Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance

Automatica

Volumn 43, Issue 10, 2007, Pages 1698-1712

  Pillonetto, Gianluigi ^a   Bell, Bradley M ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bayesian function learning; Markov chain Monte Carlo; Nonparametric identification; Regularization; Splines

Indexed keywords

BAYESIAN NETWORKS; DYNAMICAL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

BAYESIAN FUNCTION LEARNING; MINIMUM VARIANCE ESTIMATES; NONPARAMETRIC IDENTIFICATION; REGULARIZATION;

DECONVOLUTION;

EID: 34548499071     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2007.02.025     Document Type: Article

References (38)

1. Anderson B.D.O., and Moore J.B. Optimal filtering (1979), Prentice-Hall, Englewood Cliffs, NJ
2. Aronszajn N. Theory of reproducing kernels. Transactions of the American Mathematical Society 68 (1950) 337-404
3. Bell B.M., and Pillonetto G. Estimating parameters and stochastic functions of one variable using nonlinear measurements models. Inverse Problems 20 3 (2004) 627-646
4. Bertero M. Linear inverse and ill-posed problems. Advances in Electronics and Electron Physics 75 (1989) 1-120
5. Bertero M., and Boccacci P. Introduction to inverse problems in imaging (1998), IOP Publishing
6. Carlin B.P., and Louiz T.A. Bayes and empirical bayes methods for data analysis (1996), Chapman & Hall, London
7. Craven P., and Wahba G. Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik 31 (1979) 377-403
8. Cucker F., and Smale S. On the mathematical foundations of learning. Bulletin of the American Mathematical Society 39 (2001) 1-49
9. 2 filtering and deconvolution. Automatica 37 (2001) 1443-1449
10. De Nicolao G., Sparacino G., and Cobelli C. Nonparametric input estimation in physiological systems: Problems, methods and case studies. Automatica 33 (1997) 851-870
11. De Nicolao G., and Trecate G.F. Consistent identification of narx models via regularization networks. IEEE Transactions on Automatic Control 44 (1999) 2045-2049
12. De Nicolao G., and Trecate G.F. Regularization networks: Fast weight calculation via kalman filtering. IEEE Transactions on Neural Networks 12 (2001) 228-235
13. De Nicolao G., and Trecate G.F. Regularization networks for inverse problems: A state space approach. Automatica 39 (2003) 669-676
14. Donoho D.L., and Johnstone I.M. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 3 (1994) 425-455
15. Evgeniou, T., Pontil, M., & Poggio, T. (1999). A unified framework for regularization networks and support vector machines. CBCL Paper 171, Massachusetts Institute of Technology, Cambridge, MA, March 1999.
16. Figueiredo M.A.T., and Nowak R.D. Wavelet-based image estimation: An empirical Bayes approach using jeffrey's noninformative prior. IEEE Transactions on Image Processing 10 9 (2001) 1322-1331
17. Franke, R. (1979). A critical comparison of some methods for interpolation of scattered data. Technical Report NPS-53-79-003, Naval Postgraduate School.
18. Gilks W.R., Richardson S., and Spiegelhalter D.J. Markov chain Monte Carlo in practice (1996), Chapman & Hall, London
19. Green P., and Silverman B. Nonparametric regression and generalized linear models (1994), Chapman & Hall, London
20. Green P.J., and Mira A. Delayed rejection in reversible jump metropolis-hastings. Biometrika 88 (2001) 1035-1053
21. Hastings W.K. Monte Carlo sampling methods using Markov chain and their applications. Biometrika 57 (1970) 97-109
22. Jaakkola, T. S., & Haussler, D. (1998). Exploiting generative models in discriminative classifiers. In M. S. Kearns, S. A. Solla, & D. A. Cohn (Eds.), Advances in neural information processing systems (Vol. 11). Cambridge, MA: MIT Press.
23. Magni P., Bellazzi R., and De Nicolao G. Bayesian function learning using mcmc methods. IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (1998) 1219-1331
24. Olshen A.B., and O'Sullivan F. Camouflaged deconvolution with application to blood curve modeling in fdg pet studies. Journal of the American Statistical Association 92 (1997) 1293-1303
25. Osuna E., Freund R., and Girosi F. Training support vector machines: An application to face detection. Proceedings of computer vision and pattern recognition (1997) 130-136
26. Pillonetto G., and Bell B.M. Deconvolution of nonstationary physical signals: A smooth variance model for insulin secretion rate. Inverse Problems 20 2 (2004) 367-383
27. Pillonetto G., and Cobelli C. Identifiability of the stochastic semi-blind deconvolution problem for a class of time-invariant linear systems. Automatica 43 (2007) 647-654
28. Poggio T., and Girosi F. Networks for approximation and learning. Proceedings of the IEEE 78 (1990) 1481-1497
29. Raftery A.E., and Lewis S.M. Markov chain Monte Carlo in practice. In: Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds). Implementing MCMC (1996), Chapman & Hall, London 115-130
30. Rice J.A. Choice of smoothing parameter in deconvolution problems. Contemporary Mathematics 59 (1986) 137-151
31. Roberts G., Gelman A., and Gilks W. Weak convergence and optimal scaling of random walk metropolis algorithms. Annales of Applied Probability 7 (1997) 110-120
32. Schwartz L. Radon measures on arbitrary topological spaces and cylindrical measures (1973), Oxford University Press, New York
33. Sun S., Egerstedt M.B., and Martin C.F. Control theoretic smoothing splines. IEEE Transactions on Automatic Control 45 (2000) 2271-2279
34. Tierney L., and Mira A. Some adaptive Monte Carlo methods for Bayesian inference. Statistics in Medicine 18 (1999) 2507-2515
35. Trecate, G. F., Williams, C. K. I., & Opper, M. (1999). Finite-dimensional approximation of Gaussian processes. Advances in neural information processing systems (Vol. 11). Cambridge, MA: MIT Press.
36. Tychonov A.N., and Arsenin V.Y. Solutions of ill-posed problems (1977), Winston/Wiley, Washington, DC
37. Wahba G. Spline models for observational data (1990), SIAM, Philadelphia, PA
38. Yaglom, A. M. (1987). Correlation theory of stationary and related random functions (Vol. 1). New York: Springer.