{"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/flexible-mean-field-variational-inference","title":"Flexible mean field variational inference using mixtures of non-overlapping exponential families","arxiv_id":"2010.06768","date":"2020-10-14","proceeding":"NeurIPS 2020 12","authors":["Jeffrey P. Spence"],"abstract":"Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however, analytically obtaining a posterior distribution over the parameters of interest is intractable for all but the simplest cases. As a result practitioners must rely on either sampling algorithms such as Markov chain Monte Carlo or variational methods to obtain an approximate posterior. Mean field variational inference is a particularly simple and popular framework that is often amenable to analytically deriving closed-form parameter updates. When all distributions in the model are members of exponential families and are conditionally conjugate, optimization schemes can often be derived by hand. Yet, I show that using standard mean field variational inference can fail to produce sensible results for models with sparsity-inducing priors, such as the spike-and-slab. Fortunately, such pathological behavior can be remedied as I show that mixtures of exponential family distributions with non-overlapping support form an exponential family. In particular, any mixture of a diffuse exponential family and a point mass at zero to model sparsity forms an exponential family. Furthermore, specific choices of these distributions maintain conditional conjugacy. I use two applications to motivate these results: one from statistical genetics that has connections to generalized least squares with a spike-and-slab prior on the regression coefficients; and sparse probabilistic principal component analysis. The theoretical results presented here are broadly applicable beyond these two examples.","url_abs":"https://arxiv.org/abs/2010.06768v1","url_pdf":"https://arxiv.org/pdf/2010.06768v1.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":"flexible-mean-field-variational-inference","repo_url":"https://github.com/jeffspence/non_overlapping_mixtures","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"variable-selection","task_name":"Variable Selection"},{"task_slug":"variational-inference","task_name":"Variational Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2010.06768","atlas_url":"https://app.syntology.ai/?focus=2010.06768","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2010.06768"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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/jeffspence/non_overlapping_mixtures","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":2},"by_repo_kind":{"official":{"samples":2,"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":"093b3d4195543209","entry":"approximation","repo":"jeffspence/non_overlapping_mixtures","repo_kind":"official","path":"code/pyro_code_discrete.py","file_url":"https://github.com/jeffspence/non_overlapping_mixtures/blob/HEAD/code/pyro_code_discrete.py","link_basis":"first_harvest_node","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":"093b3d4195543209"}},{"code_sha256_prefix":"86920c0cc3aa732b","entry":"prs_guide","repo":"jeffspence/non_overlapping_mixtures","repo_kind":"official","path":"code/pyro_code_discrete.py","file_url":"https://github.com/jeffspence/non_overlapping_mixtures/blob/HEAD/code/pyro_code_discrete.py","link_basis":"first_harvest_node","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":"86920c0cc3aa732b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}