MCMC and SMC model selection

[J.F. Gomes De Freitas]

Dear colleagues,

The following papers and Matlab software on MCMC algorithms for batch and 
on-line learning are now available from my website:

http://svr-www.eng.cam.ac.uk/~jfgf/publications.html
http://svr-www.eng.cam.ac.uk/~jfgf/software.html

KEYWORDS: Reversible jump MCMC, model selection, sequential Monte Carlo, 
particle filters, AIC, MDL, simulated annealing, robust priors, geometric 
convergence proofs.

PAPER 1: Sequential Bayesian Estimation and Model Selection Applied to 
Neural Networks. Technical report CUED/F-INFENG/TR 341, Cambridge 
University Department of Engineering, May 1999. 

PAPER 2: Robust Full Bayesian Learning for Neural Networks. Technical report
CUED/F-INFENG/TR 343, Cambridge University Department of Engineering, May 
1999. 

The abstracts follow:

Paper 1:
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In this paper, we address the complex problem of sequential Bayesian
estimation and model selection. This problem does not usually admit any
type of closed-form analytical solutions and, as a result, one has to
resort to numerical methods. We propose here an original
sequential simulation-based strategy to perform the necessary
computations. It combines sequential importance sampling, a
selection procedure and reversible jump MCMC moves. We demonstrate
the effectiveness of the method by applying it to radial basis
function networks. The approach can be easily extended to other
interesting on-line model selection problems.

Paper 2:
=======
In this paper, we propose a  hierarchical full Bayesian model for neural 
networks. This model treats the model dimension (number of neurons), 
model parameters, regularisation parameters and noise parameters as 
random variables that need to be estimated. We develop a reversible jump 
Markov chain Monte Carlo (MCMC) method to perform the necessary computations.
We find that the results obtained using this method are not only better 
than the ones reported previously, but also appear to be robust with 
respect to the prior specification.

In addition, we propose a novel and computationally efficient reversible 
jump MCMC simulated annealing algorithm to optimise neural networks. This 
algorithm enables us to maximise the joint posterior distribution of the 
network parameters and the number of basis function. It performs a global 
search in the joint space of the parameters and number of parameters, 
thereby surmounting the problem of local minima. We show that by 
calibrating the full hierarchical Bayesian prior, we can obtain the 
classical AIC, BIC and MDL model selection criteria within a penalised 
likelihood framework. Finally, we present a geometric convergence theorem 
for the algorithm with homogeneous transition kernel and a convergence 
theorem for the reversible jump MCMC simulated annealing method.


I hope some of you find them interesting and, as always, feedback of all 
sorts is most welcome.

Nando

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JFG de Freitas (Nando)
Speech, Vision and Robotics Group
Information Engineering
Cambridge University
CB2 1PZ England
http://svr-www.eng.cam.ac.uk/~jfgf        
Tel (01223) 302323 (H)                 
    (01223) 332754 (W)
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