Stacked Gaussian Process Learning

Abstract

Triggered by a market relevant application that involves making joint predictions of pedestrian and public transit flows in urban areas, we address the question of how to utilize hidden common cause relations among variables of interest in order to improve performance in the two related regression tasks. Specifically, we propose stacked Gaussian process learning, a meta-learning scheme in which a base Gaussian process is enhanced by adding the posterior covariance functions of other related tasks to its covariance function in a stage-wise optimization. The idea is that the stacked posterior covariances encode the hidden common causes among variables of interest that are shared across the related regression tasks. Stacked Gaussian process learning is efficient, capable of capturing shared common causes, and can be implemented with any kind of standard Gaussian process regression model such as sparse approximations and relational variants. Our experimental results on real-world data from the market relevant application show that stacked Gaussian processes learning can significantly improve prediction performance of a standard Gaussian process.

Gaussian Process Decentralized Data Fusion and Active Sensing for Spatiotemporal Traffic Modeling and Prediction in Mobility-on-Demand Systems

“…The work of [15] used GP to represent the traffic flow over a network of only highways and defined the correlation of speeds between highway segments to depend only on the geodesic (i.e., shortest path) distance of these segments with respect to the network topology; their features are not considered. The work of [43] maintained a mixture of two independent GPs for flow prediction such that the correlation structure of one GP utilized road segment features while that of the other GP depended on manually specified relations (instead of geodesic distance) between segments with respect to an undirected network topology. Different from the above works, we propose a relational GP whose correlation structure exploits the geodesic distance between segments based on the topology of a directed road network with vertices denoting road segments and edges indicating adjacent segments weighted by dissimilarity of their features, hence tightly integrating the features and relational information.…”

“…The first two equalities expand the second component by the same trick as that in (43). The third and fourth equalities exploit (10) and (12), respectively.…”

“…By using similar tricks in (43) and (44), we can derive the expressions of the remaining two components.…”

“…The third equality is due to the definition of global summary (11). The fourth and fifth equalities are due to (43) and (44) The first equality is by definition (24). The second equality is due to (40).…”

Local Gaussian Processes for Efficient Fine-Grained Traffic Speed Prediction

“…"Short-term" can be subjectively defined based on the temporal scale of the sensor readings. strated to be an effective tool for modeling and predicting various traffic phenomena such as mobility demand [8], traffic congestion [25], short-term traffic volume [44], travel time [18], and pedestrian and public transit flows in urban areas [28]. Indeed, comparative studies on short-term traffic volume prediction showed that GPs outperform other methods such as autoregressive integrated moving average, support vector machine, and multilayer feedforward neural network for the task [44], [48].…”