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370
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 564 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
The Infinite Hidden Markov Model
 Machine Learning
, 2002
"... We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. Th ..."
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Cited by 488 (33 self)
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We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying statetransition matrix, and the expected number of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infiniteconsider, for example, symbols being possible words appearing in English text.
DecisionTheoretic Planning: Structural Assumptions and Computational Leverage
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1999
"... Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives ..."
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Cited by 417 (4 self)
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Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory. This paper presents an overview and synthesis of MDPrelated methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to de...
The Lumière Project: Bayesian User Modeling for Inferring the Goals and Needs of Software Users
 In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence
, 1998
"... The Lumi`ere Project centers on harnessing probability and utility to provide assistance to computer software users. We review work on Bayesian user models that can be employed to infer a user's needs by considering a user's background, actions, and queries. Several problems were tackled in Lumi`ere ..."
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Cited by 308 (17 self)
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The Lumi`ere Project centers on harnessing probability and utility to provide assistance to computer software users. We review work on Bayesian user models that can be employed to infer a user's needs by considering a user's background, actions, and queries. Several problems were tackled in Lumi`ere research, including (1) the construction of Bayesian models for reasoning about the timevarying goals of computer users from their observed actions and queries, (2) gaining access to a stream of events from software applications, (3) developing a language for transforming system events into observational variables represented in Bayesian user models, (4) developing persistent profiles to capture changes in a user's expertise, and (5) the development of an overall architecture for an intelligent user interface. Lumi`ere prototypes served as the basis for the Office Assistant in the Microsoft Office '97 suite of productivity applications. 1 Introduction Uncertainty is...
Tractable inference for complex stochastic processes
 In Proc. UAI
, 1998
"... The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a gi ..."
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Cited by 265 (13 self)
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The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy. 1
An Algorithm for Probabilistic Planning
, 1995
"... We define the probabilistic planning problem in terms of a probability distribution over initial world states, a boolean combination of propositions representing the goal, a probability threshold, and actions whose effects depend on the executiontime state of the world and on random chance. Adoptin ..."
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Cited by 258 (18 self)
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We define the probabilistic planning problem in terms of a probability distribution over initial world states, a boolean combination of propositions representing the goal, a probability threshold, and actions whose effects depend on the executiontime state of the world and on random chance. Adopting a probabilistic model complicates the definition of plan success: instead of demanding a plan that provably achieves the goal, we seek plans whose probability of success exceeds the threshold. In this paper, we present buridan, an implemented leastcommitment planner that solves problems of this form. We prove that the algorithm is both sound and complete. We then explore buridan's efficiency by contrasting four algorithms for plan evaluation, using a combination of analytic methods and empirical experiments. We also describe the interplay between generating plans and evaluating them, and discuss the role of search control in probabilistic planning. 3 We gratefully acknowledge the comment...
RaoBlackwellised Particle Filtering for Dynamic Bayesian Networks
"... Particle filters (PFs) are powerful samplingbased inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and nonstationarity. They have appeared in several fields under such names as “conde ..."
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Cited by 256 (10 self)
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Particle filters (PFs) are powerful samplingbased inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and nonstationarity. They have appeared in several fields under such names as “condensation”, “sequential Monte Carlo” and “survival of the fittest”. In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as RaoBlackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that RaoBlackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely nonstationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some Þnite dimensional optimal filters.
Exploiting structure in policy construction
 IJCAI95, pp.1104–1111
, 1995
"... Markov decision processes (MDPs) have recently been applied to the problem of modeling decisiontheoretic planning. While traditional methods for solving MDPs are often practical for small states spaces, their effectiveness for large AI planning problems is questionable. We present an algorithm, call ..."
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Cited by 226 (22 self)
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Markov decision processes (MDPs) have recently been applied to the problem of modeling decisiontheoretic planning. While traditional methods for solving MDPs are often practical for small states spaces, their effectiveness for large AI planning problems is questionable. We present an algorithm, called structured policy iteration (SPI), that constructs optimal policies without explicit enumeration of the state space. The algorithm retains the fundamental computational steps of the commonly used modified policy iteration algorithm, but exploitsthe variable and propositionalindependencies reflected in a temporal Bayesian network representation of MDPs. The principles behind SPI can be applied to any structured representation of stochastic actions, policies and value functions, and the algorithm itself can be used in conjunction with recent approximation methods. 1
An Online Mapping Algorithm for Teams of Mobile Robots
 International Journal of Robotics Research
, 2001
"... We propose a new probabilistic algorithm for online mapping of unknown environments with teams of robots. At the core of the algorithm is a technique that combines fast maximum likelihood map growing with a Monte Carlo localizer that uses particle representations. The combination of both yields an o ..."
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Cited by 190 (14 self)
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We propose a new probabilistic algorithm for online mapping of unknown environments with teams of robots. At the core of the algorithm is a technique that combines fast maximum likelihood map growing with a Monte Carlo localizer that uses particle representations. The combination of both yields an online algorithm that can cope with large odometric errors typically found when mapping an environment with cycles. The algorithm can be implemented distributedly on multiple robot platforms, enabling a team of robots to cooperatively generate a single map of their environment. Finally, an extension is described for acquiring threedimensional maps, which capture the structure and visual appearance of indoor environments in 3D.
SPUDD: Stochastic planning using decision diagrams
 In Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence
, 1999
"... Recently, structured methods for solving factored Markov decisions processes (MDPs) with large state spaces have been proposed recently to allow dynamic programming to be applied without the need for complete state enumeration. We propose and examine a new value iteration algorithm for MDPs that use ..."
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Cited by 178 (17 self)
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Recently, structured methods for solving factored Markov decisions processes (MDPs) with large state spaces have been proposed recently to allow dynamic programming to be applied without the need for complete state enumeration. We propose and examine a new value iteration algorithm for MDPs that uses algebraic decision diagrams (ADDs) to represent value functions and policies, assuming an ADD input representation of the MDP. Dynamic programming is implemented via ADD manipulation. We demonstrate our method on a class of large MDPs (up to 63 million states) and show that significant gains can be had when compared to treestructured representations (with up to a thirtyfold reduction in the number of nodes required to represent optimal value functions). 1