{"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/approximation-complexity-of-maximum-a","title":"Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks","arxiv_id":"1703.06045","date":"2017-03-17","proceeding":null,"authors":["Diarmaid Conaty","Denis D. Mauá","Cassio P. de Campos"],"abstract":"We discuss the computational complexity of approximating maximum a posteriori\ninference in sum-product networks. We first show NP-hardness in trees of height\ntwo by a reduction from maximum independent set; this implies\nnon-approximability within a sublinear factor. We show that this is a tight\nbound, as we can find an approximation within a linear factor in networks of\nheight two. We then show that, in trees of height three, it is NP-hard to\napproximate the problem within a factor $2^{f(n)}$ for any sublinear function\n$f$ of the size of the input $n$. Again, this bound is tight, as we prove that\nthe usual max-product algorithm finds (in any network) approximations within\nfactor $2^{c \\cdot n}$ for some constant $c < 1$. Last, we present a simple\nalgorithm, and show that it provably produces solutions at least as good as,\nand potentially much better than, the max-product algorithm. We empirically\nanalyze the proposed algorithm against max-product using synthetic and\nrealistic networks.","url_abs":"http://arxiv.org/abs/1703.06045v5","url_pdf":"http://arxiv.org/pdf/1703.06045v5.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":"approximation-complexity-of-maximum-a","repo_url":"https://github.com/RenatoGeh/gospn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1703.06045","atlas_url":"https://app.syntology.ai/?focus=1703.06045","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}