Andrieu, C., de Freitas, J. F. G. and Doucet, A. (2000). Robust full Bayesian learning for radial basis networks, to appear in Neural Computation.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of Bayesian learning of model structure and model parameters [AdFDJ03] Moreover, model selection can also be addressed in the same framework with reverse jump MCMC (RJ MCMC) Gre95] by constructing reversible moves between parameter spaces of di#erent dimensions. In particular, Andrieu et.al. AdFD01] applied RJ MCMC to the learning of radial basis function (RBF) neural networks by introducing birth death and split merge moves to the RBF kernels. This is similar to our case of learning variable number of Gaussians in the feature space that correspond to the emission probabilities. In this ....

Christophe Andrieu, Nando de Freitas, and Arnaud Doucet. Robust full bayesian learning for radial basis networks. Neural Computation, 13:2359--2407, 2001.

....the global optimum in probability if certain constraints [10] are satisfied for the proposal distribution and if the acceptance probability are evaluated accordingly, yet the speed of convergence largely depends on the goodness of the proposals. Model adaptation for HHMM involves moves similar to [11] since many changes in the state space involve changing the number of Gaussian kernels that associates states in the lowest level with observations. We included four general types of movement in the state space, as can be illustrated form the tree structured representation of the HHMM in figure ....

....to merge two states at level d into one, by collapsing their children into one set and decreasing the number of nodes at level d by one. 4) Swap(d) to swap the parents of two states at level d, whose parent nodes at level d 1 was not originally the same. Compared to the RBF network in [11], this special move is needed for HHMM, since its multi level structure is nonhomogeneous within the same size of overall state space. Moreover, we are not including birth death moves for simplicity, since these moves can be reached with multiple moves of split merge. There are usually three ....

C. Andrieu, N. de Freitas, and A. Doucet, "Robust full bayesian learning for radial basis networks," Neural Computation, vol. 13, pp. 2359--2407, 2001.

No context found.

Andrieu, C., de Freitas, J. F. G. and Doucet, A. (2000). Robust full Bayesian learning for radial basis networks, to appear in Neural Computation.

....technique known as Rao Blackwellisation (Robert and Casella 1999, pp. 116 119) The marginalisation is carried out using Kalman ltering methods. The Kalman lter has been previously used to improve the eciency of particle ltering (Bergman, 2 Doucet and Gordon 2001, Doucet, Godsill and Andrieu 2000). The algorithm presented here extends to analysis to more complex models. Our simulations demonstrate that it improves the performance of standard methods. The rest of the paper is organised as follows. Section 2 describes the statistical model and the estimation objectives. In Section 3, we give ....

Andrieu, C., de Freitas, N. and Doucet, A. (1999a). Robust full Bayesian learning for radial basis networks, To appear in Neural Computation.

.... models that enable us to, for example, achieve robustness with respect to the speci cation of the prior distributions (no parameter tuning) perform model selection, extend point estimators to average estimators and consider di erent loss functions in a principled way: see for example (Andrieu, de Freitas and Doucet 2000, Bernardo and Smith 1994) We follow a hierarchical Bayesian strategy, where the unknown parameters , fp(wjl; c) p(c) p(ajd; c) g are regarded as being drawn from appropriate prior distributions. We acknowledge our uncertainty about the exact form of the prior by specifying it in terms ....

Andrieu, C., de Freitas, N. and Doucet, A. (2000). Robust full Bayesian learning for radial basis networks, to appear in Neural Computation.

.... to combine several samplers into mixtures and cycles of the individual samplers (Robert and Casella 1999) This way we can have global proposals to explore large regions of the parameter space and local proposals to discover ner details of the target distribution (Andrieu and Doucet 1999, Andrieu, de Freitas and Doucet 2000). If the transition kernels K 1 and K 2 have invariant distribution p( each, then the cycle hybrid kernel K 1 K 2 and the mixture hybrid kernel K 1 (1 )K 2 , for 0 1, are also transition kernels with invariant distribution p( In this paper, we adopt a mixture where, with probability ....

Andrieu, C., de Freitas, J. F. G. and Doucet, A. (2000). Robust full Bayesian learning for radial basis networks, to appear in Neural Computation.

.... modelling: The Bayesian perspective lays the groundwork for more complex models that enable us to implement more general generative models, achieve robustness with respect to the speci cation of the prior distributions (no parameter tuning) and perform model selection (averaging) see for example (Andrieu, de Freitas and Doucet 2000b, Bernardo and Smith 1994) 2.2.1 Priors on the mixing variables The allocation variables z i are assumed to be drawn from a multinomial distribution, z i M nc (1; which admits the density p(z i j ) nc Y c=1 I c (z i ) c It is convenient to place a conjugate Dirichlet prior on ....

....we discuss the simple Bayes, empirical Bayes and hierarchical Bayes approaches for modelling the hyper parameters. 2.4. 1 Simple Bayes and Ockham s razor Instead of attempting to compute the hyper parameters using MCMC integration or optimisation by variational bounds and evidence maximisation (Andrieu et al. 2000b, Ghahramani and Beal 2000, Mackay and Peto 1995) we could instead set the hyper parameters using intuition and heuristic knowledge. The main reason for this is that the parameter set in multimedia applications is so large that avoiding extra parameters is one of the main design constraints. ....

[Article contains additional citation context not shown here]

Andrieu, C., de Freitas, J. F. G. and Doucet, A. (2000b). Robust full Bayesian learning for radial basis networks, to appear in Neural Computation.

No context found.

C. Andrieu, J. de Freitas, and A. Doucet. Robust full Bayesian learning for radial basis networks. Neural Computation, 13(10):2359--2407, 2001.

No context found.

C. Andrieu, J. F. G. deFreitas, and A. Doucet, "Robust full Bayesian learning for radial basis networks," Neural Comput., vol. 13, no. 10, pp. 2359--2407, Oct. 2001.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC