A MINSAT Approach for Learning in Logic Domains

This paper describes a method for learning logic relationships that correctly classify a given data set. The method derives from given logic data certain minimum cost satisfiability problems, 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.

[1]  L Delpuech,et al.  Models of Neural Networks, Deuxième édition, E Domany, JL van Hemmen, K Schulten. Springer Verlag, Marseille (1995) , 1997 .

[2]  Klaus Truemper,et al.  A method for controlling errors in two-class classification , 1999, Proceedings. Twenty-Third Annual International Computer Software and Applications Conference (Cat. No.99CB37032).

[3]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  David H. Wolpert,et al.  Stacked generalization , 1992, Neural Networks.

[6]  V. Chandru,et al.  Optimization Methods for Logical Inference , 1999 .

[7]  Mauricio G. C. Resende,et al.  A continuous approach to inductive inference , 1992, Math. Program..

[8]  O. Mangasarian,et al.  Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis , 1989 .

[9]  Robert C. Holte,et al.  Very Simple Classification Rules Perform Well on Most Commonly Used Datasets , 1993, Machine Learning.

[10]  Pat Langley,et al.  Models of Incremental Concept Formation , 1990, Artif. Intell..

[11]  Y. Crama,et al.  Cause-effect relationships and partially defined Boolean functions , 1988 .

[12]  William Nick Street,et al.  Breast Cancer Diagnosis and Prognosis Via Linear Programming , 1995, Oper. Res..

[13]  F. Glover,et al.  Simple but powerful goal programming models for discriminant problems , 1981 .

[14]  Klaus Truemper,et al.  Effective logic computation , 1998 .

[15]  Stephen Muggleton,et al.  Inductive Logic Programming: Issues, Results and the Challenge of Learning Language in Logic , 1999, Artif. Intell..

[16]  Soundar R. T. Kumara,et al.  Generating logical expressions from positive and negative examples via a branch-and-bound approach , 1994, Comput. Oper. Res..

[17]  Leo Breiman,et al.  Stacked regressions , 2004, Machine Learning.

[18]  Tomas Kocka,et al.  Effective Dimensions of Hierarchical Latent Class Models , 2011, J. Artif. Intell. Res..

[19]  Toshihide Ibaraki,et al.  Positive and Horn Decomposability of Partially Defined Boolean Functions , 1997, Discret. Appl. Math..

[20]  Raymond J. Mooney,et al.  Symbolic and neural learning algorithms: An experimental comparison , 1991, Machine Learning.

[21]  Ned Freed,et al.  EVALUATING ALTERNATIVE LINEAR PROGRAMMING MODELS TO SOLVE THE TWO-GROUP DISCRIMINANT PROBLEM , 1986 .

[22]  Hemant K. Bhargava,et al.  Data Mining by Decomposition: Adaptive Search for Hypothesis Generation , 1999, INFORMS J. Comput..

[23]  Sebastian Thrun,et al.  The MONK''s Problems-A Performance Comparison of Different Learning Algorithms, CMU-CS-91-197, Sch , 1991 .

[24]  J. Ross Quinlan,et al.  Combining Instance-Based and Model-Based Learning , 1993, ICML.

[25]  Evangelos Triantaphyllou,et al.  On the minimum number of logical clauses inferred from examples , 1996, Comput. Oper. Res..

[26]  Eytan Domany,et al.  Models of Neural Networks I , 1991 .

[27]  Simon Kasif,et al.  A System for Induction of Oblique Decision Trees , 1994, J. Artif. Intell. Res..

[28]  Ching Y. Suen,et al.  Application of majority voting to pattern recognition: an analysis of its behavior and performance , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[29]  William W. Cohen Pac-Learning Non-Recursive Prolog Clauses , 1995, Artif. Intell..

[30]  O. Mangasarian,et al.  Robust linear programming discrimination of two linearly inseparable sets , 1992 .

[31]  W. T. Illingworth,et al.  Practical guide to neural nets , 1991 .

[32]  Toshihide Ibaraki,et al.  Logical Analysis of Binary Data with Missing Bits , 1999, Artif. Intell..

[33]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[34]  Toshihide Ibaraki,et al.  An Implementation of Logical Analysis of Data , 2000, IEEE Trans. Knowl. Data Eng..

[35]  Olvi L. Mangasarian,et al.  Mathematical Programming in Neural Networks , 1993, INFORMS J. Comput..

[36]  Mostefa Golea Average case analysis of a learning algorithm for µ-DNF expressions , 1995, EuroCOLT.

[37]  Paul S. Bradley,et al.  Mathematical Programming for Data Mining: Formulations and Challenges , 1999, INFORMS J. Comput..

[38]  Leo Breiman,et al.  Bias, Variance , And Arcing Classifiers , 1996 .

[39]  D. Rubinfeld,et al.  Hedonic housing prices and the demand for clean air , 1978 .