## Expectation maximization and complex duration distributions for continuous time Bayesian networks (2005)

### Cached

### Download Links

Venue: | In UAI ’05 |

Citations: | 18 - 6 self |

### BibTeX

@INPROCEEDINGS{Nodelman05expectationmaximization,

author = {Uri Nodelman},

title = {Expectation maximization and complex duration distributions for continuous time Bayesian networks},

booktitle = {In UAI ’05},

year = {2005},

pages = {421--430}

}

### OpenURL

### Abstract

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning the parameters and structure of a CTBN from partially observed data. We show how to apply expectation maximization (EM) and structural expectation maximization (SEM) to CTBNs. The availability of the EM algorithm allows us to extend the representation of CTBNs to allow a much richer class of transition durations distributions, known as phase distributions. This class is a highly expressive semi-parametric representation, which can approximate any duration distribution arbitrarily closely. This extension to the CTBN framework addresses one of the main limitations of both CTBNs and DBNs — the restriction to exponentially / geometrically distributed duration. We present experimental results on a real data set of people’s life spans, showing that our algorithm learns reasonable models — structure and parameters — from partially observed data, and, with the use of phase distributions, achieves better performance than DBNs. 1

### Citations

8198 | Maximum likelihood from incomplete data via the EM algorithm
- Dempster, Laird, et al.
- 1977
(Show Context)
Citation Context ...ore, learning networks from partially observed data is an important problem with real-world significance. In this paper, we provide an algorithm, based on the Expectation Maximization (EM) algorithm (=-=Dempster et al., 1977-=-), for learning CTBN parameters from partially observable data. We also provide an extension, based on structural EM (Friedman 1997; 1998), for learning the network structure from such data. Our algor... |

839 | An introduction to hidden Markov models
- Rabiner, Juang
- 1986
(Show Context)
Citation Context ...ons, achieves better performance than DBNs. 1 Introduction Many applications involve reasoning about a complex system that evolves over time. Standard frameworks, such as hidden Markov models (HMMs) (=-=Rabiner & Juang, 1986-=-) and dynamic Bayesian networks (DBNs) (Dean & Kanazawa, 1989), discretize time at fixed intervals, known as time slices, and then model the system as evolving discretely from one time slice to the ne... |

563 |
Matrix-Geometric Solutions in Stochastic Models
- Neuts
(Show Context)
Citation Context ... are simply exponential distributions. The general class is highly expressive: any distribution can be approximated with arbitrary precision by a phase distribution with some finite number of phases (=-=Neuts, 1981-=-). A commonly used subclass of phase distributions is the Erlangian-p which can be constructed with a chain-structured subsystem of p phases, where all phases have the same exit intensity. 5.2 CTBN Du... |

462 |
A model for reasoning about persistence and causation
- Dean, Kanazawa
- 1989
(Show Context)
Citation Context ...ny applications involve reasoning about a complex system that evolves over time. Standard frameworks, such as hidden Markov models (HMMs) (Rabiner & Juang, 1986) and dynamic Bayesian networks (DBNs) (=-=Dean & Kanazawa, 1989-=-), discretize time at fixed intervals, known as time slices, and then model the system as evolving discretely from one time slice to the next. However, in many systems, there is no natural time granul... |

237 |
On cox processes and credit risky securities
- Lando
- 1998
(Show Context)
Citation Context ...ver continuous time. For discrete state systems, such representations include event history analysis (Blossfeld et al., 1988; Blossfeld & Rohwer, 1995) and Markov process models (Duffie et al., 1996; =-=Lando, 1998-=-). Nodelman et al. (2002) extend these representations with ideas from the framework of Bayesian networks, to define continuous time Bayesian networks (CTBNs) — a structured representation for complex... |

218 | The Bayesian structural EM algorithm - Friedman - 1998 |

121 | Learning Belief Networks in the Presence of Missing Values and Hidden
- Friedman
- 1995
(Show Context)
Citation Context ...rithm, based on the Expectation Maximization (EM) algorithm (Dempster et al., 1977), for learning CTBN parameters from partially observable data. We also provide an extension, based on structural EM (=-=Friedman 1997-=-; 1998), for learning the network structure from such data. Our algorithm also provides us with a solution to one of the major limitations of both CTBN and DBN models — their use of a transition model... |

60 | Continuous time Bayesian networks - Nodelman, Shelton, et al. - 2002 |

22 |
Probability distributions of phase type
- Neuts
- 1975
(Show Context)
Citation Context ...r limitations of both CTBN and DBN models — their use of a transition model which evolves exponentially (or geometrically) with time. In particular, we build on the rich class of phase distributions (=-=Neuts 1975-=-; 1981), showing how to integrate them into a CTBN model, and how to use our EM algorithm to learn them from data. We present results of our learning algorithm on real world data related to people’s l... |

20 |
Expectation propagation for continuous time Bayesian networks
- Nodelman, Koller, et al.
- 2005
(Show Context)
Citation Context ...ssages αt, β w. It must also be able to extract the relevant sufficient statistics — themselves a sum over an exponentially large space — from the approximate messages efficiently. A companion paper (=-=Nodelman et al., 2005-=-) provides a cluster graph inference algorithm which can be used to perform this type of approximate inference. For each segment [ti, ti+1) of continuous fixed evidence, we construct a cluster graph d... |

18 |
Event History Analysis
- Blossfeld, Hammerle, et al.
- 1989
(Show Context)
Citation Context ...tion of different variables in the system. Another approach is to model such systems as evolving over continuous time. For discrete state systems, such representations include event history analysis (=-=Blossfeld et al., 1988-=-; Blossfeld & Rohwer, 1995) and Markov process models (Duffie et al., 1996; Lando, 1998). Nodelman et al. (2002) extend these representations with ideas from the framework of Bayesian networks, to def... |

18 | Parameter estimation of partially observed continuous time stochastic processes via the EM algorithm - Dembo, Zeitouni - 1986 |

15 | Maximum likelihood theory for incomplete data from an exponential family - Sundberg - 1974 |

12 | D.S.: Extending continuous time Bayesian networks - Gopalratnam, Kautz, et al. |

10 |
Techniques of Event History Modeling
- Blossfeld, Rowher
- 1995
(Show Context)
Citation Context ...les in the system. Another approach is to model such systems as evolving over continuous time. For discrete state systems, such representations include event history analysis (Blossfeld et al., 1988; =-=Blossfeld & Rohwer, 1995-=-) and Markov process models (Duffie et al., 1996; Lando, 1998). Nodelman et al. (2002) extend these representations with ideas from the framework of Bayesian networks, to define continuous time Bayesi... |

1 |
Fitting phasetype dist via the EM algorithm
- Asmussen, Nerman, et al.
- 1996
(Show Context)
Citation Context ...cular, EM is not required necessary to learn distributions in these classes; however, these subclasses have several drawbacks, including reduced expressivity, especially with small numbers of phases (=-=Asmussen et al., 1996-=-). Our method, as it is based on a general EM algorithm, allows the use of general phase distributions in CTBNs without restriction. When using this phase modelling method, the structure of the intens... |

1 |
Recursive valuation of defaultable sec
- Duffie, Schroder, et al.
- 1996
(Show Context)
Citation Context ...systems as evolving over continuous time. For discrete state systems, such representations include event history analysis (Blossfeld et al., 1988; Blossfeld & Rohwer, 1995) and Markov process models (=-=Duffie et al., 1996-=-; Lando, 1998). Nodelman et al. (2002) extend these representations with ideas from the framework of Bayesian networks, to define continuous time Bayesian networks (CTBNs) — a structured representatio... |

1 | An EM algorithm for training hidden substitution models - Holmes, Rubin - 2002 |

1 | CTBNs for inferring users’ presence and activities with extensions for modeling and evaluation - Nodelman, Horvitz - 2003 |