A Bayesian Learning Approach to Wireless Outdoor Heatmap Construction Using Deep Gaussian Process

We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian Process (GP). The proposed approach employs a two-layer hierarchy that is capable of modeling more complex input-output relations than the standard single-layer GP. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead to find the optimal model parameters. Typically, inducing points are used to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may degrade the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experimental results show that the proposed approach can achieve superior performance on various training and testing data configurations compared to canonical deep GP schemes, DNN-based and GP-based methods.