Hidden Markov Models, a.k.a. State-Space Models

22 Aug 2019 16:26

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Yet Another Inadequate Placeholder

See also: Chains with Complete Connections; Ergodic Theory of Markov and Related Processes; Filtering and State Estimation; Inference for Markov and Hidden Markov Models; Markov Models; Prediction Processes; Markovian (and Conceivably Causal) Representations of Stochastic Processes;

Recommended, bigger picture:
• Andrew M. Fraser, Hidden Markov Models and Dynamical Systems [Review: Statistics of Moving Shadows]
• Hans R. Künsch, "State Space and Hidden Markov Models", pp. 109--173 in Ole E. Barndorff-Nielsen, David R. Cox and Claudia Klüppelberg (eds.), Complex Stochastic Systems
• Lawrence R. Rabiner, "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition", Proceedings of the IEEE 77 (1989): 257--286

Recommended, close-ups:
• M. J. Beal, Z. Ghahramani and C. E. Rasmussen, "The Infinite Hidden Markov Model", in NIPS 14 [link]
• Robert J. Elliott, Lakhdar Aggoun and John B. Moore, Hidden Markov Models: Estimation and Control
• Zoubin Ghahramani and Michael I. Jordan, "Factorial Hidden Markov Models," Machine Learning 29 (1997): 245--273
• D. Hernando, V. Crespi and G. Cybenko, "Efficient Computation of the Hidden Markov Model Entropy for a Given Observation Sequence", IEEE Transactions on Information Theory 51 (2005): 2681--2685 [By "hidden Markov model entropy" they mean the Shannon entropy of the set of hidden-state trajectories compatible with the observation sequence. This has certain connections to the Lloyd-Pagels "thermodynamic depth" complexity measure...]
• Seyoung Kim and Padhraic Smyth, "Segmental Hidden Markov Models with Random Effects for Waveform Modeling", Journal of Machine Learning Research 7 (2006): 945--969
• Jie Li, Jiaxin Wang, Yannan Zhao and Zehong Yang, "Self-adaptive design of hidden Markov models,", Pattern Recognition Letters 25 (2004): 197--210 [A penalized maximum-likelihood approach to selecting the right number of states and, potentially, architecture for HMMs. The penalization scheme is based on various entropies associated with the HMM; it's hard to give these as straight-forward an information-theoretic interpretation as one would like --- it definitely does not seem to be a description length.]

To read:
• David Andrieux, "Bounding the coarse graining error in hidden Markov dynamics", arxiv:1104.1025
• Olivier Aycard, Jean-Francois Mari and Richard Washington, "Learning to automatically detect features for mobile robots using second-order Hidden Markov Models", cs.AI/0501068
• M. Cassandro, A. Galves and E. Löcherbach, "Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields", Journal of Statistical Physics 147 (2012): 795--807, arxiv:1111.1177
• P. Dupont, F. Denis and Y. Esposito, "Links between probabilistic automata and hidden Markov models: probability distributions, learning models and induction algorithms", Pattern Recognition 38 (2005): 1349--1371
• Guangyue Han and Brian Marcus, "Analyticity of Entropy Rate in Families of Hidden Markov Chains", math.PR/0507235
• Andrew Kempe, "Look-Back and Look-Ahead in the Conversion of Hidden Markov Models into Finite State Transducers", cmp-lg/9802001
• Yujian Li, "Hidden Markov models with states depending on observations", Pattern Recognition Letters 26 (2005): 977--984 [From the abstract, this sounds like a rediscovery of stochastic finite automata.]
• Brian Marcus, Karl Petersen and Tsachy Weissman (eds.), Entropy of Hidden Markov Processes and Connections to Dynamical Systems [blurb]
• Mohammad Rezaeian, "Hidden Markov Process: A New Representation, Entropy Rate and Estimation Entropy", cs.IT/0606114
• Sajid Siddiqi and Andrew Moore, "Fast Inference and Learning in Large-State-Space HMMs", ICML 2005 [Abstract, PDF]
• Sajid Siddiqi, Byron Boots, Geoffrey Gordon, "Reduced-Rank Hidden Markov Models", Journal of Machine Learning Research Proceedings 9 (2010): 741--748
• Padhraic Smyth, "Belief networks, hidden Markov models, and Markov random fields: a unifying view", Pattern Recognition Letters 18 (1997): 1261--1268 [PDF preprint]
• Padhraic Smyth, David Heckerman and Michael I. Jordan, "Probabilistic Independence Networks for Hidden Markov Probability Models", Neural Computation 9 (1997): 227--269 [PDF preprint. Reprinted in Jordan and Sejnowski (eds.), Graphical Models, pp. 1--44]
• Vladislav B. Tadic and Arnaud Doucet, "Exponential forgetting and geometric ergodicity for optimal filtering in general state-space models", Stochastic Processes and their Applications 115 (2005): 1408--1436
• Ryan Turner, Marc Deisenroth, Carl Rasmussen, "State-Space Inference and Learning with Gaussian Processes", Journal of Machine Learning Research Proceedings 9 (2010): 868--875
• Ramon van Handel, "Observability and nonlinear filtering", Probability Theory and Related Fields 145 (2009): 35--74, arxiv:0708.3412
• M. Vidyasagar, Hidden Markov Processes: Theory and Applications to Biology
• Ingmar Visser and Maarten Speekenbrink, "depmixS4: An R Package for Hidden Markov Models", Journal of Statistical Software 36 (2010): 7
• L. Xie, V. A. Ugrinovskii and I. R. Petersen, "Probabilistic Distances Between Finite-State Finite-Alphabet Hidden Markov Models", IEEE Transactions on Automatic Control 50 (2005): 505--511
• G. G. Yin and V. Kirshnamurthy, "LMS Algorithms for Tracking Slow Markov Chains With Applications to Hidden Markov Estimation and Adaptive Multiuser Detection", IEEE Transactions on Information Theory 51 (2005): 2475--2490
• Xiaoxi Zhang, Timothy D. Johnson, Roderick J. A. Little, Yue Cao, "Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation", Annals of Applied Statistics 2 (2008): 736--755 = arxiv:0807.4672
• Or Zuk, Eytan Domany, Ido Kanter, Michael Aizenman
  • "Taylor series expansions for the entropy rate of Hidden Markov Processes", cs.IT/0510005
  • "From finite-system entropy to entropy rate for a Hidden Markov Process", cs.IT/0510016