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—We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c = 1, º, m. For a two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y) = 1/(1 + e-y). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide… (More)

In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes by gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies… (More)

Two popular approaches to forming bounds in approximate Bayesian inference are local variational methods and minimal Kullback-Leibler divergence methods. For a large class of models we explicitly relate the two approaches , showing that the local variational method is equivalent to a weakened form of Kullback-Leibler Gaussian approximation. This gives a… (More)

We investigate Gaussian Kullback-Leibler (G-KL) variational approximate inference techniques for Bayesian generalised linear models and various extensions. In particular we make the following novel contributions: sufficient conditions for which the G-KL objective is differentiable and convex are described; constrained parameterisations of Gaussian… (More)

- Daniel S Levine, Emilio Frazzoli, John Deyst, Karen Willcox, Nick Roy, Erica Funkhouser +8 others
- 2010

This thesis introduces the Information-rich Rapidly-exploring Random Tree (IRRT), an extension of the RRT algorithm that embeds information collection as predicted using Fisher information matrices. The primary contribution of this trajectory generation algorithm is target-based information maximization in general (possibly heavily constrained)… (More)

We propose a simple information-theoretic approach to soft clustering based on maximizing the mutual information I(x, y) between the unknown cluster labels y and the training patterns x with respect to parameters of specifically constrained encoding distributions. The constraints are chosen such that patterns are likely to be clustered similarly if they lie… (More)

We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman 'Filter' and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard Kim smoothing approach by… (More)

The full Bayesian method for applying neural networks to a prediction problem is to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these inte-grals are not tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian… (More)

- David Barber, Christopher K I Williams
- 1997

The full Bayesian method for applying neural networks to a prediction problem is to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these inte-grals are not tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian… (More)

We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. Based on interaction with the environment, an estimate of the transition matrix is obtained from which the optimal decision policy is formed. The classical maximum likelihood point estimate of the transition model does not reflect the uncertainty in… (More)