🤖 AI Summary
This work addresses the scalability challenge in Gaussian process quantile regression arising from non-conjugate likelihoods by proposing an efficient inference framework based on sparse Gaussian processes. The method introduces inducing variables to model the quantile function and leverages Laplace approximation for scalable posterior inference. It further decomposes predictive uncertainty into a conditional prior variance and a posterior inducing variance, enabling a novel dual-adaptive mechanism that dynamically optimizes inducing point locations and guides sequential data acquisition. Experimental results demonstrate that the proposed approach maintains the accuracy of Laplace approximation while significantly outperforming fixed sampling strategies, offering clear advantages in both inducing point placement efficiency and model complexity control.
📝 Abstract
Quantile regression aims to estimate the conditional quantiles of a response variable from observed data. In a Bayesian setting, Gaussian process quantile regression provides uncertainty quantification but faces significant computational challenges due to the nonconjugacy of the asymmetric Laplace likelihood and the cost of posterior inference. We develop a sparse Gaussian process framework in which the quantile function is represented through a reduced set of inducing variables and posterior inference is performed using a Laplace approximation. A decomposition of the predictive uncertainty into conditional-prior and posterior-induced variance components is then exploited to drive two complementary adaptive mechanisms: inducing-input infilling and data acquisition. These mechanisms are combined within a sequential algorithm that allocates computational effort toward the dominant source of predictive uncertainty and adaptively controls model complexity. Numerical experiments on benchmark problems demonstrate the accuracy of the Laplace approximation, the benefits of variance-based inducing-input placement, and the effectiveness of the proposed sequential enrichment strategy compared with predefined data-acquisition strategies.