Publications

Logarithmic asymptotics for polynomial threshold functionsPreprint

Martin Anthony. arXiv:2610.34378.

Almost every Boolean function has central threshold degreePreprint

Martin Anthony. arXiv:2610.15057.

Counting and covering in nearest-neighbour representations of Boolean functionsPreprint

Martin Anthony. arXiv:2609.23094.

Finite-Sample Coverage Audits for High-Recall Candidate Generation: Certification and Learning-Theoretic DesignPreprint

Martin Anthony and Kaveh Salehzadeh Nobari. arXiv:2607.21480.

Chamber geometry and specification numbers of Boolean threshold functionsPreprint

Martin Anthony. arXiv:2606.29477.

Generalised Eigenvalue Geometry of Semantic Adversarial AttacksPreprint

Martin Anthony and Kaveh Salehzadeh Nobari. arXiv:2606.19212.

Mathematics for Economics and Finance: Methods and Modelling, second editionBook

Martin Anthony and Norman Biggs. Cambridge University Press, 2024.

Large-width machine learning algorithm

Martin Anthony and Joel Ratsaby. Progress in Artificial Intelligence 9, 275–285.

Large width nearest prototype classification on general distance spaces

Martin Anthony and Joel Ratsaby. Theoretical Computer Science 738, 65–79.

Large-width bounds for learning half-spaces on distance spaces

Martin Anthony and Joel Ratsaby. Discrete Applied Mathematics 243, 73–89.

Classification based on prototypes with spheres of influence

Martin Anthony and Joel Ratsaby. Information and Computation 256, 372–380.

Quadratic reformulations of nonlinear binary optimization problems

Martin Anthony, Endre Boros, Yves Crama and Aritanan Gruber. Mathematical Programming (Series A) 162 (1), 115–144.

Multi-category classifiers and sample width

Martin Anthony and Joel Ratsaby. Journal of Computer and System Sciences 82 (8), 1223–1231.

Quadratization of symmetric pseudo-Boolean functions

Martin Anthony, Endre Boros, Yves Crama and Aritanan Gruber. Discrete Applied Mathematics 203, 1–12.

A probabilistic approach to case-based inference

Martin Anthony and Joel Ratsaby. Theoretical Computer Science 598, 61–75.

Learning bounds via sample width for classifiers on finite metric spaces

Martin Anthony and Joel Ratsaby. Theoretical Computer Science 529, 2–10.

A hybrid classifier based on boxes and nearest neighbors

Martin Anthony and Joel Ratsaby. Discrete Applied Mathematics 172, 1–11.

Maximal-margin case-based inference

Martin Anthony and Joel Ratsaby. Proceedings of UKCI 2013, September 2013.

Quantifying accuracy of learning via sample width

Martin Anthony and Joel Ratsaby. Proceedings of the 2013 IEEE Symposium on Foundations of Computational Intelligence, Singapore, April 2013.

Generalization error bounds for logical analysis of data

Martin Anthony. Discrete Applied Mathematics 160, 1407–1415.

Robust cutpoints in the logical analysis of numerical data

Martin Anthony and Joel Ratsaby. Discrete Applied Mathematics 160, 355–364.

Analysis of a multi-category classifier

Martin Anthony and Joel Ratsaby. Discrete Applied Mathematics 160 (16–17), 2329–2338.

A new imputation method for incomplete binary data

Munevver Mine Subasi, Ersoy Subasi, Martin Anthony and Peter L. Hammer. International Symposium on Artificial Intelligence and Mathematics, January 2012.

The performance of a new hybrid classifier based on boxes and nearest neighbors

Martin Anthony and Joel Ratsaby. International Symposium on Artificial Intelligence and Mathematics, January 2012.

Linear Algebra: Concepts and MethodsBook

Martin Anthony and Michele Harvey. Cambridge University Press. ISBN 9780521279482.

Further Linear AlgebraGuide

Martin Anthony and Michele Harvey. University of London.

Probability Theory in Machine LearningChapter

Martin Anthony. In Encyclopedia of the Sciences of Learning (ed. Norbert M. Seel), Springer. ISBN 9781441914279.

A new imputation method for incomplete binary data

Munevver Mine Subasi, Ersoy Subasi, Martin Anthony and Peter L. Hammer. Discrete Applied Mathematics 159 (10), 1040–1047.

AlgebraGuide

Martin Anthony and Michele Harvey. University of London.

The Beauty of Maths

Martin Anthony. LSE Connect, Summer 2011. An expository article for non-mathematicians.

Maximal width learning of binary functions

Martin Anthony and Joel Ratsaby. Theoretical Computer Science 411, 138–147.

Probabilistic Learning of Boolean FunctionsChapter

Martin Anthony. In Boolean Models and Methods in Mathematics, Computer Science, and Engineering (ed. Y. Crama and P. L. Hammer), Cambridge University Press. ISBN 9780521847520.

Decision Lists and Related Classes of Boolean FunctionsChapter

Martin Anthony. In Boolean Models and Methods in Mathematics, Computer Science, and Engineering (ed. Y. Crama and P. L. Hammer), Cambridge University Press. ISBN 9780521847520.

Neural Networks and Boolean FunctionsChapter

Martin Anthony. In Boolean Models and Methods in Mathematics, Computer Science, and Engineering (ed. Y. Crama and P. L. Hammer), Cambridge University Press. ISBN 9780521847520.

On constructing threshold networks for pattern classificationChapter

Martin Anthony. In Constructive Neural Networks (eds. Leonardo Franco, David Elizondo, Jose Jerez), Springer Studies in Computational Intelligence 258.

Using a similarity measure for credible classification

Munevver Mine Subasi, Ersoy Subasi, Martin Anthony and Peter L. Hammer. Discrete Applied Mathematics 157 (5–6), 1104–1112.

Aspects of discrete mathematics and probability in the theory of machine learning

Martin Anthony. Discrete Applied Mathematics 156 (6), 883–902.

On the generalization error of fixed combinations of classifiers

Martin Anthony. Journal of Computer and System Sciences 73 (5), 725–734.

Advanced Mathematical AnalysisGuide

Martin Anthony. University of London Press.

A Boolean measure of similarity

Martin Anthony and Peter L. Hammer. Discrete Applied Mathematics 154 (16).

The influence of oppositely classified examples on the generalization complexity of Boolean functions

Leonardo Franco and Martin Anthony. IEEE Transactions on Neural Networks 17 (3), 578–590.

A new constructive approach for creating all linearly separable (threshold) functions

Leonardo Franco, Jose Luis Subirats, Martin Anthony and Jose Jerez. Proceedings of the 2006 IEEE International Joint Conference on Neural Networks.

Abstract MathematicsGuide

Martin Anthony. University of London Press.

Advanced Linear AlgebraGuide

Martin Anthony and Michele Harvey. University of London Press.

On data classification by iterative linear partitioning

Martin Anthony. Discrete Applied Mathematics 144 (1–2), 2–16.

On learning a function of perceptrons

Martin Anthony. Proceedings of the 2004 IEEE International Joint Conference on Neural Networks.

On a generalization complexity measure for Boolean functions

Leonardo Franco and Martin Anthony. Proceedings of the 2004 IEEE International Joint Conference on Neural Networks.

Some connections between learning and optimization

Martin Anthony. Discrete Applied Mathematics 144 (1–2), 17–26.

Partitioning points by parallel planes

Martin Anthony. Discrete Mathematics 282.

Generalization error bounds for threshold decision lists

Martin Anthony. Journal of Machine Learning Research 5, 189–217.

Data classification by multithreshold functions

Martin Anthony. Workshop on Discrete Mathematics and Data Mining, 3rd SIAM Conference on Data Mining, San Francisco, May 2003.

Accuracy of classification by iterative linear thresholding

Martin Anthony. Workshop on Discrete Mathematics and Data Mining, 3rd SIAM Conference on Data Mining, San Francisco, May 2003.

PAC learning and artificial neural networksChapter

Martin Anthony and Norman Biggs. In The Handbook of Brain Theory and Neural Networks, second edition (ed. Michael A. Arbib), Bradford Books / MIT Press.

Uniform Glivenko-Cantelli theorems and concentration of measure in the mathematical modelling of learningReport

Martin Anthony. CDAM Research Report LSE-CDAM-2002-07, May 2002.

Matemática Para la Economía y las FinanzasBook

Martin Anthony and Norman Biggs. Cambridge University Press. Spanish translation of Mathematics for Economics and Finance. ISBN 848323248.

Mathematical modelling of generalization

Martin Anthony. In Neural Nets: WIRN VIETRI 2002 (eds. M. Marinaro, R. Tagliaferri), Springer LNCS 2486.

The classification of undergraduate degrees in the United Kingdom: an analysis of problems with the honours systemReport

Martin Anthony. MA Research Report, Institute of Education.

Mathematics 1Guide

Martin Anthony. University of London Press.

Mathematics 2Guide

Martin Anthony. University of London Press.

Discrete Mathematics of Neural Networks: Selected TopicsBook

Martin Anthony. SIAM Monographs on Discrete Mathematics and Applications 8, SIAM, Philadelphia. ISBN 0-89871-480-X.

Function learning from interpolation

Martin Anthony and Peter Bartlett. Combinatorics, Probability and Computing.

Neural Network Learning: Theoretical FoundationsBook

Martin Anthony and Peter Bartlett. Cambridge University Press. ISBN 0-521-57353-X.

Accuracy of techniques for the logical analysis of data

Martin Anthony. Discrete Applied Mathematics 96, 247–257.

Further Mathematics for EconomistsGuide

Martin Anthony. A subject guide for External Programmes, University of London.

Cross-validation for binary classification by real-valued functions

Martin Anthony and Sean B. Holden. Proceedings of the 1998 Annual Conference on Computational Learning Theory (COLT’98), Madison, Wisconsin, ACM Press.

Quantitative MethodsGuide

Martin Anthony, R. Hewins and C. Phillips. A subject guide for External Programmes, University of London. ISBN 0718715209.

Structural risk minimization over data-dependent hierarchies

John Shawe-Taylor, Peter L. Bartlett, Robert C. Williamson and Martin Anthony. IEEE Transactions on Information Theory 44 (5), 1926–1940.

Probabilistic generalization of functions and dimension-based uniform convergence results

Martin Anthony. Statistics and Computing 8 (1), 5–14.

Artificial neural networksChapter

Martin Anthony. In Graph Connections (eds. Lowell Beineke and Robin Wilson), Oxford University Press.

Probabilistic analysis of learning in artificial neural networks: the PAC model and its variants

Martin Anthony. Neural Computing Surveys 1, 1–47.

Mathematics for EconomistsGuide

Martin Anthony. A subject guide for External Programmes, University of London, June 1997. ISBN 0718714431.

A sufficient condition for polynomial distribution-dependent learnability

Martin Anthony and John Shawe-Taylor. Discrete Applied Mathematics 77 (1), 1–12.

A framework for structural risk minimisation

John Shawe-Taylor, Peter L. Bartlett, Robert C. Williamson and Martin Anthony. Proceedings of the 1996 Annual Conference on Computational Learning Theory (COLT’96), 68–76, ACM Press.

Valid generalisation from approximate interpolation

Martin Anthony, Peter Bartlett, Yuval Ishai and John Shawe-Taylor. Combinatorics, Probability and Computing 5, 191–214.

Mathematics for Economics and Finance: Methods and ModellingBook

Martin Anthony and Norman Biggs. Cambridge University Press. Reprinted several times, with Japanese and Chinese editions. ISBN 0-521-55913-8 (h/b), 0-521-55113-7 (p/b).

Threshold functions, decision lists, and the representation of Boolean functionsReport

Martin Anthony. NeuroCOLT Technical Report NC-TR-96-028.

Mathematics (for Diploma in Economics)Guide

Martin Anthony. A subject guide for External Programmes, University of London, May 1996. ISBN 0718713508.

A computational learning theory view of economic forecasting with neural netsChapter

Martin Anthony and Norman Biggs. In Neural Networks in the Capital Markets (ed. A. N. Refenes), Wiley.

Interpolation and learning in artificial neural networks

Martin Anthony. Proceedings of the 1995 IEEE International Conference on Neural Networks, Perth, IEEE Press.

On specifying Boolean functions by labelled examples

Martin Anthony, Graham Brightwell and John Shawe-Taylor. Discrete Applied Mathematics 61, 1–25.

Classification by polynomial surfaces

Martin Anthony. Discrete Applied Mathematics 61, 91–103.

Function learning from interpolation

Martin Anthony and Peter Bartlett. Proceedings of EuroCOLT’95, Springer-Verlag, 211–221.

The Vapnik-Chervonenkis dimension of a random graph

Martin Anthony, Graham Brightwell and Colin Cooper. Discrete Mathematics 138, 43–56.

PAC learning and artificial neural networksChapter

Martin Anthony and Norman Biggs. In The Handbook of Brain Theory and Neural Networks (ed. Michael A. Arbib), Bradford Books / MIT Press.

Valid generalisation of functions from close approximations on a sample

Martin Anthony and John Shawe-Taylor. In Computational Learning Theory: EuroCOLT’93, 95–108, Oxford University Press.

Probabilistic learning theory, with emphasis on sample complexityReport

Martin Anthony. Report 94-002, Sonderforschungsbereich 343, Universität Bielefeld.

Quantifying generalisation in linearly weighted neural networks

Martin Anthony and Sean B. Holden. Complex Systems 8, 91–114.

On the mean chromatic number

Martin Anthony. Discrete Mathematics 125, 11–14.

Computational Learning Theory: EuroCOLT’93Edited

John Shawe-Taylor and Martin Anthony (eds.). Oxford University Press. ISBN 0-19-853492-2.

Computational learning theory for artificial neural networksChapter

Martin Anthony and Norman Biggs. In Mathematical Approaches to Neural Networks (ed. J. G. Taylor), North-Holland, 25–63.

Bounds on the complexity of testing and loading neurons

Martin Anthony and John Shawe-Taylor. ICANN’93: Proceedings of the International Conference on Artificial Neural Networks, Springer-Verlag.

On the power of linearly weighted neural networks

Martin Anthony and Sean B. Holden. ICANN’93: Proceedings of the International Conference on Artificial Neural Networks, Springer-Verlag.

Using the perceptron algorithm to find consistent hypotheses

Martin Anthony and John Shawe-Taylor. Combinatorics, Probability and Computing 4 (2), 385–387.

On the power of polynomial discriminators and radial basis function networks

Martin Anthony and Sean B. Holden. Proceedings of the Sixth Annual Workshop on Computational Learning Theory, Santa Cruz, 158–164, ACM Press.

A result of Vapnik with applications

Martin Anthony and John Shawe-Taylor. Discrete Applied Mathematics 47, 207–217.

Bounding sample-size with the Vapnik-Chervonenkis dimension

John Shawe-Taylor, Martin Anthony and Norman Biggs. Discrete Applied Mathematics 42 (1), 65–73.

The mean chromatic number of paths and cycles

Martin Anthony and Norman Biggs. Discrete Mathematics 120, 227–231.

Computational Learning Theory: An IntroductionBook

Martin Anthony and Norman Biggs. Cambridge University Press. Reprinted in paperback, 1997. ISBN 0-521-59922-9 (h/b), 0-521-41603-5 (p/b).

Classes of feedforward neural networks and their circuit complexity

John Shawe-Taylor, Martin Anthony and Walter Kern. Neural Networks 5 (6), 971–977.

On exact specification by examples

Martin Anthony, Graham Brightwell, Dave Cohen and John Shawe-Taylor. Proceedings of the Fifth Annual Workshop on Computational Learning Theory, Santa Cruz, 311–318, ACM Press.

On deviation of relative frequencies from probabilitiesReport

Martin Anthony. LSE Mathematics Preprint Series LSE-MPS-2.

Sample sizes for multiple output threshold networks

John Shawe-Taylor and Martin Anthony. Network: Computation in Neural Systems 2, 107–117.

Uniform Convergence and LearnabilityThesis

Martin Anthony. PhD thesis, University of London.

The learnability of formal concepts

Martin Anthony, Norman Biggs and John Shawe-Taylor. COLT 90: Proceedings of the Third Annual Workshop on Computational Learning Theory, Rochester NY, 246–257, Morgan Kaufmann.

Some remarks on authentication systems

Martin Anthony, Keith Martin, Jennifer Seberry and Peter Wild. In Advances in Cryptology: Auscrypt’90, Lecture Notes in Computer Science 453, 122–139.

Computing chromatic polynomials

Martin Anthony. Ars Combinatoria 90, 216–220.