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Harmonic Theory and Machine Learning
Keywords:
Neural Networks, Machine Learning, Potential Theory, Polynomial ApproximationAbstract
A natural inference mechanism is presented : the Black Box problem is transformed into a Dirichlet's problem on the closed cube. Then it is solved in closed polynomial form, together with a Mean-Value theorem and a Maximum Principle.A generalization to Polytopes and a reduction of any Dirichlet problem on compacta is mapp ed into a unit cub e in more dimensions.An algorithm for calculating the solution is suggested.
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References
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[2] Bundy A. : The Computer Modelling of Mathematical Reasoning . Academic Press 1983.
[3] Chaitin G.:A theory of program size formally identical to Information Theory. Journal ACM vol.22 num.3 July 1975.
[4] Courant R. & Hilbert D. : Methods of Mathematical Physics. Interscience publishers 1953.
[5] Hand D. Mannila H. Smyth P. : Princples of Datamining . M.I.T Press 2001.
[6] Kelley J. : General Topology. Van Nostrand University series in higher mathematics 1955.
[7] Kon M.A. & Plaskota L.: Information Complexity of Neural Networks. Neural Networks 2000.
[8] Mashkar H.N. : Neural Networks & Approximation Theory. Neural Networks 9 721-722.
[9] Mendelson E. : Introduction to Mathematical Logic. Van Nostrand 1964.
[10] Nicolis G.&Prigogine I. : Exploring Complexity. Freeman & Co New York 1989.
[11] Poggio T. & Girossi F. : Regularization Algorithms for learning that are equivalent to multilayer Networks. Science 247 978-982.
[12] Rapallini U. & Nanclares J. : Intérprete NeuPro utilizando la NeuPro Abstract Machine. XI Congreso Argentino de Ciencias de la Computación. Concordia Entre Ríos octubre de 2005.
[13] Shannon C.: A Mathematical Theory of Communication. Univ. of Illinois Press 1949.
[14] Sussman H. : Semigroup representations bilinear approximation of input/output maps and generalized inputs. Lecture notes in Economics & Math.Systems. Mathematical Systems Theory 131 Udine 1975 Springer Verlag.
[15] Tom Mitchel: Machine Learning. WCB/McGraw Hill 1997.
[16] Traub J.F.&Werschultz :Complexity & Information Cambridge University Press 1999 Cambridge.
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Published
2007-10-01
How to Cite
Nanclares, J., & Rapallini, U. M. A. (2007). Harmonic Theory and Machine Learning. Journal of Computer Science and Technology, 7(03), p. 249–255. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/778
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