Minimum Energy Information Fusion in Sensor Networks

In this paper we consider how to organize the sharing of information in a distributed network of sensors and data processors so as to provide explanations for sensor readings with minimal expenditure of energy. We point out that the Minimum Description Length principle provides an approach to information fusion that is more naturally suited to energy minimization than traditional Bayesian approaches. In addition we show that for networks consisting of a large number of identical sensors Kohonen self-organization provides an exact solution to the problem of combining the sensor outputs into minimal description length explanations.Comment: postscript, 8 pages. Paper 65 in Proceedings of The 2nd International Conference on Information Fusio

Finding a Path is Harder than Finding a Tree

I consider the problem of learning an optimal path graphical model from data and show the problem to be NP-hard for the maximum likelihood and minimum description length approaches and a Bayesian approach. This hardness result holds despite the fact that the problem is a restriction of the polynomially solvable problem of finding the optimal tree graphical model

Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Chasing Lambda

Recent astronomical observations of SNIa, CMB, as well as BAO in the Sloan Digital Sky Survey, suggest that the current Universe has entered a stage of an accelerated expansion with the transition redshift at $z \simeq 0.5$. While the simplest candidates to explain this fact is cosmological constant/vacuum energy, there exists a serious problem of coincidence. In theoretical cosmology we can find many possible approaches alleviating this problem by applying new physics or other conception of dark energy. We consider state of art candidates for the description of accelerating Universe in the framework of the Bayesian model selection. We point out advantages as well as troubles of this approach. We find that the combination of four data bases gives a stringent posterior probability of the $\Lambda$CDM model which is 74%. This fact is a quantitative exemplification of a turmoil in modern cosmology over the $\Lambda$ problem.Comment: Talk presented at the "A Century of Cosmology - Past, Present and Future" conference, S.Servolo(Venice), Italy, August 27-31 2007. To be published in Il Nuovo Ciment

Learning Locally Minimax Optimal Bayesian Networks

We consider the problem of learning Bayesian network models in a non-informative setting, where the only available information is a set of observational data, and no background knowledge is available. The problem can be divided into two different subtasks: learning the structure of the network (a set of independence relations), and learning the parameters of the model (that fix the probability distribution from the set of all distributions consistent with the chosen structure). There are not many theoretical frameworks that consistently handle both these problems together, the Bayesian framework being an exception. In this paper we propose an alternative, information-theoretic framework which sidesteps some of the technical problems facing the Bayesian approach. The framework is based on the minimax-optimal Normalized Maximum Likelihood (NML) distribution, which is motivated by the Minimum Description Length (MDL) principle. The resulting model selection criterion is consistent, and it provides a way to construct highly predictive Bayesian network models. Our empirical tests show that the proposed method compares favorably with alternative approaches in both model selection and prediction tasks.

Bank credit risk : evidence from Tunisia using Bayesian networks

In this article, a problem of measurement of credit risk in bank is studied. The approach suggested to solve it uses a Bayesian networks. After the data-gathering characterizing of the customers requiring of the loans, this approach consists initially with the samples collected, then the setting in works about it of various network architectures and combinations of functions of activation and training and comparison between the results got and the results of the current methods used. To address this problem we will try to create a graph that will be used to develop our credit scoring using Bayesian networks as a method. After, we will bring out the variables that affect the credit worthiness of the beneficiaries of credit. Therefore this article will be divided so the first part is the theoretical side of the key variables that affect the rate of reimbursement and the second part a description of the variables, the research methodology and the main results. The findings of this paper serve to provide an effective decision support system for banks to detect and alleviate the rate of bad borrowers through the use of a Bayesian Network model. This paper contributes to the existing literature on customers’ default payment and risk associated to allocating loans.peer-reviewe

Modelling Survival Data to Account for Model Uncertainty: A Single Model or Model Averaging?

This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a\ud mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single ???best??? model, where\ud ???best??? is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to\ud account for model uncertainty. This was illustrated using a case study in which the aim was the description of\ud lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate\ud that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the\ud data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample\ud size was reduced, no single model was revealed as ???best???, suggesting that a BMA approach would be appropriate.\ud Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can\ud provide robust predictions and facilitate more detailed investigation of the relationships between gene expression\ud and patient survival