Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Abduction Using Neural Models

by

Madan Bharadwaj

Instructor:

Dr.Avelino Gonzalez

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Agenda

• Introduce the Concept

• Why Neural Approach ?

• UNIFY

• Hopfield Model

• Critique

• Summary

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Abduction & NN’s

• What are Neural Networks?

• What is Abduction?

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

The Analogy

Figure 1: Handwritten Characters. A’s and B’s

Figure 2: After training the Neural Network classifies data into classes

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Major References

• “A Unified Model for Abduction-Based Reasoning” by Ayeb et al

• “A Neural Architecture for a Class of Abduction Problems” by Goel et al

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Types of Abd. Problems

• 4 Major Types

• Open & Incompatible Classes

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

UNIFY

• NN Architecture reflects problem dynamics

• Tackles all 4 classes

• Architecture incrementally introduced

• Simple Architecture

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

UNIFY - Initial Model

Inhibitory Weights

Excitatory Weights

Hypothesis LayerObservation Layer

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

The Algorithm

• Initialize cells and weights

• Update cells and weights

• Check Termination condition

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

UNIFIED MODEL

Intermediate Layer

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Modifications

• Incompatibility Weights

• Modified Equations

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Experiments

• Toy Problems

• Real Life Problem

• Results very encouraging

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Hopfield Model

• Energy Function approach

• Only linear and monotonic classes

• Partition data into sub domains

• Map sub domains

• Minimize Energy Function

• ART Model also proposed

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Critique

• Fuzzy Framework essential for abduction

• Neural Networks still abstract

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Future Avenues

• Cancellation Class

• Better designs using ART

• Evolving Architectures

• Other Approaches

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

Summary

• Neural Network Approach feasible

• UNIFY is better

• Vast scope for further research

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

References

[1].       B.Ayeb, S.Wang and J.Ge, “A Unified Model for Abduction-Based Reasoning” IEEE Transaction on Systems, Man and Cybernetics – Part A: Systems and Humans, Vol 28, No. 4, July 1998

[2].       A.K. Goel and J. Ramanujam, “A Neural Architecture for a Class of Abduction Problems”, IEEE Transaction on Systems, Man and Cybernetics – Part B – Cybernetics, Vol. 26, No. 6, December 1996

[3].       _____, “A Connectionist Model for Diagnostic Problem Solving: Part II”, IEEE Transaction on Systems, Man and Cybernetics., Vol19, pp. 285-289, 1989

[4].       A. Goel, J. Ramanujam and P. Sadayappan, “Towards a ‘neural’ architecture of abductive reasoning”, in Proc. 2nd Int. Conf. Neural Networks, 1988, pp. I-681-I-688.

[5].       D.Poole, A. Mackworth and R.Goebel, “Computational Intelligence: A Logical Approach”, pp 319-343, Oxford University Press, 1998.

[6].       C. Christodoulou and M. Georgiopoulos, “Applications of Neural Networks in Electromagnetics”, Boston: Artech House, 2001.

[7].       Castro, J.L.; Mantas, C.J.; Benitez, J.M., “Interpretation of artificial neural networks by means of fuzzy rules”, IEEE Transactions on Neural Networks, Volume: 13 Issue: 1, Jan. 2002. Page(s): 101 –116

[8].       T. Bylander, D. Allemang, M. C. Tanner, and J. R. Josephon, “The computational complexity of abduction,” Artif. Intell., vol. 49, pp. 25–60, 1991.

Paper on “Abduction using Neural Models” for the Course “Intelligent Diagnostics” at UCF. Fall ‘02

A n y Q u e s t i o n s . . .