Open access
Date
2023Type
- Conference Paper
ETH Bibliography
yes
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Abstract
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and symmetries, by turning them into a vertex set of an appropriate metagraph. Building on this, we describe the class of priors that respect this structure and are analogous to the Euclidean isotropic processes, like squared exponential or Matérn. We propose an efficient computational technique for the ostensibly intractable problem of evaluating these priors’ kernels, making such Gaussian processes usable within the usual toolboxes and downstream applications. We go further to consider sets of equivalence classes of unweighted graphs and define the appropriate versions of priors thereon. We prove a hardness result, showing that in this case, exact kernel computation cannot be performed efficiently. However, we propose a simple Monte Carlo approximation for handling moderately sized cases. Inspired by applications in chemistry, we illustrate the proposed techniques on a real molecular property prediction task in the small data regime. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000652282Publication status
publishedExternal links
Book title
Proceedings of The 26th International Conference on Artificial Intelligence and StatisticsJournal / series
Proceedings of Machine Learning ResearchVolume
Pages / Article No.
Publisher
PMLREvent
Subject
Gaussian ProcessesOrganisational unit
03908 - Krause, Andreas / Krause, Andreas
Funding
180544 - NCCR Catalysis (phase I) (SNF)
608881 - ETH Zurich Postdoctoral Fellowship Program II (EC)
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ETH Bibliography
yes
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