Bayesian approach for neural networks : review and case studies

 LAMPINEN Jouko
 Laboratory of Computational Engineering, Helsinki University of Technology

 VEHTARI Aki
 Laboratory of Computational Engineering, Helsinki University of Technology
Search this Article
Author(s)

 LAMPINEN Jouko
 Laboratory of Computational Engineering, Helsinki University of Technology

 VEHTARI Aki
 Laboratory of Computational Engineering, Helsinki University of Technology
Journal

 Neural Networks

Neural Networks 14(3), 257274, 20010401
References: 57

1
 Ensemble learning in Bayesian neural networks

BARBER D.
Neural networks and machine learning 168, 215237, 1998
Cited by (1)

2
 <no title>

BERGER J. O.
Statistical design theory and Bayesian analysis, Springer series in statistics, 1985
Cited by (1)

3
 On the development of reference priors

BERGER J. O.
Bayesian statistics 4, 3560, 1992
Cited by (2)

4
 <no title>

BERNARDO J. M.
Bayesian Theory, 1994
Cited by (17)

5
 <no title>

BISHOP C. M.
Neural Networks for Pattern Recognition, 1995
Cited by (116)

6
 Regression with inputdependent noise: a Bayesian treatment

BISHOP C. M.
Advances in neural information processing systems 9, 347353, 1997
Cited by (1)

7
 <no title>

BREIMAN L.
Classification and Regression Trees, 1984
Cited by (111)

8
 Assessing convergence of Markov chain Monte Carlo algorithms

BROOKS S. P.
Statistics and Computing 8(4), 319335, 1999
Cited by (1)

9
 Bayesian backpropagation

BUNTINE W. L.
Complex Systems 5(6), 603643, 1991
Cited by (1)

10
 Model determination using samplingbased methods

GELFAND A. E.
Markov chain Monte Carlo in practice, 145162, 1996
Cited by (1)

11
 Inference and monitoring convergence

GELMAN A.
Markov chain Monte Carlo in practice, 131144, 1996
Cited by (1)

12
 <no title>

GELMAN A.
Bayesian data analysis. Texts in statistical science, 1995
Cited by (1)

13
 Bayesian treatment of the independent Studentt linear model

GEWEKE J.
Journal of Applied Econometrics 8, S19S40, 1993
Cited by (1)

14
 <no title>

GILKS W. R.
Markov chain Monte Carlo, 1996
Cited by (1)

15
 Empirical evaluation of Bayesian sampling for neural classifiers

HUSMEIER D.
ICANN '98: Proceedings of the Eighth International Conference on Artificial Neural Networks, 1998
Cited by (1)

16
 <no title>

JEFFREYS J.
Theory of probability, 1961
Cited by (1)

17
 An introduction to variational methods for graphical models

JORDAN M. I.
Learning in graphical models 89, 1998
Cited by (1)

18
 Neural network ensembles, crossvalidation, and active learning

KROGH A.
Advances in neural information processing systems 7, 231238, 1995
Cited by (1)

19
 Using background knowledge in multilayer perceptron learning

LAMPINEN J.
SCIA '97: Proceedings of the Tenth Scandinavian Conference on Image Analysis 2, 545549, 1997
Cited by (1)

20
 Using Bayesian neural network to solve the inverse problem in electrical impedance tomography

LAMPINEN J.
SCIA '99: Proceedings of the 11th Scandinavian Conference on Image Analysis 1, 8793, 1999
Cited by (1)

21
 <no title>

LEMM J. C.
Prior information and generalized questions, 1996
Cited by (1)

22
 <no title>

LEMM J. C.
Bayesian field theory, 1999
Cited by (1)

23
 Bayesian training of backpropagation networks by the hybrid Monte Carlo method

NEAL R. M.
Technical report CRGTR921, 1992
Cited by (1)

24
 <no title>

NEAL R. M.
Bayesian learning for neural networks, volume 118 of Lecture notes in statistics, 1996
Cited by (1)

25
 Assessing relevance determination methods using DELVE

NEAL R. M.
Neural networks and machine learning 168, 97129, 1998
Cited by (1)

26
 Regression and classification using Gaussian process priors (with discussion)

NEAL R. M.
Bayesian statistics 6, 475501, 1999
Cited by (1)

27
 Evaluation of Gaussian processes and other methods for nonlinear regression

RASMUSSEN C. E.
PhD thesis, Department of Computer Science, University of Toronto, 1996
Cited by (2)

28
 <no title>

ROBERTS C. P.
Monte Carlo statistical methods, Springer texts in statistics, 1999
Cited by (1)

29
 <no title>

SARLE W. S.
How to measure importance of inputs? [online], 1997
Cited by (1)

30
 <no title>

SPIEGELHALTER D.
BUGS 0. 5^* Examples Volume 1 (version i), 1996
Cited by (1)

31
 Bayesian neural networks with correlating residuals

VEHTARI A.
IJCNN '99: Proceedings of the 1999 International Joint Conference on Neural Networks [CDROM], 1999
Cited by (1)

32
 <no title>

VEHTARI A.
On Bayesian model assessment and choice using crossvalidation predictive densities, 2000
Cited by (1)

33
 Using Bayesian neural networks to classify forest scenes

VEHTARI A.
Proceedings of SPIE 3522, 6673, 1998
Cited by (1)

34
 On MCMC sampling in Bayesian MLP neural networks

VEHTARI A.
IJCNN '2000: Proceedings of the 2000 International Joint Conference on Neural Networks 1, 317322, 2000
Cited by (1)

35
 <no title>

WINTHER O.
Bayesian mean field algorithms for neural networks and Gaussian processes, 1998
Cited by (1)

36
 <no title>

WOLPERT D. H.
No free lunch theorems for search, 1995
Cited by (3)

37
 <no title>

YANG R.
A catalog of noninformative priors, 1997
Cited by (1)

38
 Curvaturedriven smoothing : A learning algorithm for feedforward networks

BISHOP C. M.
IEEE Trans. Neural Netw. 4(5), 882884, 1993
Cited by (6)

39
 Sequential monte carlo methods for optimisation of neural network models

DE FREITAS J. F. G.
Neural Computation 12, 955993, 2000
Cited by (2)

40
 Approximate statistical tests for comparing supervised classification learning algorithms

DIETTERICH T. G.
Neural Computation 10(7), 18951923, 1998
Cited by (7)

41
 <no title>

DUANE S.
Phys. Lett. B 195, 216, 1987
Cited by (10)

42
 The predictive sample reuse method with applications

GEISSER S.
Journal of the American Statistical Association 70(350), 320328, 1975
DOI Cited by (2)

43
 Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images

GEMAN S.
IEEE Trans. Patt. Anal. & Mach. Intell. PAMI6, 721741, 1984
Cited by (361)

44
 Information about hyperparameters in hierarchical models

GOEL P. K.
Journal of the American Statistical Association 76(373), 140147, 1981
DOI Cited by (1)

45
 <no title>

HASTINGS W. K.
Biometrika 57, 97109, 1970
DOI Cited by (14)

46
 Bayes factors

KASS R. E.
The Journal of the American Statistical Association 90, 773795, 1995
DOI Cited by (12)

47
 The selection of prior distributions by formal rules

KASS R. E.
Journal of the American Statistical Association 91(435), 13431370, 1996
DOI Cited by (1)

48
 A practical Bayesian framework for backpropagation networks

MACKAY D. J. C.
Neural Computation 4, 448472, 1992
DOI Cited by (37)

49
 Bayesian Nonlinear Modeling for the Energy Prediction Competition

MACKAY D. J. C.
ASHRAE Transactions 100(2), 10531062, 1994
Cited by (5)

50
 Probable networks and plausible predictionsa review of practical Bayesian methods for supervised neural networks

MACKAY D. J. C.
Network : Computation in Neural Systems 6, 469505, 1995
Cited by (17)

51
 Issues in Bayesian analysis of neural network models

MULLER P.
Neural Computation 10(3), 571592, 1998
Cited by (1)

52
 Bayesian neural networks for classification: how useful is the evidence framework?

PENNY W. D.
Neural Networks 12(6), 877892, 1999
DOI Cited by (1)

53
 A review of bayesian neural networks with an application to near infrared spectroscopy

THODBERG H. H.
IEEE Transactions on Neural Networks 7, 5672, 1996
Cited by (6)

54
 Electrical Impedance Tomography with Basis Constraints

VAUHKONEN M.
Inverse Problems 13(2), 523530, 1997
DOI Cited by (2)

55
 Using Bayesian neural networks to classify segmented images

VIVARELLI F.
Proceedings of the Fifth IEE International Conference on Artificial Neural Networks, 268273, 1997
Cited by (2)

56
 The existence of a priori distinctions between learning algorithms

WOLPERT D. H.
Neural Computation 8(7), 13911420, 1996
Cited by (1)

57
 The lack of a priori distinction between learning algorithms

WOLPERT D. H.
Neural Computation 8(7), 13411390, 1996
Cited by (1)
Cited by: 1

1
 Invariance priors for Bayesian feedforward neural networks

TOUSSAINT Udo v. , GORI Silvio , DOSE Volker
Neural networks : the official journal of the International Neural Network Society 19(10), 15501557, 20061201
References (19)