{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stationary-kernels-and-gaussian-processes-on","title":"Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case","arxiv_id":"2208.14960","date":"2022-08-31","proceeding":null,"authors":["Iskander Azangulov","Andrei Smolensky","Alexander Terenin","Viacheslav Borovitskiy"],"abstract":"Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many applications, particularly in physical sciences and engineering, but also in areas such as geostatistics and neuroscience, invariance to symmetries is one of the most fundamental forms of prior information one can consider. The invariance of a Gaussian process' covariance to such symmetries gives rise to the most natural generalization of the concept of stationarity to such spaces. In this work, we develop constructive and practical techniques for building stationary Gaussian processes on a very large class of non-Euclidean spaces arising in the context of symmetries. Our techniques make it possible to (i) calculate covariance kernels and (ii) sample from prior and posterior Gaussian processes defined on such spaces, both in a practical manner. This work is split into two parts, each involving different technical considerations: part I studies compact spaces, while part II studies non-compact spaces possessing certain structure. Our contributions make the non-Euclidean Gaussian process models we study compatible with well-understood computational techniques available in standard Gaussian process software packages, thereby making them accessible to practitioners.","url_abs":"https://arxiv.org/abs/2208.14960v4","url_pdf":"https://arxiv.org/pdf/2208.14960v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"stationary-kernels-and-gaussian-processes-on","repo_url":"https://github.com/imbirik/liestationarykernels","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2208.14960","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2208.14960"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/imbirik/liestationarykernels","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":3},"by_repo_kind":{"official":{"samples":3,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"3a19ff86ece77ad1","entry":"GOE_sampler","repo":"imbirik/liestationarykernels","repo_kind":"official","path":"src/lie_stationary_kernels/utils.py","file_url":"https://github.com/imbirik/liestationarykernels/blob/HEAD/src/lie_stationary_kernels/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"3a19ff86ece77ad1"}},{"code_sha256_prefix":"c401d5bc00d564da","entry":"triu_ind","repo":"imbirik/liestationarykernels","repo_kind":"official","path":"src/lie_stationary_kernels/utils.py","file_url":"https://github.com/imbirik/liestationarykernels/blob/HEAD/src/lie_stationary_kernels/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c401d5bc00d564da"}},{"code_sha256_prefix":"9478a12bcf71e83f","entry":"vander_det","repo":"imbirik/liestationarykernels","repo_kind":"official","path":"src/lie_stationary_kernels/utils.py","file_url":"https://github.com/imbirik/liestationarykernels/blob/HEAD/src/lie_stationary_kernels/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9478a12bcf71e83f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}