{"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/bayesian-sparse-reconstruction-a-brute-force","title":"Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning","arxiv_id":"1809.04598","date":"2018-09-12","proceeding":null,"authors":["Edward Higson","Will Handley","Michael Hobson","Anthony Lasenby"],"abstract":"We present a principled Bayesian framework for signal reconstruction, in\nwhich the signal is modelled by basis functions whose number (and form, if\nrequired) is determined by the data themselves. This approach is based on a\nBayesian interpretation of conventional sparse reconstruction and\nregularisation techniques, in which sparsity is imposed through priors via\nBayesian model selection. We demonstrate our method for noisy 1- and\n2-dimensional signals, including astronomical images. Furthermore, by using a\nproduct-space approach, the number and type of basis functions can be treated\nas integer parameters and their posterior distributions sampled directly. We\nshow that order-of-magnitude increases in computational efficiency are possible\nfrom this technique compared to calculating the Bayesian evidences separately,\nand that further computational gains are possible using it in combination with\ndynamic nested sampling. Our approach can also be readily applied to neural\nnetworks, where it allows the network architecture to be determined by the data\nin a principled Bayesian manner by treating the number of nodes and hidden\nlayers as parameters.","url_abs":"http://arxiv.org/abs/1809.04598v2","url_pdf":"http://arxiv.org/pdf/1809.04598v2.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":"bayesian-sparse-reconstruction-a-brute-force","repo_url":"https://github.com/ejhigson/bsr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}