Abstract

We present a new method for obtaining local error bars, i.e., estimates of the confidence in the predicted value that depend on the input. We approach this problem of nonlinear regression in a maximum likelihood framework. We demonstrate our technique first on computer generated data with locally varying, normally distributed target noise. We then apply it to the laser data from the Santa Fe Time Series Competition. Finally, we extend the technique to estimate error bars for iterated predictions, and apply it to the exact competition task where it gives the best performance to date. 1 Obtaining Error Bars Using a Maximum Likelihood Framework 1.1 Motivation and Concept Feed-forward artificial neural networks are widely used and well-suited for nonlinear regression. They can be interpreted as predicting the expected value of the conditional target distribution as a function of (or "conditioned on") the input pattern (e.g., Buntine & Weigend, 1991). This target distribution in re...

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