Bayesian approach for neural networks—review and case studies

Lampinen, Jouko; Vehtari, Aki

doi:10.1016/s0893-6080(00)00098-8

Cited by 282 publications

(166 citation statements)

References 23 publications

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“…These works are reviewed in Bishop (1995), MacKay (1995) and Lampinen and Vehtari (2001). Unlike standard neural network design, the Bayesian approach considers probability distributions in the weight space of the network.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Support Vector Regression Using a Unified Loss Function

Chu

Keerthi

Ong

2004

IEEE Trans. Neural Netw.

117

114

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In this paper, we use a unified loss function, called the soft insensitive loss function, for Bayesian support vector regression. We follow standard Gaussian processes for regression to set up the Bayesian framework, in which the unified loss function is used in the likelihood evaluation. Under this framework, the maximum a posteriori estimate of the function values corresponds to the solution of an extended support vector regression problem. The overall approach has the merits of support vector regression such as convex quadratic programming and sparsity in solution representation. It also has the advantages of Bayesian methods for model adaptation and error bars of its predictions. Experimental results on simulated and real-world data sets indicate that the approach works well even on large data sets.

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Section: Introductionmentioning

confidence: 99%

Bayesian Support Vector Regression Using a Unified Loss Function

Chu

Keerthi

Ong

2004

IEEE Trans. Neural Netw.

117

114

View full text Add to dashboard Cite

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“…For example: (1) for seismic event classification (Dystart and Pulli, 1990), (2) well log analysis (Aristodemou et al, 2005;Maiti et al, 2007;Maiti and Tiwari, 2007, 2010b, (3) first arrival picking (Murat and Rudman, 1992), (4) earthquake prediction (Feng et al, 1997), (5) inversion (Raiche, 1991;Devilee et al, 1999), (6) parameter estimation in geophysics (Macias et al, 2000), (7) prediction of aquifer water level (Coppola Jr. et al, 2005), (8) magneto-telluric data inversion (Spichak and Popova, 2000), (9) magnetic interpretations (Bescoby et al, 2006), (10) signal discrimination (Maiti and Tiwari, 2010a), (11) modeling (Sri Lakshmi and Tiwari, 2009), (12) DC resistivity inversion (Qady and Ushijima, 2001;Lampinen and Vehtari, 2001;Singh et al, 2005Singh et al, , 2006Singh et al, , 2010.…”

Section: S Maiti Et Al: Inversion Of DC Resistivity Data Of Koyna Rmentioning

confidence: 99%

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Maiti¹,

Gupta²,

Erram³

et al. 2011

Nonlin. Processes Geophys.

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Abstract. Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M = 6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity data lacks precise information due to intrinsic non-linearity in the data structures. Here we present a new technique based on the Bayesian neural network (BNN) theory using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme. The new method is applied to invert one and two-dimensional Direct Current (DC) vertical electrical sounding (VES) data acquired around the Koyna region in India. Prior to apply the method on actual resistivity data, the new method was tested for simulating synthetic signal. In this approach the objective/cost function is optimized following the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) sampling based algorithm and each trajectory was updated by approximating the Hamiltonian differential equations through a leapfrog discretization scheme. The stability of the new inversion technique was tested in presence of correlated red noise and uncertainty of the result was estimated using the BNN code. The estimated true resistivity distribution was compared with the results of singular value decomposition (SVD)-based conventional resistivity inversion results. Comparative results based on the HMC-based Bayesian Neural Network are in good agreement with the existing model results, however in some cases, it also provides more detail and precise results, which appears to be justified with local geological and structural deCorrespondence to: S. Maiti (saumen maiti2002@yahoo.co.in) tails. The new BNN approach based on HMC is faster and proved to be a promising inversion scheme to interpret complex and non-linear resistivity problems. The HMC-based BNN results are quite useful for the interpretation of fractures and lineaments in seismically active region.

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“…where x is a d-dimensional input vector, w denotes the weights, and indices i and j correspond to input and hidden units, respectively (Lampinen & Vehtari, 2001). Arrangement of layers and units in an ANN called architecture (Doan & Yuiliong, 2004).…”

Section: Artificial Neural Networkmentioning

confidence: 99%