Adaptive Cholesky Gaussian Processes
This work addresses computational bottlenecks in Gaussian process inference for large datasets, though it appears incremental as it builds on existing Cholesky decomposition methods.
The paper tackles the problem of scaling Gaussian process regression to large datasets by approximating the model using a subset of data, with the subset size selected adaptively during inference, achieving computational efficiency with minimal overhead.
We present a method to approximate Gaussian process regression models for large datasets by considering only a subset of the data. Our approach is novel in that the size of the subset is selected on the fly during exact inference with little computational overhead. From an empirical observation that the log-marginal likelihood often exhibits a linear trend once a sufficient subset of a dataset has been observed, we conclude that many large datasets contain redundant information that only slightly affects the posterior. Based on this, we provide probabilistic bounds on the full model evidence that can identify such subsets. Remarkably, these bounds are largely composed of terms that appear in intermediate steps of the standard Cholesky decomposition, allowing us to modify the algorithm to adaptively stop the decomposition once enough data have been observed.