Classification using linear models with uncertain weights

Linear models were trained on a simple two-class two-dimensional data set. The network connections, which were crisp, real numbers, were then replaced with interval ranges of real numbers. Crisp input data was propagated through these uncertain-weighted networks to give interval ranges on the output values. The classification rates of the networks could be adjusted by the level of uncertainty in the connections, allowing the user to specify an acceptable misclassification rate and choosing the network with the best corresponding correct classification rate. Vertex propagation, interval arithmetic and affine arithmetic were used to represent the uncertainty in networks with linear and softmax output activation functions and were benchmarked against a simple output threshold approach. It was found that, although the network responses varied, the various techniques returned similar relative classification rates.