Adaptive Cholesky Gaussian Processes

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  • Simon Bartels
  • Kristoffer Stensbo-Smidt
  • Pablo Moreno-Muñoz
  • Boomsma, Wouter
  • Jes Frellsen
  • Søren Hauberg
We present a method to approximate Gaussian process regression models to 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.
Original languageEnglish
JournalProceedings of Machine Learning Research
Pages (from-to)408--452
Number of pages44
Publication statusPublished - 2023
Event26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain
Duration: 25 Apr 202327 Apr 2023


Conference26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023

ID: 344671585