{"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/generalised-bayesian-inference-for-discrete","title":"Generalised Bayesian Inference for Discrete Intractable Likelihood","arxiv_id":"2206.08420","date":"2022-06-16","proceeding":null,"authors":["Takuo Matsubara","Jeremias Knoblauch","François-Xavier Briol","Chris. J. Oates"],"abstract":"Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper addresses this computational challenge through the development of a novel generalised Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalised posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant. The statistical properties of the generalised posterior are analysed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalised posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalised Bayesian inference at low computational cost.","url_abs":"https://arxiv.org/abs/2206.08420v2","url_pdf":"https://arxiv.org/pdf/2206.08420v2.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":"generalised-bayesian-inference-for-discrete","repo_url":"https://github.com/takuomatsubara/discrete-fisher-bayes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.08420","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.08420"}},"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/takuomatsubara/discrete-fisher-bayes","reach":null}],"summary":{"ran_violates":1,"ran_honours":1,"unverified":1},"by_repo_kind":{"official":{"samples":3,"ran":2,"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":3,"samples":[{"code_sha256_prefix":"557876ecb0b10ddd","entry":"loss_func_0","repo":"takuomatsubara/discrete-fisher-bayes","repo_kind":"official","path":"CMP/code_beta.py","file_url":"https://github.com/takuomatsubara/discrete-fisher-bayes/blob/HEAD/CMP/code_beta.py","link_basis":"first_harvest_node","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"557876ecb0b10ddd"}},{"code_sha256_prefix":"c515e962e8311c8e","entry":"loss_func_x","repo":"takuomatsubara/discrete-fisher-bayes","repo_kind":"official","path":"CMP/code_beta.py","file_url":"https://github.com/takuomatsubara/discrete-fisher-bayes/blob/HEAD/CMP/code_beta.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"c515e962e8311c8e"}},{"code_sha256_prefix":"5d74354491091cd4","entry":"get_beta_lyddon","repo":"takuomatsubara/discrete-fisher-bayes","repo_kind":"official","path":"CMP/code_beta.py","file_url":"https://github.com/takuomatsubara/discrete-fisher-bayes/blob/HEAD/CMP/code_beta.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"5d74354491091cd4"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}