Anthony, Martin


Professor Martin Anthony  

Department

Position held

Department of Mathematics

Professor of Mathematics

Experience keywords:

discrete mathematics; Boolean functions; machine learning

Research summary > [Click to expand]

The mathematical theory of machine learning, artificial neural networks, evolutionary computation and data mining; Boolean functions; discrete mathematics and its applications.

Contact Points

LSE phone number:

020 7955 7623

Publications

LSE Research Online, Funnelback Search

2014

Anthony, Martin and Ratsaby, Joel (2014) A hybrid classifier based on boxes and nearest neighbors Discrete Applied Mathematics, 172. 1-11. ISSN 0166-218X

Anthony, Martin and Ratsaby, Joel (2014) Learning bounds via sample width for classifiers on finite metric spaces Theoretical Computer Science, 529. 2-10. ISSN 0304-3975

2013

Anthony, Martin and Ratsaby, Joel (2013) Large margin case-based reasoning RUTCOR Research Reports, RRR 2-2013. Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA.

Anthony, Martin and Ratsaby, Joel (2013) Quantifying accuracy of learning via sample width Proceedings of the 2013 IEEE Symposium on Foundations of Computational Intelligence (Foci): 2013 IEEE Symposium Series on Com. 84-90. ISSN 9781467359016

Anthony, Martin and Ratsaby, Joel (2013) Maximal-margin case-based inference In: Jin, Yaochu and Thomas, Spencer Angus, (eds.) 2013 13th Uk Workshop on Computational Intelligence (Ukci): Management School Foyer, University of Surrey, Guildford, Surrey, Uk. IEEE Conference Publications. Institute of Electrical and Electronics Engineers, New York, USA, 112-119. ISBN 9781479915682

2012

Anthony, Martin and Harvey, Michele (2012) Further linear algebra

Anthony, Martin (2012) Probability in machine learning In: Seel, Norbert M. , (ed.) Encyclopedia of the Sciences of Learning. Springer Verlag. ISBN 9781441914279

Anthony, Martin and Ratsaby, Joel (2012) The performance of a new hybrid classifier based on boxes and nearest neighbors

Subasi, Munevver Mine and Subasi, Ersoy and Anthony, Martin and Hammer, Peter L. (2012) A new imputation method for incomplete binary data

Anthony, Martin and Ratsaby, Joel (2012) Sample width for multi-category classifiers RUTCOR Research Reports, RRR 29-2012. RUTCOR, Rutgers University, Piscataway, New Jersey, USA.

Anthony, Martin and Ratsaby, Joel (2012) Robust cutpoints in the logical analysis of numerical data Discrete Applied Mathematics, 160 (4 - 5). 355-364. ISSN 0166-218X

Anthony, Martin (2012) Generalization error bounds for the logical analysis of data Discrete Applied Mathematics, 160 (10-11). 1407-1415. ISSN 0166-218X

Anthony, Martin and Harvey, Michele (2012) Linear algebra: concepts and methods Cambridge University Press, Cambridge, UK. ISBN 9780521279482

Anthony, Martin and Ratsaby, Joel (2012) Learning on finite metric spaces RUTCOR research reports, RRR 19-2012. Center for Operations Research, Rutgers University, Piscataway, New Jersey.

Anthony, Martin and Ratasaby, Joel (2012) Analysis of a multi-category classifier Discrete Applied Mathematics, 160 (16-17). 2329-2338. ISSN 0166-218X

Anthony, Martin and Ratsaby, Joel (2012) Using boxes and proximity to classify data into several categories RUTCOR research reports, RRR 7-2012. Center for Operations Research, Rutgers University, Piscataway, New Jersey.

2011

Anthony, Martin and Harvey, Michele (2011) Algebra

Anthony, Martin (2011) The beauty of maths LSE Connect (1 Jan 2011) 19

Anthony, Martin and Ratsaby, Joel (2011) The performance of a new hybrid classifier based on boxes and nearest neighbors RUTCOR research reports, RRR 17-2011. Center for Operations Research, Rutgers University, Piscataway, New Jersey.

Anthony, Martin (2011) Generalization error bounds for the logical analysis of data Rutcor Research Report, 1-2011. Rutgers University, New Jersey, USA.

Subasi, Munevver Mine and Subasi, Ersoy and Anthony, Martin and Hammer, Peter L. (2011) A new imputation method for incomplete binary data Discrete Applied Mathematics, 159 (10). 1040-1047. ISSN 0166-218X

2010

Anthony, Martin (2010) Neural networks and boolean functions In: Crama, Yves and Hammer, Peter L., (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering. Encyclopedia of mathematics and its applications (134). Cambridge University Press, New York, USA, 554-576. ISBN 9780521847520

Anthony, Martin (2010) Probabilistic learning of boolean functions In: Grama, Yves and Hammer, Peter L., (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering. Encyclopedia of mathematics and its applications (134). Cambridge University Press, New York, USA, 197-220. ISBN 9780521847520

Anthony, Martin (2010) Decision lists and related classes of boolean functions In: Crama, Yves and Hammer, Peter L., (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering. Encyclopedia of mathematics and its applications (134). Cambridge University Press, New York, USA, 577-598. ISBN 9780521847520

Anthony, Martin and Ratsaby, Joel (2010) Maximal width learning of binary functions Theoretical Computer Science, 411 (1). 138-147. ISSN 0304-3975

2009

Subasi, Mine and Subasi, Ersoy and Anthony, Martin and Hammer, P.L. (2009) A new imputation method for incomplete binary data RUTCOR research report, RRR 15-2009. RUTCOR, Rutgers University.

Anthony, Martin (2009) On constructing threshold networks for pattern classification In: Franco, Leonardo and Elizondo, David A. and Jerez, José M., (eds.) Constructive Neural Networks. Studies in computational intelligence (258). Springer, Berlin, Germany, 71-82. ISBN 9783642045110

Subasi, M. and Subasi, E. and Anthony, Martin and Hammer, P. L. (2009) Using a similarity measure for credible classification Discrete Applied Mathematics, 157 (5). 1104-1112. ISSN 0166-218X

2008

Anthony, Martin (2008) Aspects of discrete mathematics and probability in the theory of machine learning Discrete Applied Mathematics, 156 (6). 883-902. ISSN 0166-218X

2007

Anthony, Martin (2007) On the generalization error of fixed combinations of classifiers Journal of Computer and System Sciences, 73 (5). 725-734. ISSN 0022-0000

Anthony, Martin (2007) Advanced mathematical analysis 2790041. University of London Press, London, UK.

2006

Anthony, Martin (2006) Abstract mathematics University of London Press, London.

Anthony, Martin and Harvey, M (2006) Advanced linear algebra University of London Press, London, UK. ISBN 0387978372

Anthony, Martin and Hammer, Peter Ladislaw (2006) A Boolean measure of similarity Discrete Applied Mathematics, 154 (16). 2242-2246. ISSN 0166-218X

Anthony, Martin and Franco, Leonardo (2006) The influence of oppositely classified examples on the generalization complexity of Boolean functions IEEE Transactions on Neural Networks, 17 (3). 578-590. ISSN 1045-9227

Franco, L. and Subirats, J.L. and Anthony, Martin and Jerez, J.M. (2006) A new constructive approach for creating all linearly separable (threshold) functions In: International Joint Conference on Neural Networks, 2006. Ijcnn '06. IEEE, Vancouver, Canada, 4791-4796.

Anthony, Martin and Ratsaby, Joel (2006) Maximal width learning of binary functions CDAM research report series, CDAM-LSE-2006-11. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

2005

Anthony, Martin (2005) Learning boolean functions CDAM research report series, CDAM-LSE-2005-24. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2005) Decision lists CDAM research report series, CDAM-LSE-2005-23. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2005) Connections between neural networks and boolean functions CDAM research report series, CDAM-LSE-2005-25. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin and Hammer, P. L. and Subasi, E. and Subasi, M. (2005) Using a similarity measure for credible classification CDAM research report series, CDAM-LSE-2005-22. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

2004

Anthony, Martin (2004) Partitioning points by parallel planes Discrete Mathematics, 282 (1-3). 17-21. ISSN 0012-365X

Anthony, Martin (2004) On data classification by iterative linear partitioning Discrete Applied Mathematics, 144 (1-2). 2-16. ISSN 0166-218X

Anthony, Martin (2004) Generalization error bounds for threshold decision lists Journal of Machine Learning Research, 5 (Feb). 189-217. ISSN 1532-4435

Franco, Leonardo and Anthony, Martin (2004) On a generalisation complexity measure for boolean functions In: Proceedings of the IEEE 2004 International Joint Conference on Neural Networks. IEEE Press. ISBN 0780383591

Anthony, Martin (2004) Some connections between learning and optimization Discrete Applied Mathematics, 144 (1-2). 17-26. ISSN 0166-218X

Anthony, Martin (2004) On Learning a Function of Perceptrons In: Proceedings of the IEEE 2004 International Joint Conference on Neural Networks. IEEE Press, 967-972. ISBN 0780383591

Anthony, Martin and Hammer, Peter L. (2004) A Boolean measure of similarity RUTCOR research reports, 27-2004. Rutgers Center for Operations Research, Rutgers University, New Jersey, USA.

Anthony, Martin (2003) Accuracy of classification by iterative linear thresholding

Anthony, Martin (2003) Links between learning and optimization: a brief tutorial CDAM research report series, LSE-CDAM-2003-02. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2003) Boolean functions and artificial neural networks CDAM research report series, LSE-CDAM-2003-01. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2003) Margin-based generalization error bounds for threshold decision lists CDAM research report series, LSE-CDAM-2003-09. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Franco, Leonardo and Anthony, Martin (2003) The influence of opposite examples and randomness on the generalization complexity of Boolean functions CDAM research report series, LSE-CDAM-2003-21. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2003) On Boolean combinations of definitive classifiers CDAM Research Report Series, LSE-CDAM-2003-22. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2003) Learning multivalued multithreshold functions CDAM Research Report Series, LSE-CDAM-2003-03. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

2002

Anthony, Martin (2002) Analysis of data with threshold decision lists CDAM research report series, LSE-CDAM-2002-12. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2002) Mathematical modelling of generalization In: Marinaro, M. and Tagliaferri, R., (eds.) Neural Nets: 13th Italian Workshop on Neural Nets, Wirn Vietri 2002 Vietri Sul Mare, Italy, May 30-June 1, 2002. Lecture notes in computer science (2486). Springer, Berlin; New York, 181-189. ISBN 9783540442653

Anthony, Martin (2002) The sample complexity and computational complexity of Boolean function learning CDAM research report series, LSE-CDAM-2002-13. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2002) Decision lists and threshold decision lists CDAM research report series, LSE-CDAM-2002-11. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2002) Partitioning points by parallel planes CDAM research report series, LSE-CDAM-2002-10. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

Anthony, Martin (2002) Uniform Glivenko-Cantelli theorems and concentration of measure in the mathematical modelling of learning CDAM research report series, LSE-CDAM-2002-07. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

2001

Anthony, Martin (2001) Discrete mathematics of neural networks: selected topics SIAM monographs on discrete mathematics and applications. Society for industrial and applied mathematics, New York. ISBN 9780898714807

2000

Anthony, Martin and Bartlett, Peter L. (2000) Function learning from interpolation Combinatorics, Probability and Computing, 9 (3). 213-225. ISSN 0963-5483

1999

Anthony, Martin and Bartlett, P (1999) Neural network learning: theoretical foundations Cambridge University Press, Cambridge, UK. ISBN 052157353x

Anthony, Martin (1999) Accuracy of techniques for the logical analysis of data Discrete Applied Mathematics, 96-97 (1-3). 247-257. ISSN 0166-218X

1995

Anthony, Martin and Biggs, Norman (1995) Pac learning and artificial neural networks In: Arbib, Michael A., (ed.) Handbook of Brain Theory and Neural Networks. MIT Press, Cambridge, MA, USA, 694-697. ISBN 9780262011488


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