{"type":"ScholarlyArticle","title":"Hidden 1-Counter Markov Models and How to Learn Them","authors":[{"name":"Mehmet Kurucan","slug":"mehmet-kurucan","given":"Mehmet","family":"Kurucan","affiliation":"Ardahan University , Ardahan , Turkey"},{"name":"Mete Özbaltan","slug":"mete-ozbaltan","given":"Mete","family":"Özbaltan","affiliation":"Erzurum Technical University , Erzurum , Turkey"},{"name":"Sven Schewe","slug":"sven-schewe","given":"Sven","family":"Schewe","affiliation":"University of Liverpool , Liverpool , UK"},{"name":"Dominik Wojtczak","slug":"dominik-wojtczak","given":"Dominik","family":"Wojtczak","affiliation":"University of Liverpool , Liverpool , UK"}],"abstract":"We introduce hidden 1-counter Markov models (H1MMs) as an attractive sweet spot between standard hidden Markov models (HMMs) and probabilistic context-free grammars (PCFGs). Both HMMs and PCFGs have a variety of applications, e.g., speech recognition, anomaly detection, and bioinformatics. PCFGs are more expressive than HMMs, e.g., they are more suited for studying protein folding or natural language processing. However, they suffer from slow parameter fitting, which is cubic in the observation sequence length. The same process for HMMs is just linear using the well-known forward-backward algorithm. We argue that by adding to each state of an HMM an integer counter, e.g., representing the number of clients waiting in a queue, brings its expressivity closer to PCFGs. At the same time, we show that parameter fitting for such a model is computationally inexpensive: it is bi-linear in the length of the observation sequence and the maximal counter value, which grows slower than the observation length. The resulting model of H1MMs allows us to combine the best of both worlds: more expressivity with faster parameter fitting.","doi":"10.24963/ijcai.2022/673","url":"https://ijcai.org/proceedings/2022/673","pdf":"https://ijcai.org/proceedings/2022/0673.pdf","markdown":"https://ijcai.org/proceedings/2022/673.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/673","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Uncertainty in AI","track":"Main Track","number":673,"pages":{"first":4857,"last":4863},"keywords":["Machine Learning: Bayesian Learning","Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis","Machine Learning: Time-series; Data Streams","Uncertainty in AI: Graphical Models","Uncertainty in AI: Bayesian Networks"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986946","length_sec":90,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985089","length_sec":359,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Bahi-Jaber and Pontier, 2003] Narges Bahi-Jaber and Do- minique Pontier. Modeling transmission of directly trans- mitted infectious diseases using colored stochastic petri nets. Mathematical biosciences, 185(1):1-13, 2003.","title":"Modeling transmission of directly transmitted infectious diseases using colored stochastic petri nets","authors":"Bahi-Jaber Pontier, ; Pontier","year":"2003","venue":"Mathematical biosciences","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baker, 1979] James K Baker. Trainable grammars for speech recognition. The Journal of the Acoustical Soci- ety of America, 65(S1):S132-S132, 1979.","title":"Trainable grammars for speech recognition","authors":"K James, Baker","year":"1979","venue":"The Journal of the Acoustical Society of America","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Baum and Petrie, 1966] Leonard E Baum and Ted Petrie. Statistical inference for probabilistic functions of finite state markov chains. The annals of mathematical statis- tics, 37(6):1554-1563, 1966.","title":"Statistical inference for probabilistic functions of finite state markov chains","authors":"E Leonard, Ted Baum, Petrie","year":"1966","venue":"The annals of mathematical statistics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Baum et al., 1970] Leonard E Baum, Ted Petrie, George Soules, and Norman Weiss. A maximization technique oc- curring in the statistical analysis of probabilistic functions of markov chains. The annals of mathematical statistics, 41(1):164-171, 1970.","title":"A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains","authors":"Leonard E Baum, Ted Petrie, George Soules, Norman Weiss","year":"1970","venue":"The annals of mathematical statistics","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Ben-Amram and Genaim, 2013] Amir M Ben-Amram and Samir Genaim. On the linear ranking problem for integer linear-constraint loops. In Proceedings of the 40th Annual ACM Symposium on Principles of programming languages (POPL), pages 51-62, 2013.","title":"On the linear ranking problem for integer linear-constraint loops","authors":"Samir Amir M Ben-Amram, Genaim","year":"2013","venue":"Proceedings of the 40th Annual ACM Symposium on Principles of programming languages (POPL)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bilmes, 2000] Jeff Bilmes. A gentle tutorial of the em algo- rithm and its application to parameter estimation for gaus- sian mixture and hidden markov models. Technical Report ICSI-TR-97-021, University of Berkeley, 4, 06 2000.","title":"A gentle tutorial of the em algorithm and its application to parameter estimation for gaussian mixture and hidden markov models","authors":"Jeff Bilmes","year":"2000","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Braverman, 2006] Mark Braverman. Termination of integer linear programs. In International conference on computer aided verification, pages 372-385. Springer, 2006.","title":"Termination of integer linear programs","authors":"Mark Braverman","year":"2006","venue":"International conference on computer aided verification","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chappelier et al., 1998] J.-C. Chappelier, M. Rajman, and Ch-Lausanne. A generalized cyk algorithm for parsing stochastic cfg, 1998.","title":"A generalized cyk algorithm for parsing stochastic cfg","authors":"J.-C Chappelier, M Rajman, Ch-Lausanne","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chitic and Rosu, 2004] Cristiana Chitic and Daniela Rosu. On validation of xml streams using finite state ma- chines. In Proceedings of the 7th International Workshop on the Web and Databases: colocated with ACM SIG- MOD/PODS 2004, pages 85-90, 2004.","title":"On validation of xml streams using finite state machines","authors":"Cristiana Chitic, Daniela Rosu","year":"2004","venue":"Proceedings of the 7th International Workshop on the Web and Databases: colocated with ACM SIG-MOD/PODS 2004","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Eisner, 2016] Jason Eisner. Inside-outside and forward- backward algorithms are just backprop (tutorial paper). In Proceedings of the Workshop on Structured Prediction for NLP, pages 1-17, Austin, TX, November 2016. Associa- tion for Computational Linguistics.","title":"Inside-outside and forwardbackward algorithms are just backprop","authors":"Jason Eisner","year":"2016","venue":"Proceedings of the Workshop on Structured Prediction for NLP","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Etessami and Yannakakis, 2009] Kousha Etessami and Mi- halis Yannakakis. Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations. Journal of the ACM (JACM), 56(1):1-66, 2009.","title":"Kousha Etessami and Mihalis Yannakakis. Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations","authors":"Yannakakis Etessami","year":"2009","venue":"Journal of the ACM (JACM)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Etessami et al., 2010] Kousha Etessami, Dominik Wo- jtczak, and Mihalis Yannakakis. Quasi-birth-death pro- cesses, tree-like qbds, probabilistic 1-counter automata, and pushdown systems. Perform. Eval., 67(9):837-857, September 2010.","title":"Quasi-birth-death processes, tree-like qbds, probabilistic 1-counter automata, and pushdown systems","authors":"Kousha Etessami, Dominik Wojtczak, Mihalis Yannakakis","year":"2010","venue":"Perform. Eval","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Fine et al., 1998] Shai Fine, Yoram Singer, and Naftali Tishby. The hierarchical hidden markov model: Analysis and applications. Machine learning, 32(1):41-62, 1998.","title":"The hierarchical hidden markov model: Analysis and applications","authors":"Shai Fine, Yoram Singer, Naftali Tishby","year":"1998","venue":"Machine learning","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Fischer et al., 1968] Patrick C Fischer, Albert R Meyer, and Arnold L Rosenberg. Counter machines and counter languages. Mathematical systems theory, 2(3):265-283, 1968.","title":"Counter machines and counter languages","authors":"Albert R Patrick C Fischer, Arnold L Meyer, Rosenberg","year":"1968","venue":"Mathematical systems theory","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Galassi et al., 2007] Ugo Galassi, Attilio Giordana, and Lorenza Saitta. Incremental construction of structured hid- den markov models. In IJCAI, pages 798-803, 2007.","title":"Incremental construction of structured hidden markov models","authors":"Ugo Galassi, Attilio Giordana, Lorenza Saitta","year":"2007","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2007/128"},{"position":16,"raw":"[Lee and Ng, 2005] Honglak Lee and Andrew Y Ng. Spam deobfuscation using a hidden markov model. In CEAS, 2005.","title":"Spam deobfuscation using a hidden markov model","authors":"Lee, Ng ; ] Honglak Lee, Andrew Y Ng","year":"2005","venue":"CEAS","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Lee et al., 2007] Seunghak Lee, Iryoung Jeong, and Se- ungjin Choi. Dynamically weighted hidden markov model for spam deobfuscation. In IJCAI, volume 7, pages 2523- 2529, 2007.","title":"Dynamically weighted hidden markov model for spam deobfuscation","authors":"Lee","year":"2007","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2007/406"},{"position":18,"raw":"[Mayr et al., 2006] Richard Mayr, Antonín Kucera, and Javier Esparza. Model checking probabilistic pushdown automata. Logical Methods in Computer Science, 2, 2006.","title":"Model checking probabilistic pushdown automata","authors":"Richard Mayr, Antonín Kucera, Javier Esparza","year":"2006","venue":"Logical Methods in Computer Science","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Rabiner, 1990] Lawrence R. Rabiner. A tutorial on hidden markov models and selected applications in speech recog- nition. In Alex Waibel and Kai-Fu Lee, editors, Readings in Speech Recognition, pages 267-296.","title":"A tutorial on hidden markov models and selected applications in speech recognition","authors":"Lawrence R Rabiner","year":null,"venue":"Readings in Speech Recognition","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Sakharov and Sakharov, 2018] Alexander Sakharov and Timothy Sakharov. The viterbi algorithm for subsets of stochastic context-free languages. Information Processing Letters, 135:68 -72, 2018.","title":"The viterbi algorithm for subsets of stochastic context-free languages","authors":"Alexander Sakharov, Timothy Sakharov","year":"2018","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Skounakis et al., 2003] Marios Skounakis, Mark Craven, and Soumya Ray. Hierarchical hidden markov models for information extraction. In IJCAI, pages 427-433, 2003.","title":"Hierarchical hidden markov models for information extraction","authors":"Marios Skounakis, Mark Craven, Soumya Ray","year":"2003","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2003/64"},{"position":22,"raw":"[Wojtczak, 2009] Dominik Wojtczak. Recursive Probabilis- tic Models: efficient analysis and implementation. PhD thesis, University of Edinburgh, UK, 2009.","title":"Recursive Probabilistic Models: efficient analysis and implementation","authors":"Dominik Wojtczak","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}