PolynomialTime Learnability in the Limit of Strictly Deterministic Automata
, 1995
"... . This paper deals with the polynomialtime learnability of a language class in the limit from positive data, and discusses the learning problem of a subclass of deterministic finite automata (DFAs), called strictly deterministic automata (SDAs), in the framework of learning in the limit from positi ..."
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Cited by 13 (0 self)
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. This paper deals with the polynomialtime learnability of a language class in the limit from positive data, and discusses the learning problem of a subclass of deterministic finite automata (DFAs), called strictly deterministic automata (SDAs), in the framework of learning in the limit from positive data. We first discuss the difficulty of Pitt's definition in the framework of learning in the limit from positive data, by showing that any class of languages with an infinite descending chain property is not polynomialtime learnable in the limit from positive data. We then propose new definitions for polynomialtime learnability in the limit from positive data. We show in our new definitions that the class of SDAs is iteratively, consistently polynomialtime learnable in the limit from positive data. In particular, we present a learning algorithm that learns any SDA M in the limit from positive data, satisfying the properties that (i) the time for updating a conjecture is at most O(`m)...
Robust Learning  Rich and Poor
 Journal of Computer and System Sciences
, 2000
"... A class C of recursive functions is called robustly learnable in the sense I (where I is any success criterion of learning) if not only C itself but even all transformed classes \Theta(C) where \Theta is any general recursive operator, are learnable in the sense I. It was already shown before, see ..."
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Cited by 7 (3 self)
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A class C of recursive functions is called robustly learnable in the sense I (where I is any success criterion of learning) if not only C itself but even all transformed classes \Theta(C) where \Theta is any general recursive operator, are learnable in the sense I. It was already shown before, see [Ful90, JSW98], that for I = Ex (learning in the limit) robust learning is rich in that there are classes being both not contained in any recursively enumerable class of recursive functions and, nevertheless, robustly learnable. For several criteria I, the present paper makes much more precise where we can hope for robustly learnable classes and where we cannot. This is achieved in two ways. First, for I = Ex, it is shown that only consistently learnable classes can be uniformly robustly learnable. Second, some other learning types I are classified as to whether or not they contain rich robustly learnable classes. Moreover, the first results on separating robust learning from unifor...
Learning in Friedberg Numberings
 Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, 2007, Proceedings. Springer, Lecture Notes in Artificial Intelligence
"... Abstract. In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the recursively enumerable languages, but have simpler grammar equivalence problem compared to acceptable numberings. We show that every explanatorily learnable class can be l ..."
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Abstract. In this paper we consider learnability in some special numberings, such as Friedberg numberings, which contain all the recursively enumerable languages, but have simpler grammar equivalence problem compared to acceptable numberings. We show that every explanatorily learnable class can be learnt in some Friedberg numbering. However, such a result does not hold for behaviourally correct learning or finite learning. One can also show that some Friedberg numberings are so restrictive that all classes which can be explanatorily learnt in such Friedberg numberings have only finitely many infinite languages. We also study similar questions for several properties of learners such as consistency, conservativeness, prudence, iterativeness and non Ushaped learning. Besides Friedberg numberings, we also consider the above problems for programming systems with Krecursive grammar equivalence problem. 1
On the Strength of Incremental Learning
, 1999
"... . This paper provides a systematic study of incremental learning from noisefree and from noisy data, thereby distinguishing between learning from only positive data and from both positive and negative data. Our study relies on the notion of noisy data introduced in [22]. The basic scenario, nam ..."
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Cited by 7 (4 self)
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. This paper provides a systematic study of incremental learning from noisefree and from noisy data, thereby distinguishing between learning from only positive data and from both positive and negative data. Our study relies on the notion of noisy data introduced in [22]. The basic scenario, named iterative learning, is as follows. In every learning stage, an algorithmic learner takes as input one element of an information sequence for a target concept and its previously made hypothesis and outputs a new hypothesis. The sequence of hypotheses has to converge to a hypothesis describing the target concept correctly. We study the following refinements of this scenario. Bounded examplememory inference generalizes iterative inference by allowing an iterative learner to additionally store an a priori bounded number of carefully chosen data elements, while feedback learning generalizes it by allowing the iterative learner to additionally ask whether or not a particular data ele...
Results on MemoryLimited UShaped Learning
"... Abstract. Ushaped learning is a learning behaviour in which the learner first learns a given target behaviour, then unlearns it and finally relearns it. Such a behaviour, observed by psychologists, for example, in the learning of pasttenses of English verbs, has been widely discussed among psychol ..."
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Abstract. Ushaped learning is a learning behaviour in which the learner first learns a given target behaviour, then unlearns it and finally relearns it. Such a behaviour, observed by psychologists, for example, in the learning of pasttenses of English verbs, has been widely discussed among psychologists and cognitive scientists as a fundamental example of the nonmonotonicity of learning. Previous theory literature has studied whether or not Ushaped learning, in the context of Gold’s formal model of learning languages from positive data, is necessary for learning some tasks. It is clear that human learning involves memory limitations. In the present paper we consider, then, the question of the necessity of Ushaped learning for some learning models featuring memory limitations. Our results show that the question of the necessity of Ushaped learning in this memorylimited setting depends on delicate tradeoffs between the learner’s ability to remember its own previous conjecture, to store some values in its longterm memory, to make queries about whether or not items occur in previously seen data and on the learner’s choice of hypotheses space. 1
Reflective Inductive Inference of Recursive Functions
, 2002
"... In this paper, we investigate reflective inductive inference of recursive functions. A reflective IIM is a learning machine that is additionally able to assess its own competence. First, we formalize reflective learning... ..."
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Cited by 6 (0 self)
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In this paper, we investigate reflective inductive inference of recursive functions. A reflective IIM is a learning machine that is additionally able to assess its own competence. First, we formalize reflective learning...