Abstract
Bayesian inference using Gaussian processes on large datasets have been studied extensively over the past few years. However, little attention has been given on how to apply these on a high resolution input space. By approximating the set of test points (where we want to make predictions, not the set of training points in the dataset) by a kd-tree, a multi-resolution data structure arises that allows for considerable gains in performance and memory usage without a significant loss of accuracy. In this paper, we study the feasibility and efficiency of constructing and using such a kd-tree in Gaussian process regression. We propose a cut-off rule that is easy to interpret and to tune. We show our findings on generated toy data in a 3D point cloud and a simulated 2D vibrometry example. This survey is beneficial for researchers that are working on a high resolution input space. The kd-tree approximation outperforms the naïve Gaussian process implementation in all experiments.
Highlights
Over the past few decades, Gaussian processes (GPs) [1] have proved themselves in a wide variety of fields: geostatistics [2], robotics and adaptive control [3], vehicle pattern recognition and trajectory modelling [4], econometrics [5], indoor map construction and localization [6], reinforcement learning [7], non-rigid shape recovery [8] and time series forecasting [9]
GPs provide predictions accompanied by an uncertainty interval
Big datasets are not an issue in our research, as we aim to gain a maximum amount of information about a large number of test points on a mesh or point cloud by using as few training points as possible
Summary
Over the past few decades, Gaussian processes (GPs) [1] have proved themselves in a wide variety of fields: geostatistics [2], robotics and adaptive control [3], vehicle pattern recognition and trajectory modelling [4], econometrics [5], indoor map construction and localization [6], reinforcement learning [7], non-rigid shape recovery [8] and time series forecasting [9]. GPs provide predictions accompanied by an uncertainty interval These properties are of utmost importance in the medical world [11], in finance [5] or in predictive maintenance [12]. They have a built in mechanism against overfitting [13]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
