Scalable Deep Basis Kernel Gaussian Processes

Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is constructed from a small set of neural-network-parameterized basis functions with an explicit low-rank structure. This formulation immediately enables linear-complexity inference with respect to the number of samples, possibly without inducing points. DBKs provide a unifying perspective that recovers sparse deep kernel learning and Gaussian Bayesian last-layer methods as special cases. We further identify that naively maximizing the marginal likelihood can lead to oversimplified uncertainty and rank-deficient solutions. To address this, we introduce a mini-batch stochastic objective that directly targets the predictive distribution with decoupled regularization. Empirically, DBKs show advantages in predictive accuracy, uncertainty quantification, and computational efficiency across a range of large-scale regression benchmarks.