Constructing Normalized Nonconformity Measures based on Maximizing Predictive Efficiency

The problem of regression in the inductive conformal prediction framework is addressed to provide prediction intervals that are optimized by predictive efficiency. A differentiable function is used to approximate the exact optimization problem of minimizing predictive inefficiency on a training data set using a conformal predictor based on a parametric normalized nonconformity measure. Gradient descent is then used to find a solution. Since the optimization approximates the conformal predictor, this method is called surrogate conformal predictor optimization. Experiments are reported that show that it results in conformal predictors that provide improved predictive efficiency for regression problems on several data sets, whilst remaining reliable. It is also shown that the optimal parameter values typically differ for different confidence levels. Using house price data, alternative measures of inefficiency are explored to address different application requirements.