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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 39 (29 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
Learning OneVariable Pattern Languages Very Efficiently on Average, in Parallel, and by Asking Queries
, 1997
"... A pattern is a finite string of constant and variable symbols. The language generated by a pattern is the set of all strings of constant symbols which can be obtained from the pattern by substituting nonempty strings for variables. We study the learnability of onevariable pattern languages in the ..."
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Cited by 17 (8 self)
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A pattern is a finite string of constant and variable symbols. The language generated by a pattern is the set of all strings of constant symbols which can be obtained from the pattern by substituting nonempty strings for variables. We study the learnability of onevariable pattern languages in the limit with respect to the update time needed for computing a new single hypothesis and the expected total learning time taken until convergence to a correct hypothesis. Our results are as follows. First, we design a consistent and setdriven learner that, using the concept of descriptive patterns, achieves update time O(n 2 log n), where n is the size of the input sample. The best previously known algorithm for computing descriptive onevariable patterns requires time O(n 4 log n) (cf. Angluin [2]). Second, we give a parallel version of this algorithm that requires time O(log n) and O(n 3 = log n) processors on an EREWPRAM. Third, using a modified version of the sequential algorithm a...
An AverageCase Optimal OneVariable Pattern Language Learner
 Journal of Computer and System Sciences
, 2000
"... A new algorithm for learning onevariable pattern languages from positive data is proposed and analyzed with respect to its averagecase behavior. We consider the total learning time that takes into account all operations till convergence to a correct hypothesis is achieved. For almost all meaningfu ..."
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Cited by 3 (1 self)
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A new algorithm for learning onevariable pattern languages from positive data is proposed and analyzed with respect to its averagecase behavior. We consider the total learning time that takes into account all operations till convergence to a correct hypothesis is achieved. For almost all meaningful distributions defining how the pattern variable is replaced by a string to generate random examples of the target pattern language, it is shown that this algorithm converges within an expected constant number of rounds and a total learning time that is linear in the pattern length. Thus, our solution is averagecase optimal in a strong sense. Though onevariable pattern languages can neither be finitely inferred from positive data nor PAClearned, our approach can also be extended to a probabilistic finite learner that exactly infers all onevariable pattern languages from positive data with high confidence. It is a long standing open problem whether pattern languages can be learned in...
Efficient Learning of OneVariable Pattern Languages from Positive Data
, 1996
"... A pattern is a finite string of constant and variable symbols. The language generated by a pattern is the set of all strings of constant symbols which can be obtained from the pattern by substituting nonempty strings for variables. Descriptive patterns are a key concept for inductive inference o ..."
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Cited by 3 (3 self)
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A pattern is a finite string of constant and variable symbols. The language generated by a pattern is the set of all strings of constant symbols which can be obtained from the pattern by substituting nonempty strings for variables. Descriptive patterns are a key concept for inductive inference of pattern languages. A pattern is descriptive for a given sample if the sample is contained in the language L() generated by and no other pattern having this property generates a proper subset of the language L(). The best previously known algorithm for computing descriptive onevariable patterns requires time O(n log n), where n is the size of the sample. We present a simpler and more efficient algorithm solving the same problem in time O(n log n). In addition, we give a parallel version of this algorithm that requires time O(log n) and O(n = log n) processors on an EREWPRAM. Previously, no parallel algorithm was known for this problem. Using a
Parsimony Hierarchies for Inductive Inference
 Journal of Symbolic Logic
"... Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requi ..."
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Cited by 2 (1 self)
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Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A limcomputable function is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "notsonearly" minimal size, e.g., to be within a limcomputable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are limcomputable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of limcomputability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the limcomputable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight.
Learning kVariable Pattern Languages Efficiently Stochastically Finite on Average from Positive Data
 PROC. 4TH INTERNATIONAL COLLOQUIUM ON GRAMMATICAL INFERENCE," LNAI
, 1998
"... The present paper deals with the averagecase analysis of the LangeWiehagen (1991) algorithm learning the class of all pattern languages in the limit from positive data. Let A = f0; 1; : : :g be any nonempty finite alphabet containing at least two elements. Furthermore, let X = fx i i 2 Ng be an ..."
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Cited by 1 (1 self)
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The present paper deals with the averagecase analysis of the LangeWiehagen (1991) algorithm learning the class of all pattern languages in the limit from positive data. Let A = f0; 1; : : :g be any nonempty finite alphabet containing at least two elements. Furthermore, let X = fx i i 2 Ng be an infinite set of variables such that A " X = ; . Patterns are nonempty strings over A[X . L(ß) , the language generated by pattern ß is the set of strings which can be obtained by substituting nonnull strings from A 3 for the variables of the pattern ß . The LangeWiehagen (1991) algorithm is analyzed with respect to its total learning time, i.e., the overall time taken by the algorithm until convergence. The expectation of the total learning time is carefully analyzed and exponentially shrinking tail bounds for it are established for a large class of probability distributions. For every pattern ß containing k different variables it is shown that Lange and Wiehagen's algorithm posses...