Estimating the support of a high-dimensional distribution

Neural Computation

Volumn 13, Issue 7, 2001, Pages 1443-1471

  Schölkopf, Bernhard ^a   Platt, John C ^b   Shawe Taylor, John ^c   Smola, Alex J ^d   Williamson, Robert C ^d  

^a MICROSOFT RESEARCH   (United Kingdom)

^b MICROSOFT RESEARCH   (United States)

^c UNIVERSITY OF LONDON   (United Kingdom)

^d AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000487102     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976601750264965     Document Type: Article

References (49)

1. Ben-David, S., & Lindenbaum, M. (1997). Learning distributions by their density levels: A paradigm for learning without a teacher. Journal of Computer and System Sciences, 55, 171-182.
2. Bertsekas, D. P. (1995). Nonlinear programming. Belmont, MA: Athena Scientific.
3. Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992). A training algorithm for optimal margin classifiers. In D. Haussier (Ed.), Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory (pp. 144-152). Pittsburgh, PA: ACM Press.
4. Chevalier, J. (1976). Estimation du support et du contour du support d'une loi de probabilité. Annales de l'Institut Henri Poincaré. Section B. Calcul des Probabilités et Statistique. Nouvelle Série, 12(4),: 339-364.
5. Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.
6. Cuevas, A., & Fraiman, R. (1997). A plug-in approach to support estimation. Annals of Statistics, 25(6), 2300-2312. 1997.
7. Devroye, L., & Wise, G. L. (1980). Detection of abnormal behaviour via nonparametric estimation of the support. SIAM Journal on Applied Mathematics, 38(3), 480-488.
8. Einmal, J. H. J., & Mason, D. M. (1992). Generalized quantile processes. Annals of Statistics, 20(2), 1062-1078.
9. Gayraud, G. (1997). Estimation of functional of density support. Mathematical Methods of Statistics, 6(1), 26-46.
10. Geffroy, J. (1964). Sur un problème d'estimation géométrique. Publications de l'Institut de Statistique de l'Université de Paris, 13, 191-210.
11. Girosi, F. (1998). An equivalence between sparse approximation and support vector machines. Neural Computation, 10(6), 1455-1480.
12. Hartigan, J. A. (1987). Estimation of a convex density contour in two dimensions. Journal of the American Statistical Association, 82, 267-270.
13. Hayton, P., Schölkopf, B., Tarassenko, L., & Anuzis, P. (in press). Support vector novelty detection applied to jet engine vibration spectra. In T. Leen, T. Dietterich, & V. Tresp (Eds)., Advances in neural information processing systems, 13.
14. Joachims, T. (1999). Making large-scale SVM learning practical. In B. Schölkopf, C. J. C. Burges, & A. J. Smola (Eds.), Advances in kernel methods - Support vector learning (pp. 169-184). Cambridge, MA: MIT Press.
15. Keerthi, S. S., Shevade, S. K., Bhattacharyya, C., & Murthy, K. R. K. (1999). Improvements to Platt's SMO algorithm for SVM classifier design (Tech. Rep. No. CD-99-14). Singapore: Department of Mechanical and Production Engineering, National University of Singapore.
16. Korostelev, A. P., & Tsybakov, A. B. (1993). Minimax theory of image reconstruction. New York: Springer-Verlag.
17. Müller, D. W. (1992). The excess mass approach in statistics. Heidelberg: Beiträge zur Statistik, Universität Heidelberg.
18. Nolan, D. (1991). The excess mass ellipsoid. Journal of Multivariate Analysis, 39, 348-371.
19. Platt, J. (1999). Fast training of support vector machines using sequential minimal optimization. In B. Schölkopf, C. J. C. Burges, & A. J. Smola (Eds.), Advances in kernel methods - Support vector learning, (pp. 185-208). Cambridge, MA: MIT Press.
20. Poggio, T., & Girosi, F. (1990). Networks for approximation and learning. Proceedings of the IEEE, 78(9).
21. Polonik, W. (1995a). Density estimation under qualitative assumptions in higher dimensions. Journal of Multivariate Analysis, 55(1), 61-81.
22. Polonik, W. (1995b). Measuring mass concentrations and estimating density contour clusters - an excess mass approach. Annals of Statistics, 23(3), 855-881.
23. Polonik, W. (1997). Minimum volume sets and generalized quantile processes. Stochastic Processes and their Applications, 69, 1-24.
24. Sager, T. W. (1979). An iterative method for estimating a multivariate mode and isopleth. Journal of the American Statistical Association, 74(366), 329-339.
25. Schölkopf, B., Burges, C. J. C., & Smola, A. J. (1999). Advances in kernel methods -Support vector learning. Cambridge, MA: MIT Press.
26. Schölkopf, B., Burges, C., & Vapnik, V. (1995). Extracting support data for a given task. In U. M. Fayyad & R. Uthurusamy (Eds.), Proceedings, First International Conference on Knowledge Discovery and Data Mining. Menlo Park, CA: AAAI Press.
27. Schölkopf, B., Platt, J., Shawe-Taylor, J., Smola, A. J., & Williamson, R. C. (1999). Estimating the support of a high-dimensional distribution (Tech. Rep. No. 87). Redmond, WA: Microsoft Research. Available online at: http://www.research.microsoft.com/scripts/pubs/view.asp?TR_ID=MSR-TR-99-87.
28. Schölkopf, B., Platt, J., & Smola, A. J. (2000). Kernel method for percentile feature extraction (Tech. Rep. No. 22). Redmond, WA: Microsoft Research.
29. Schölkopf, B., Smola, A., & Müller, K. R. (1999). Kernel principal component analysis. In B. Schölkopf, C. J. C. Burges, & A. J. Smola (Eds.), Advances in kernel methods - Support vector learning (pp. 327-352). Cambridge, MA: MIT Press.
30. Schölkopf, B., Smola, A., Williamson, R. C., & Bartlett, P. L. (2000). New support vector algorithms. Neural Computation, 12, 1207-1245.
31. Schölkopf, B., Williamson, R., Smola, A., & Shawe-Taylor, J. (1999). Single-class support vector machines. In J. Buhmann, W. Maass, H. Ritter, & N. Tishby, editors (Eds.) Unsupervised learning (Rep. No. 235) (pp. 19-20). Dagstuhl, Germany.
32. Shawe-Taylor, J., & Cristianini, N. (1999). Margin distribution bounds on generalization. In Computational Learning Theory: 4th European Conference (pp. 263-273). New York: Springer-Verlag.
33. Shawe-Taylor, J., & Cristianini, N. (2000). On the generalisation of soft margin algorithms. IEEE Transactions on Information Theory. Submitted.
34. Shawe-Taylor, J., & Williamson, R. C. (1999). Generalization performance of classifiers in terms of observed covering numbers. In Computational Learning Theory: 4th European Conference (pp. 274-284). New York: Springer-Verlag.
35. Smola, A., & Schölkopf, B. (in press). A tutorial on support vector regression. Statistics and Computing.
36. Smola, A., Schölkopf, B., & Müller, K.-R. (1998). The connection between regularization operators and support vector kernels. Neural Networks, 11, 637-649.
37. Smola, A., Mika, S., Schölkopf, B., & Williamson, R. C. (in press). Regularized principal manifolds. Machine Learning.
38. Still, S., & Schölkopf, B. (in press). Four-legged walking gait control using a neuromorphic chip interfaced to a support vector learning algorithm. In T. Leen, T. Diettrich, & P. Anuzis (Eds.), Advances in neural information processing systems, 13. Cambridge, MA: MIT Press.
39. Stoneking, D. (1999). Improving the manufacturability of electronic designs. IEEE Spectrum, 36(6), 70-76.
40. Tarassenko, L., Hayton, P., Cerneaz, N., & Brady, M. (1995). Novelty detection for the identification of masses in mammograms. In Proceedings Fourth IEE International Conference on Artificial Neural Networks (pp. 442-447). Cambridge.
41. Tax, D. M. J., & Duin, R. P. W. (1999). Data domain description by support vectors. In M. Verleysen (Ed.), Proceedings ESANN (pp. 251-256). Brussels: D Facto.
42. Tsybakov, A. B. (1997). On nonparametric estimation of density level sets. Annals of Statistics, 25(3), 948-969.
43. Vapnik, V. (1995). The nature of statistical learning theory. New York: Springer-Verlag.
44. Vapnik, V. (1998). Statistical learning theory. New York: Wiley.
45. Vapnik, V., & Chapelle, O. (2000). Bounds on error expectation for SVM. In A. J. Smola, P. L. Bartlett, B. Schölkopf, & D. Schuurmans (Eds.), Advances in large margin classifiers (pp. 261-280). Cambridge, MA: MIT Press.
46. Vapnik, V., & Chervonenkis, A. (1974). Theory of pattern recognition. Nauka, Moscow. [In Russian] (German translation: W. Wapnik & A. Tscherwonenkis, Theorie der Zeichenerkennung, Akademie-Verlag, Berlin, 1979).
47. Vapnik, V., & Lerner, A. (1963). Pattern recognition using generalized portrait method. Automation and Remote Control, 24.
48. Williamson, R. C., Smola, A. J., & Schölkopf, B. (1998). Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators (Tech. Rep. No. 19) NeuroCOLT. Available online at: http://www.neurocolt.com, 1998. Also: IEEE Transactions on Information Theory (in press).
49. Williamson, R. C., Smola, A. J., & Schölkopf, B. (2000). Entropy numbers of linear function classes. In N. Cesa-Bianchi & S. Goldman (Eds.), Proceedings of the 13th Annual Conference on Computational Learning Theory (pp. 309-319). San Mateo, CA: Morgan Kaufman.