Simulation-Extrapolation Gaussian Processes for Input Noise Modeling

Input noise is common in situations when data either is coming from unreliable sensors or previous outputs are used as current inputs. Nevertheless, most regression algorithms do not model input noise, inducing thus bias in the regression. We present a method that corrects this bias by repeated regression estimations. In simulation extrapolation we perturb the inputs with additional input noise and by observing the effect of this addition on the result, we estimate what would the prediction be without the input noise. We extend the examination to a non-parametric probabilistic regression, inference using Gaussian processes. We conducted experiments on both synthetic data and in robotics, i.e., Learning the transition dynamics of a dynamical system, showing significant improvements in the accuracy of the prediction.