{"type":"ScholarlyArticle","title":"Algorithmic Improvements in Approximate Counting for Probabilistic Inference: From Linear to Logarithmic SAT Calls","authors":[{"name":"Supratik Chakraborty","slug":"supratik-chakraborty","given":"Supratik","family":"Chakraborty","affiliation":""},{"name":"Kuldeep S. Meel","slug":"kuldeep-s-meel","given":"Kuldeep S.","family":"Meel","affiliation":""},{"name":"Moshe Y. Vardi","slug":"moshe-y-vardi","given":"Moshe Y.","family":"Vardi","affiliation":""}],"abstract":"Probabilistic inference via model counting has emerged as a scalable technique with strong formal guarantees, thanks to recent advances in hashing-based approximate counting. State-of-the-art hashing-based counting algorithms use an NP oracle, such that the number of oracle invocations grows linearly in the number of variables n in the input constraint. We present a new approach to hashing-based approximate model counting in which the number of oracle invocations grows logarithmically in n, while still providing strong theoretical guarantees. We use this technique to design an algorithm for #CNF with strongly probably approximately correct (SPAC) guarantees, i.e. PAC guarantee plus expected return value matching the exact model count. Our experiments show that this algorithm outperforms state-of-the-art techniques for approximate counting by 1-2 orders of magnitude in running time. We also show that our algorithm can be easily adapted to give a new fully polynomial randomized approximation scheme (FPRAS) for #DNF.","doi":null,"url":"https://ijcai.org/proceedings/2016/503","pdf":"https://ijcai.org/proceedings/2016/0503.pdf","markdown":"https://ijcai.org/proceedings/2016/503.md","bibtex":"https://ijcai.org/proceedings/2016/bibtex/503","volume":{"slug":"2016","title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2016","url":"https://ijcai.org/proceedings/2016/","year":2016,"location":"New York, NY, USA","dates":"9–15 July 2016","editors":"Subbarao Kambhampati","isbn":"978-1-57735-770-4; 978-1-57735-771-1","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":503,"pages":{"first":3569,"last":3575},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}