Estimation of individual prediction reliability using the local sensitivity analysis

For a given prediction model, some predictions may be reliable while others may be unreliable. The average accuracy of the system cannot provide the reliability estimate for a single particular prediction. The measure of individual prediction reliability can be important information in risk-sensitive applications of machine learning (e.g. medicine, engineering, business). We define empirical measures for estimation of prediction accuracy in regression. Presented measures are based on sensitivity analysis of regression models. They estimate reliability for each individual regression prediction in contrast to the average prediction reliability of the given regression model. We study the empirical sensitivity properties of five regression models (linear regression, locally weighted regression, regression trees, neural networks, and support vector machines) and the relation between reliability measures and distribution of learning examples with prediction errors for all five regression models. We show that the suggested methodology is appropriate only for the three studied models: regression trees, neural networks, and support vector machines, and test the proposed estimates with these three models. The results of our experiments on 48 data sets indicate significant correlations of the proposed measures with the prediction error.