There exist radar-based algorithms designed to detect circulations in the atmosphere. Not all detected circulations, however, are associated with tornados on the ground. Outlined herein, is the development of a multi-layered perceptron designed to classify the two types of circulations - nontornadic and tornadic - based on various attributes of the circulations. Special emphasis is placed on the role of local minima in determining the optimal architecture via bootstrapping. 1 Introduction A great deal of effort is required to determine the optimal architecture of a Multilayered Perceptron (MLP) designed to perform a specific task. That issue is important to consider because the nonlinearities inherent in a MLP can allow it to possibly overfit data, leading to poor generalization. The nonlinearity of a MLP is determined primarily by two quantities - the number of hidden nodes, and the magnitude of the weights. This can be seen as follows: If the magnitude of the weights is restricted t...

Both knowledge-based systems and statistical models are typically concerned with making predictions about future observables. Here we focus on assessment of predictive performance and provide two techniques for improving the predictive performance of Bayesian graphical models. First, we present Bayesian model averaging, a technique for accounting for model uncertainty. Second, we describe a technique for eliciting a prior distribution for competing models from domain experts. We explore the predictive performance of both techniques in the context of a urological diagnostic problem. KEYWORDS: Prediction; Bayesian graphical model; Bayesian network; Decomposable model; Model uncertainty; Elicitation. 1 Introduction Both statistical methods and knowledge-based systems are typically concerned with combining information from various sources to make inferences about prospective measurements. Inevitably, to combine information, we must make modeling assumptions. It follows that we should car...

Image subtraction is used in many areas of machine vision to identify small changes between equivalent pairs of images. Often only a small subset of the differences will be of interest. In motion analysis only those differences caused by motion are important, and differences due to other sources only serve to complicate interpretation. Simple image subtraction detects all differences regardless of their source, and is therefore problematic to use. Superior techniques, analogous to standard statistical tests, can isolate localised differences due to motion from global differences due, for example, to illumination changes. Four such techniques are described. In particular, we introduce a new non-parametric statistical measure which allows a direct probabilistic interpretation of image differences. We expect this to be applicable to a wide range of image formation processes. Its application to medical images is discussed. 1

this paper, we present a class of query operators which, for reasons to be explained, we have called pic operators. The pic operators comprise a subclass of the general class of query operators that are expressible within the inference network framework. The subclass has been chosen to satisfy two important design criteria: 1) the operators belonging to the subclass are computationally tractable, and 2) they are intuitively plausible candidates for the modeling of query operators. A wide variety of query operators can be defined as pic operators. The work reported has been principally motivated by the search for more effective Boolean operators. Other approaches to the modeling of Boolean query operators have been tried. As with the inference network, the goal has been to generalize the classical, strict Propositional Logic interpretation of the query operators. The objective of this generalization is twofold. On the one hand, to allow for graduated inputs to the Boolean operators so that the representation of documents in terms of vectors of Boolean characteristics can be extended to vectors of feature weights. Second, to generate real valued operator output so that dichotomous relevance judgments can be replaced by document ranking in response to user's queries. A particularly notable success in this pursuit was reported by Salton, Fox and Wu [Salton et al. 1983; Salton et al. 1983]. Grounded in the geometric metaphor of the vector space model, they defined a general class of "pnorm" operators which extend the traditional operators in a natural way. The experimental results achieved were quite positive. Recent experimentation has shown that system performance is improved by replacing the inference network Boolean operator calculation used in the inquery retrieval syst...

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models’ parameters on these distributions. The small-sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating surveybased probability forecasts.

The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes. It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of “second-guessing ” experts, whose advice depends on the learner’s prediction; this paper assumes that the dependence on the learner’s prediction is continuous. 1

The theoretical background for a program for establishing expert systems on the basis of observations and expert knowledge is presented. Block recursive models form the basis of the statistical modelling. These models, together with various model selection methods for automatic model selection, are presented. Additionally, the connection between a block recursive model and expert systems based on causal probabilistic networks is treated. A medical example concerning diagnosis of coronary artery disease forms the basis for an evaluation of the expert systems established. Keywords: causal probabilistic networks, graphical association models, machine learning, model selection, selection criteria, selection strategies. 1 Introduction BIFROST is a program for semi-automatic knowledge acquisition and is a continuation developments made in (Greve, Hjsgaard, Skjth and Thiesson 1990). The objective is to obtain preliminary causal models for use in the HUGIN expert system shell (Ander...

We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner’s and his own performance using a loss function that may change over time and may be different from the loss functions used by the other experts. The learner’s goal is to perform better or not much worse than each expert, as evaluated by that expert, for all experts simultaneously. If the loss functions used by the experts are all proper scoring rules and all mixable, we show that the defensive forecasting algorithm enjoys the same performance guarantee as that attainable by the Aggregating Algorithm in the standard setting and known to be optimal. This result is also applied to the case of “specialist ” (or “sleeping”) experts. In this case, the defensive forecasting algorithm reduces to a simple modification of the Aggregating Algorithm. 1

Recently, Bayesian methods have been proposed for neural networks to solve regression and classification problems. These methods claim to overcome some difficulties encountered in the standard approach such as overfitting. However, an implementation of the full Bayesian approach to neural networks as suggested in the literature applied to classification problems is not easy. In fact we are not aware of applications of the full approach to real world classification problems.

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical performance guarantee turns out to be rather tight on these data sets, especially in the case of the more extensive tennis data. 1.