Variational Hilbert Regression with Applications to Terrain Modeling

Abstract

The ability to generate accurate terrain models is of key importance in a wide variety of robotics tasks, ranging from path planning and trajectory optimization to environment exploration and mining applications. This paper introduces a novel regression methodology for terrain modeling that takes place in a Reproducing Kernel Hilbert Space, and can approximate arbitrarily complex functions using Variational Bayesian inference. A sparse kernel is used to efficiently project input points into a high-dimensional feature vector, based on cluster information generated automatically from training data. Each kernel maintains its own regression model, and the entire set is simultaneously optimized in an iterative fashion as more data is collected, to maximize a global variational bound. Additionally, we show how kernel parameters can be jointly learned alongside the regression model parameters, to achieve a better approximation of the underlying function. Experimental results show that the proposed methodology consistently outperforms current state-of-the-art techniques, while maintaining a fully probabilistic treatment of uncertainties and high scalability to large-scale datasets.