Variational Inference for Gaussian Process Models with Linear Complexity
This work addresses scalability issues for practitioners using Gaussian process models, enabling adoption of large-scale expressive models, though it is incremental as it builds on existing variational frameworks.
The paper tackles the challenge of large-scale Gaussian process inference by proposing a novel variational model that decouples mean and covariance functions, achieving linear time and space complexity in the number of mean function parameters. Experiments on regression tasks show it greatly outperforms previous sparse variational methods.
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of complex functions. In this work, we propose a novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space. We show that this new parametrization generalizes previous models. Furthermore, it yields a variational inference problem that can be solved by stochastic gradient ascent with time and space complexity that is only linear in the number of mean function parameters, regardless of the choice of kernels, likelihoods, and inducing points. This strategy makes the adoption of large-scale expressive Gaussian process models possible. We run several experiments on regression tasks and show that this decoupled approach greatly outperforms previous sparse variational Gaussian process inference procedures.