Improved linear prediction through optimal signal discretization

We consider the problem of predicting a target signal {y},as a linear combination of a set of explanatory signals {x_i}. In order to reduce the prediction error, we determine an optimal number of thresholds and their values for each signal {x_i} by maximising the correlation between the thresholded explanatory signals and the target signal {y}. We extend this pairwise quantization technique to a true multivariate thresholder in the case that {y} and {x _i} are positive additive signals by minimising the difference between the entropy of the average of the signals and the average of the entropies of the signals. To illustrate the improvement in prediction using thresholded signals, we consider the problem of predicting the viscosity of rock slurry from reflectance spectra