| In this paper, we extend the use of moderated outputs to the support vector machine (SVM) by making use of a relationship between SVM and the evidence framework. The moderated output is more in line with the Bayesian idea that the posterior weight distribution should be taken into account upon prediction, and it also alleviates the usual tendency of assigning overly high condence to the estimated class memberships of the test patterns. Moreover, the moderated output derived here can be taken as an approximation to the posterior class probability. Hence, meaningful rejection thresholds can be assigned and outputs from several networks can be directly compared. Experimental results on both articial and real-world data are also discussed. Keywords|Support vector machine, Evidence framework, Moderated output, Bayesian I. Introduction I N recent years, there has been a lot of interest in studying the support vector machine (SVM) [1], [2], [3], [4], [5], [6], [7]. SVM is based on the i...

I examine two approximate methods for computational implementation of Bayesian hierarchical models, that is, models which include unknown hyperparameters such as regularization constants. In the `evidence framework' the model parameters are integrated over, and the resulting evidence is maximized over the hyperparameters. The optimized hyperparameters are used to define a Gaussian approximation to the posterior distribution. In the alternative `MAP' method, the true posterior probability is found by integrating over the hyperparameters. The true posterior is then maximized over the model parameters, and a Gaussian approximation is made. The similarities of the two approaches, and their relative merits, are discussed, and comparisons are made with the ideal hierarchical Bayesian solution. In moderately ill-posed problems, integration over hyperparameters yields a probability distribution with a skew peak which causes significant biases to arise in the MAP method. In contrast, the evidence framework is shown to introduce negligible predictive error, under straightforward conditions. General lessons are drawn concerning the distinctive properties of inference in many dimensions.

In this paper we propose new techniques to extract features from protein sequences. We then use the features as inputs for a Bayesian neural network (BNN) and apply the BNN to classifying protein sequences obtained from the PIR protein database maintained at the National Biomedical Research Foundation. To evaluate the performance of the proposed approach, we compare it with other protein classiers built based on sequence alignment and machine learning methods. Experimental results show the high precision of the proposed classi er and the complementarity of the bioinformatics tools studied in the paper.

In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint).