This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distribution-free (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a source of examples of the unknown concept, the learner with high probability is able to output an hypothesis that is correct on all but an arbitrarily small fraction of the instances. The concept class is weakly learnable if the learner can produce an hypothesis that performs only slightly better than random guessing. In this paper, it is shown that these two notions of learnability are equivalent.

A method is described for converting a weak learning algorithm into one that achieves arbitrarily high accuracy. This construction may have practical applications as a tool for efficiently converting a mediocre learning algorithm into one that performs extremely well. In addition, the construction has some interesting theoretical consequences, including a set of general upper bounds on the complexity of any strong learning algorithm as a function of the allowed error e.

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The Strength of Weak Learnability

Valiant's learnability model is extended to learning classes of concepts defined by regions in Euclidean space En. The methods in this paper lead to a unified treatment of some of Valiant's results, along with previous results on distribution-free convergence of certain pattern recognition algorithms. It is shown that the essential condition for distribution-free learnability is finiteness of the Vapnik-Chervonenkis dimension, a simple combinatorial parameter of the class of concepts to be learned. Using this parameter, the complexity and closure properties of learnable classes are analyzed, and the necessary and sufficient conditions are provided for feasible learnability.

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Learnability and the Vapnik-Chervonenkis dimension

The paper presents the system LERS for rule induction. The system handles inconsistencies in the input data due to its usage of rough set theory principle. Rough set theory is especially well suited to deal with inconsistencies. In this approach, inconsistencies are not corrected. Instead, system LERS computes lower and upper approximations of each concept. Then it induces certain rules and possible rules. The user has the choice to use the machine learning approach or the knowledge acquisition approach. In the first case, the system induces a single minimal discriminant description for each concept. In the second case, the system induces all rules, each in the minimal form, that can be induced from the input data. In both cases, the user has a choice between the local or global approach.

LERS-A System for Learning from Examples Based on Rough Sets

This paper examines the induction of classification rules from examples using real-world data. Real-world data is almost always characterized by two features, which are important for the design of an induction algorithm. Firstly, there is often noise present, for example, due to imperfect measuring equipment used to collect the data. Secondly the description language is often incomplete, such that examples with identical descriptions in the language will not always be members of the same class. Many induction systems make the ‘noiseless domain’ assumption that the examples do not contain errors and the description language is complete, and consequently constrain their search for rules to those for which no counterexamples exist in the data used for induction. However, in real-world domains correlations between attributes and classes in a data set are rarely without exceptions. To locate such correlations and induce rules describing them it is also necessary to consider rules which may not classify all the training examples correctly. This paper firstly discusses some of the problems presented by noise and proposes a top-down induction algorithm for induction in real-world domains. Secondly, an experimental comparison of this algorithm with other induction systems is presented using three sets of real-world medical data.

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Induction in noisy domains

A system, method and apparatus for executing a sequence analysis pipeline on genetic sequence data includes a structured ASIC formed of a set of hardwired digital logic circuits that are interconnected by physical electrical interconnects One of the physical electrical interconnects forms an input to the structured ASIC connected with an electronic data source for receiving reads of genomic data The hardwired digital logic circuits are arranged as a set of processing engines, each processing engine being formed of a subset of the hardwired digital logic circuits to perform one or more steps in the sequence analysis pipeline on the reads of genomic data Each subset of the hardwired digital logic circuits is formed in a wired configuration to perform the one or more steps in the sequence analysis pipeline

Bioinformatics systems, apparatuses, and methods executed on an integrated circuit processing platform

Homology detection in large data bases is probably the most time consuming operation in molecular genetic computing systems. Moreover, the progresses made all around the world concerning the mapping and sequencing of the genome of Homo Sapiens and other species have increased the size of data bases exponentially. Therefore even the best workstation would not be able to reach the scanning speed required. In order to answer this need we propose an algorithm, A2R2, and its implementation on a massively parallel system. Basically, two kinds of algorithms are used to search in molecular genetic data bases. The first kind is based on dynamic programming and the second on word processing, A2R2 belongs to the second kind. The structure of the motif (pattern) searched by A2R2 can support those from FAST, BLAST and FLASH algorithms. After a short presentation of the reconfigurable hardware concept and technology used in our massively parallel accelerator we present the A2R2 implementation. This parallel implementation outperforms any kind of previously published genetic data base scanning hardware or algorithms. We report up to 25 million nucleotides per scanning seconds as our best results.

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High speed pattern matching in genetic data base with reconfigurable hardware.

Some remarks about space-complexity of learning, and circuit complexity of recognizing

Présentation de l'apprentissage à partir d'exemples

We present here a learning technique which is both statistic and syntactic, by using simultaneously logical operators and counting procedures. Its modular structure makes it usable for creating the necessary redundancy for controlling the generalization of the formulas.

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Algorithms for learning logical formulas

Resume : CALM est un systeme d'apprentissage construit pour permettre un controle argumente de la facon dont un objet verifie un concept. La presentation de CALM se fera en trots parties : I CONTESTER POUR APPRENDRE 2 LE SYSTEME LOGIQUE INDUCTIF DE CALM 3 LES SYSTEMES LOGIQUES ARGUMENTATIFS DE CALM CALM a ete utilise dans differentes applications er. GEOPHYSIQUE, en BIOLOGIE MOLECULAIRE, en ETHOLOGIE, en RECONNAISSANCE SPECTRALE et en RECONNAISSANCE DE LA PAROLE. Dans toutes ces applications, l'objectif a ete de produire des concepts permettant de generaliser une classe d'exemples, puis de controler la qualite de la generalisation produite .

Jean Sallantin

Papers

High speed pattern matching in genetic data base with reconfigurable hardware.

Some remarks about space-complexity of learning, and circuit complexity of recognizing

Présentation de l'apprentissage à partir d'exemples

Algorithms for learning logical formulas

CALM : Contester pour Apprendre en Logique Modale