Sparse bayesian kernel survival analysis for modeling the growth domain of microbial pathogens

IEEE Transactions on Neural Networks

Volumn 17, Issue 2, 2006, Pages 471-481

  Cawley, Gavin C ^a   Talbot, Nicola L C ^a   Janacek, Gareth J ^a   Peck, Michael W ^b  

^a UNIVERSITY OF EAST ANGLIA   (United Kingdom)

^b INSTITUTE OF FOOD RESEARCH   (United Kingdom)

Author keywords

Bayesian learning; Kernel methods; Survival analysis

Indexed keywords

DISEASES; LEARNING SYSTEMS; MATHEMATICAL MODELS; MICROBIOLOGY;

BAYESIAN LEARNING; FOODBORNE BOTULISM; KERNEL METHODS; MICROBIAL PATHOGENS; SURVIVAL ANALYSIS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL INTELLIGENCE; BAYES THEOREM; BIOLOGICAL MODEL; CELL PROLIFERATION; CELL SURVIVAL; CLOSTRIDIUM BOTULINUM; COMPUTER SIMULATION; CYTOLOGY; FOOD CONTROL; GROWTH, DEVELOPMENT AND AGING; PHYSIOLOGY; POPULATION GROWTH; STATISTICAL ANALYSIS; STATISTICAL MODEL; SURVIVAL; SURVIVAL RATE;

ARTIFICIAL INTELLIGENCE; BAYES THEOREM; CELL PROLIFERATION; CELL SURVIVAL; CLOSTRIDIUM BOTULINUM; COMPUTER SIMULATION; DATA INTERPRETATION, STATISTICAL; FOOD MICROBIOLOGY; MODELS, BIOLOGICAL; MODELS, STATISTICAL; POPULATION GROWTH; SURVIVAL ANALYSIS; SURVIVAL RATE;

EID: 33644890436     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2005.863452     Document Type: Article

References (47)

1. D. R. Cox and D. Oakes, Analysis of Survival Data. London, U.K.: Chapman and Hall, 1984, vol. 21.
2. B. D. Ripley and R. M. Ripley, "Neural networks as statistical methods in survival analysis," in Artificial Neural Networks: Prospects for Medicine, R. Dybowski and V. Gant, Eds: Landes, 1998.
3. L. Tarassenko, R. M. Whitehouse, G. Gasparini, and A. L. Harris, "Neural network prediction of relapse in breast cancer patients," Neural Comput. Applicat., vol. 4, no. 2, pp. 105-113, 1996.
4. G. C. Cawley, M. W. Peck, and P. S. Fernández, "A neural model of time to toxin production by nonproteolytic Clostridium botulinum," in Proc. IEEE Int. Joint Conf. Neural Networks, Anchorage, AK, May 1998.
5. I. Nabney, NETLAB: Algorithms for Pattern Recognition, ser. Advances in Pattern Recognition. New York: Springer Verlag, 2001.
6. G. Schwarzer, W. Vach, and M. Schumacher, "On the misuses of artificial neural networks for prognostic and diagnostic classification in oncology," Statist. Medicine, vol. 19, pp. 541-561, 2000.
7. L. Ohno-Machado, "A comparison of Cox proportional hazards and artificial neural network models for medical prognosis," Comput. Biol. Medicine, vol. 27, no. 1, pp. 55-65, 1997.
8. P. J. G. Lisboa, H. Wong, A. Vellido, S. P. J. Kirby, P. Harris, and R. Swindwll, "Survival of breast cancer patients following surgery: A detailed assessment of the multi-layer perceptron and Cox's proportional hazard model," in Proc. Int. Joint Conf. Neural Networks, vol. 1, Anchorage, AK, May 4-9, 1998, pp. 112-116.
9. D. R. Cox, "Regression models and life-tables (with discussion), " J. Roy. Statist. Soc. (B), vol. 34, pp. 187-220, 1972.
10. K. Leistøl, P. K. Andersen, and U. Andersen, "Survival analysis and neural nets," Statist. Medicine, vol. 13, pp. 1189-1200, 1994.
11. D. Faraggi and R. Simon, "A neural network model for survival data," Statist. Medicine, vol. 14, pp. 73-82, 1995.
12. E. Biganzoli, P. Boracchi, and E. Marubini, "A general framework for neural network models on censored survival data," Neural Networks, vol. 15, no. 2, pp. 209-218, 2002.
13. B. Bakker, T. Heskes, J. Neijt, and B. Kappen, "Improving Cox survival analysis with a neural-Bayesian approach," Statist. Medicine, vol. 23, pp. 2989-3012, 2004.
14. A. Eleuteri, R. Tagliaferri, L. Milano, S. De Placido, and M. De Laurentis, "A novel neural network-based survival analysis method," Neural Networks, vol. 16, no. 5-6, pp. 855-864, 2003.
15. R. J. Foxall, G. C. Cawley, and M. W. Peck, "Modeling the growth domain of Clostridium botulinum via kernel survival analysis," in Proc. IEEE/INNS Int. Joint Conf. Neural Networks, vol. 4, Portland, OR, Jul. 20-24, 2003, pp. 2958-2963.
16. D. J. C. MacKay, "Bayesian interpolation," Neural Comput., vol. 4, no. 3, pp. 415-447, 1992.
17. D. J. C. MacKay, "A practical Bayesian framework for backprop networks," Neural Comput., vol. 4, no. 3, pp. 448-472, 1992.
18. D. J. C. MacKay, "The evidence framework applied to classification networks," Neural Comput., vol. 4, no. 5, pp. 720-736, 1992.
19. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. New York: Wiley, 1977.
20. S. Geman, E. Bienenstock, and R. Doursat, "Neural networks and the bias/variance dilemma," Neural Comput., vol. 4, no. 1, pp. 1-58, 1992.
21. J. Mercer, "Functions of positive and negative type and their connection with the theory of integral equations," Philosoph. Trans. Roy. Soc. London, A, vol. 209, pp. 415-446, 1909.
22. N. Aronszajn, "Theory of reproducing kernels," Trans. Amer. Math. Soc., vol. 68, pp. 337-404, 1950.
23. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines (and Other Kernel-Based Learning Methods). Cambridge, U.K.: Cambridge Univ. Press, 2000.
24. B. Schölkopf and A. J. Smola, Learning With Kernels - Support Vector Machines, Regularization, Optimization and Beyond. Cambridge, MA: MIT Press, 2002.
25. G. S. Kimeldorf and G. Wahba, "Some results on Tchebycheffian spline functions," J. Math. Anal. Applicat., vol. 33, pp. 82-95, 1971.
26. B. Schölkopf, R. Herbrich, and A. J. Smola, "A generalized representer theorem," in Proc. 14th Int. Conf. Computational Learning Theory, Amsterdam, The Netherlands, Jul. 16-19, 2001, pp. 416-426.
27. R. Fletcher, Practical Methods of Optimization, 2nd ed. New York: Wiley, 2000.
28. C. A. Micchelli, "Interpolation of scattered data: Distance matrices and conditionally positive definite functions," Constructive Approximation, vol. 2, pp. 11-22, 1986.
29. S. Fine and K. Scheinberg, "Efficient SVM training using low-rank kernel representations," J. Machine Learning Res., vol. 2, pp. 243-264, Dec. 2001.
30. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
31. G. Baudat and F. Anouar, "Kernel-based methods and function approximation," in Proc. IJCNN, Washington, DC, Jul. 2001, pp. 1244-1249.
32. M. Stone, "Cross-validatory choice and assessment of statistical predictions," J. Roy. Statist. Soc., vol. B 36, no. 1, pp. 111-147, 1974.
33. A. Luntz and V. Brailovsky, "On estimation of characters obtained in statistical procedure of recognition" (in Russian), Techicheskaya Kibernetica, vol. 3, 1969.
34. J. A. Nelder and R. Mead, "A simplex method for function minimization," Computer J., vol. 7, pp. 308-313, 1965.
35. W. L. Buntine and A. S. Weigend, "Bayesian back-propagation," Complex Syst., vol. 5, pp. 603-643, 1991.
36. C. M. Bishop, Neural Networks for Pattern Recognition. Cambridge, U.K.: Oxford Univ. Press, 1995.
37. R. M. Neal, Bayesian Learning for Neural Networks New York, 1996.
38. D. J. C. MacKay, "Hyperparameters: Optimize or integrate out?," in Maximum Entropy and Bayesian Methods, G. Heidbreder, Ed. New York: Kluwer, 1994.
39. B. M. Lund and M. W. Peck, "Clostridium botulinum," in The Microbiological Safety and Quality of Food, B. M. Lund, A. C. Baird-Parker, and G. W. Gould, Eds. Gaithersburg, MD: Aspen, 2000, pp. 1057-1109.
40. M. W. Peck, "Clostridium botulinum and the safety of refrigerated processed foods of extended durability," Trends Food Sci. Technol., vol. 8, pp. 186-192, 1997.
41. P. S. Fernández and M. W. Peck, "A predictive model that describes the effect of prolonged heating at 70-80 ° C and incubation at refrigeration temperatures on growth and toxigenesis by nonproteolytic Clostridium botulinum," J. Food Protection, vol. 60, pp. 1064-1071, 1997.
42. M. W. Peck, B. M. Lund, D. A. Fairbairn, A. S. Kassperson, and P. C. Undeland, "Effect of heat treatment on survival of, and growth from, spores of nonproteolytic Clostridium botulinum at refrigeration temperatures," Appl. Environ. Microbiol., vol. 61, pp. 1780-1785, 1995.
43. S. C. Stringer, N. Haque, and M. W. Peck, "Growth from spores of nonproteolytic Clostridium botulinum in heat treated vegetable juice," Appl. Environ. Microbiol., vol. 65, no. 5, pp. 2136-2142, 1999.
44. F. Carlin and M. W. Peck, "Growth and toxin production by nonproteolytic and proteolytic Clostridium botulinum in cooked vegetables," Lett. Appl. Microbiol., vol. 20, pp. 152-156, 1995.
45. E. L. Kaplan and P. Meier, "Nonparametric estimation from incomplete observations," J. Amer. Statist. Assoc., vol. 53, no. 282, pp. 457-481, Jun. 1958.
46. C. K. I. Williams, C. Qazaz, C. M. Bishop, and H. Zhu, "On the relationship between Bayesian error bars and the input data density," in Proc 4th Inst. Elec. Eng. Int. Conf. Artificial Neural Networks, Cambridge, U.K., Jun. 26-28, 1995, pp. 160-165.
47. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. London, U.K.: Chapman and Hall, 1993, vol. 57, Monographs on Statistics and Applied Probability.