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We present the Gaussian Process\nAutoregressive Regression (GPAR) model, a scalable multi-output GP model that\nis able to capture nonlinear, possibly input-varying, dependencies between\noutputs in a simple and tractable way: the product rule is used to decompose\nthe joint distribution over the outputs into a set of conditionals, each of\nwhich is modelled by a standard GP. GPAR's efficacy is demonstrated on a\nvariety of synthetic and real-world problems, outperforming existing GP models\nand achieving state-of-the-art performance on established benchmarks.","url_abs":"http://arxiv.org/abs/1802.07182v4","url_pdf":"http://arxiv.org/pdf/1802.07182v4.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":"the-gaussian-process-autoregressive","repo_url":"https://github.com/wesselb/gpar","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"the-gaussian-process-autoregressive","repo_url":"https://github.com/beartype/plum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"the-gaussian-process-autoregressive","repo_url":"https://github.com/wesselb/plum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"model","task_name":"model"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.07182","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1802.07182"}},"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. 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