Figure 2
From: Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels
Figure illustrating the premise of our proposed algorithm. Panel (a) shows the test data, measured daily maximum temperatures (\(^\circ\)C) from April 10th, 1990 across the United States (\(N=4718\)). This problem size is still well within the capabilities of a standard GP, whose posterior mean is shown in (b). If we employ a flexible, non-stationary, and compactly-supported kernel, we can learn through optimization of the marginal log-likelihood that only a few covariances are of essence for the prediction. Our sparse result is shown in (c). Panels (d) and (e) show the covariance matrix of the dense and sparse GP, respectively, where the sparse covariance only has 1.5% of the non-zero entries of the full dense matrix. The sparsity in this problem is discovered, not induced, leading to an exact GP. This principle, in combination with HPC, for truly large covariance matrices, and constrained function optimization enables GPs to be scaled to tens of millions of data points.
