Adaptive Basis Function Selection for Computationally Efficient Predictions
This work addresses computational efficiency for engineers using Basis Function expansions, though it is incremental as it builds on existing methods.
The paper tackles the quadratic computational complexity of computing predictive variance in Basis Function expansions by developing a method to automatically select the most important basis functions for prediction in sub-domains, achieving reductions of 50-75% in computational complexity while maintaining predictive accuracy.
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and straightforward model to use, they suffer from quadratic computational complexity in the number of BFs if the predictive variance is to be computed. We develop a method to automatically select the most important BFs for prediction in a sub-domain of the model domain. This significantly reduces the computational complexity of computing predictions while maintaining predictive accuracy. The proposed method is demonstrated using two numerical examples, where reductions up to 50-75% are possible without significantly reducing the predictive accuracy.