We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classifi(cid:173) cation models with Gaussian processes. In contrast to previous ap(cid:173) proaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given. Bayesian models which are based on Gaussian prior distributions on function spaces are promising non-parametric statistical tools. They have been recently introduced into the Neural Computation community (Neal 1996, Williams & Rasmussen 1996, Mackay 1997).

Recent work in decentralized, schedule-driven traffic control has demonstrated the ability to significantly improve traffic flow efficiency in complex urban road networks. However, in situations where vehicle volumes increase to the point that the physical capacity of a road network reaches or exceeds saturation, it has been observed that the effectiveness of a schedule-driven approach begins to degrade, leading to progressively higher network congestion. In essence, the traffic control problem becomes less of a scheduling problem and more of a queue management problem in this circumstance. In this paper we propose a composite approach to real-time traffic control that uses sensed information on queue lengths to influence scheduling decisions and gracefully shift the signal control strategy to queue management in high volume/high congestion settings. Specifically, queue-length information is used to establish weights for the sensed vehicle clusters that must be scheduled through a given intersection at any point, and hence bias the wait time minimization calculation. To compute these weights, we develop a model in which successive movement phases are viewed as different states of an Ising model, and parameters quantify strength of interactions. To ensure scalability, queue information is only exchanged between direct neighbors and the asynchronous nature of local intersection scheduling is preserved. We demonstrate the potential of the approach through microscopic traffic simulation of a real-world road network, showing a 60% reduction in average wait times over the baseline schedule-driven approach in heavy traffic scenarios. We also report initial field test results, which show the ability to reduce queues during heavy traffic periods.

Recent work in decentralized, schedule-driven traffic control has demonstrated the ability to significantly improve traffic flow efficiency in complex urban road networks. However, in situations where vehicle volumes increase to the point that the physical capacity of a road network reaches or exceeds saturation, it has been observed that the effectiveness of a schedule-driven approach begins to degrade, leading to progressively higher network congestion. In essence, the traffic control problem becomes less of a scheduling problem and more of a queue management problem in this circumstance. In this paper we propose a composite approach to real-time traffic control that uses sensed information on queue lengths to influence scheduling decisions and gracefully shift the signal control strategy to queue management in high volume/high congestion settings. Specifically, queue-length information is used to establish weights for the sensed vehicle clusters that must be scheduled through a given intersection at any point, and hence bias the wait time minimization calculation. To compute these weights, we develop a model in which successive movement phases are viewed as different states of an Ising model, and parameters quantify strength of interactions. To ensure scalability, queue information is only exchanged between direct neighbors and the asynchronous nature of local intersection scheduling is preserved. We demonstrate the potential of the approach through microscopic traffic simulation of a real-world road network, showing a 60% reduction in average wait times over the baseline schedule-driven approach in heavy traffic scenarios. We also report initial field test results, which show the ability to reduce queues during heavy traffic periods.

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field approaches have been used. However, mean field approximations assume a factorized distribution over node states. Such a distribution seems unlickely in the posterior, as nodes are highly correlated in the prior. Here a structured variational approach is used, where the posterior distribution over the non-evidential nodes is itself approximated by a dynamic tree. It turns out that this form can be used tractably and efficiently. The result is a set of update rules which can propagate information through the network to obtain both a full variational approximation, and the relevant marginals. The progagtion rules are more efficient than the mean field approach and give noticeable quantitative and qualitative improvement in the inference. The marginals calculated give better approximations to the posterior than loopy propagation on a small toy problem.

The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification models with Gaussian processes. In contrast to previous approaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification models with Gaussian processes. In contrast to previous approaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification modelswith Gaussian processes. In contrast to previous approaches, noknowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given. They have been recently introduced into the Neural Computation community (Neal 1996, Williams & Rasmussen 1996, Mackay 1997). If we assume fields with zero prior mean, the statistics of h is entirely defined by the second order correlations C(s, S') E[h(s)h(S')], where E denotes expectations 310 MOpper and 0. Winther with respect to the prior. Interesting examples are C(s, s') (1) C(s, s') (2) The choice (1) can be motivated as a limit of a two-layered neural network with infinitely many hidden units with factorizable input-hidden weight priors (Williams 1997).

A modification is described to the use of mean field approximations in the E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. The modification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models.

A modification is described to the use of mean field approximations in the E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. The modification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models.