Three contributions to developing an algorithm for assisting engineers indesigning analog circuits are provided in this paper. First, a method for representing highly nonlinear and noncontinuous analog circuits using Kirchoff current law potential functions within the context of a Markov field is described. Second, a relatively efficient algorithmfor optimizing the Markov field objective function is briefly described and the convergence proof is briefly sketched. And third, empirical results illustrating the strengths and limitations ofthe approach are provided within the context of a JFET transistor design problem. The proposed algorithm generated a set of circuit components for the JFET circuit model that accurately generated the desired characteristic curves. 1 Analog circuit design using Markov random fields

We propose a new Markov Chain Monte Carlo algorithm which is a generalization ofthe stochastic dynamics method. The algorithm performs exploration of the state space using its intrinsic geometric structure, facilitating efficientsampling of complex distributions. Applied to Bayesian learning in neural networks, our algorithm was found to perform at least as well as the best state-of-the-art method while consuming considerably less time. 1 Introduction

In recent years, Bayesian networks have become highly successful tool for diagnosis, analysis,and decision making in real-world domains. We present an efficient algorithm for learning Bayes networks from data.

The support vector machine (SVM) is a state-of-the-art technique for regression and classification, combining excellent generalisation properties with a sparse kernel representation. However, it does suffer from a number of disadvantages, notably the absence of probabilistic outputs,the requirement to estimate a tradeoff parameter and the need to utilise'Mercer' kernel functions. In this paper we introduce the Relevance Vector Machine (RVM), a Bayesian treatment ofa generalised linear model of identical functional form to the SVM. The RVM suffers from none of the above disadvantages, and examples demonstrate that for comparable generalisation performance, theRVM requires dramatically fewer kernel functions.

New functionals for parameter (model) selection of Support Vector Machines areintroduced based on the concepts of the span of support vectors and rescaling of the feature space. It is shown that using these functionals, onecan both predict the best choice of parameters of the model and the relative quality of performance for any value of parameter.

The problem of reinforcement learning in a non-Markov environment is explored using a dynamic Bayesian network, where conditional independence assumptionsbetween random variables are compactly represented by network parameters. The parameters are learned online, and approximations areused to perform inference and to compute the optimal value function. The relative effects of inference and value function approximations onthe quality of the final policy are investigated, by learning to solve a moderately difficult driving task. The two value function approximations, linearand quadratic, were found to perform similarly, but the quadratic model was more sensitive to initialization. Both performed below thelevel of human performance on the task.

We describe a new incremental algorithm for training linear threshold functions:the Relaxed Online Maximum Margin Algorithm, or ROMMA. ROMMA can be viewed as an approximation to the algorithm that repeatedly chooses the hyperplane that classifies previously seen examples correctlywith the maximum margin. It is known that such a maximum-margin hypothesis can be computed by minimizing the length of the weight vector subject to a number of linear constraints. ROMMA works by maintaining a relatively simple relaxation of these constraints that can be efficiently updated. We prove a mistake bound for ROMMA that is the same as that proved for the perceptron algorithm. Our analysis implies that the more computationally intensive maximum-margin algorithm alsosatisfies this mistake bound; this is the first worst-case performance guaranteefor this algorithm. We describe some experiments using ROMMA and a variant that updates its hypothesis more aggressively as batch algorithms to recognize handwritten digits. The computational complexity and simplicity of these algorithms is similar to that of perceptron algorithm,but their generalization is much better. We describe a sense in which the performance of ROMMA converges to that of SVM in the limit if bias isn't considered.

I present a simple variation of importance sampling that explicitly searches forimportant regions in the target distribution. I prove that the technique yieldsunbiased estimates, and show empirically it can reduce the variance of standard Monte Carlo estimators. This is achieved by concentrating samplesin more significant regions of the sample space. 1 Introduction It is well known that general inference and learning with graphical models is computationally hard[1] and it is therefore necessary to consider restricted architectures [13], or approximate algorithms to perform these tasks [3, 7]. Among the most convenient and successful techniques are stochastic methods which are guaranteed to converge to a correct solution in the limit oflarge samples [10, 11, 12, 15]. These methods can be easily applied to complex inference problems that overwhelm deterministic approaches.

Independent component analysis of natural images leads to emergence ofsimple cell properties, Le. linear filters that resemble wavelets or Gabor functions. In this paper, we extend ICA to explain further properties of VI cells.

The neocortex is characterized by an extensive system of recurrent excitatory connections between neurons in a given area.