Learning Local Error Bars for Nonlinear Regression

We present a new method for obtaining local error bars for nonlinear regression, i.e., estimates of the confidence in predicted values that depend on the input. We approach this problem by applying a maximumlikelihood framework to an assumed distribution of errors. We demonstrate our method first on computer-generated data with locally varying, normally distributed target noise. We then apply it to laser data from the Santa Fe Time Series Competition where the underlying system noise is known quantization error and the error bars give local estimates of model misspecification. In both cases, the method also provides a weightedregression effect that improves generalization performance.