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A Continuous Approach to Inductive Inference
 Mathematical Programming
, 1992
"... In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g ..."
Abstract

Cited by 38 (2 self)
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In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g using outputs obtained by applying a limited number of random inputs to the hidden function. Given this inputoutput sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used...
A Minsat approach for learning in logic domains
 INFORMS Journal on computing
, 2002
"... This paper describes a method for learning logic relationships that correctlyclassifya given data set. The method derives from given logic data certain minimum cost satisfiabilityproblems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method inclu ..."
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Cited by 13 (11 self)
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This paper describes a method for learning logic relationships that correctlyclassifya given data set. The method derives from given logic data certain minimum cost satisfiabilityproblems, solves these problems, and deduces from the solutions the desired logic relationships. Uses of the method include data mining, learning logic in expert systems, and identification of critical characteristics for recognition systems. Computational tests have proved that the method is fast and effective.
A Method for Controlling Errors in TwoClass Classification
, 1998
"... Two types of errors can be associated with classifying data into two categories A and B: misclassifying an item in A as one of B and, conversely, misclassifying an item in B as one of A. Tight control over these two errors is needed in many practical situations. For example, an error of one type may ..."
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Cited by 7 (5 self)
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Two types of errors can be associated with classifying data into two categories A and B: misclassifying an item in A as one of B and, conversely, misclassifying an item in B as one of A. Tight control over these two errors is needed in many practical situations. For example, an error of one type may have far more serious consequences than one of the other type. Most previous work on twoclass classifiers does not allow for such control. In this paper, we describe a general approach that supports tight error control for twoclass classification and that can utilize almost any twoclass classification method as part of the decision mechanism. The main idea is to construct from the given training data a family of classifiers and then, using the training data once more, to estimate two distributions of certain vote totals. The error control is achieved via the two estimated distributions. The control is effective if the estimates of the two distributions are close to the true distributions...
Application of a New Logic Domain Method for the Diagnosis of Hepatocellular Carcinoma
, 2001
"... In this paper we describe the application of a new learning tool for the diagnosis of hepatocellular carcinoma. The method adopted operates in the logic domain and presents several interesting features for the development of medical diagnostic systems. We consider a database of 128 patients, 64 of w ..."
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In this paper we describe the application of a new learning tool for the diagnosis of hepatocellular carcinoma. The method adopted operates in the logic domain and presents several interesting features for the development of medical diagnostic systems. We consider a database of 128 patients, 64 of which suffered from hepatocellular carcinoma, while the others suffered from cirrhosis but not from hepatocellular carcinoma. Each patient is described by a number of attributes measured in noninvasive way. The system, after the training, is able to correctly separate the 64 patients affected by cirrhosis from the others 64 affected by hepatocellular carcinoma and is now ready to produce automatic diagnosis for new patients. The hepatocellular carcinoma is one of the most widely spread malignant tumors in the world. The ability to detect the tumor in its early stages in a minimally invasive way is crucial to the treatment of patients with this disease.