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296
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
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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 758 (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.
Loopy Belief Propagation for Approximate Inference: An Empirical Study
 In Proceedings of Uncertainty in AI
, 1999
"... Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performa ..."
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Cited by 680 (18 self)
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Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performance of "Turbo Codes"  codes whose decoding algorithm is equivalent to loopy belief propagation in a chainstructured Bayesian network. In this paper we ask: is there something special about the errorcorrecting code context, or does loopy propagation work as an approximate inference scheme in a more general setting? We compare the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two realworld networks: ALARM and QMR. We find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals. However, on the QMR network, the loopy beliefs oscillated and had no obvious relationship ...
Turbo decoding as an instance of Pearl’s belief propagation algorithm
 IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 420 (16 self)
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Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the excellent experimental performance of turbo decoding is still lacking. However, we shall also show that Pearl’s algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other errorcontrol systems, including Gallager’s
On the Hardness of Approximate Reasoning
, 1996
"... Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider va ..."
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Cited by 289 (13 self)
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Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to modelcounting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the e...
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 284 (19 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...
Learning Bayesian belief networks: An approach based on the MDL principle
 Computational Intelligence
, 1994
"... A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being lear ..."
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Cited by 248 (7 self)
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A new approach for learning Bayesian belief networks from raw data is presented. The approach is based on Rissanen's Minimal Description Length (MDL) principle, which is particularly well suited for this task. Our approach does not require any prior assumptions about the distribution being learned. In particular, our method can learn unrestricted multiplyconnected belief networks. Furthermore, unlike other approaches our method allows us to tradeo accuracy and complexity in the learned model. This is important since if the learned model is very complex (highly connected) it can be conceptually and computationally intractable. In such a case it would be preferable to use a simpler model even if it is less accurate. The MDL principle o ers a reasoned method for making this tradeo. We also show that our method generalizes previous approaches based on Kullback crossentropy. Experiments have been conducted to demonstrate the feasibility of the approach. Keywords: Knowledge Acquisition � Bayes Nets � Uncertainty Reasoning. 1
A rational analysis of the selection task as optimal data selection
 67 – 215535 Deliverable 4.1
, 1994
"... Human reasoning in hypothesistesting tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed ..."
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Cited by 238 (16 self)
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Human reasoning in hypothesistesting tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed in the light of a Bayesian model of optimal data selection in inductive hypothesis testing. The model provides a rational analysis (Anderson, 1990) of the selection task that fits well with people's performance on both abstract and thematic versions of the task. The model suggests that reasoning in these tasks may be rational rather than subject to systematic bias. Over the past 30 years, results in the psychology of reasoning have raised doubts about human rationality. The assumption of human rationality has a long history. Aristotle took the capacity for rational thought to be the defining characteristic of human beings, the capacity that separated us from the animals. Descartes regarded the ability to use language and to reason as the hallmarks of the mental that separated it from the merely physical. Many contemporary philosophers of mind also appeal to a basic principle of rationality in accounting for everyday, folk psychological explanation whereby we explain each other's behavior in terms of our beliefs and desires (Cherniak, 1986; Cohen, 1981; Davidson, 1984; Dennett, 1987; but see Stich, 1990). These philosophers, both ancient and modern, share a common view of rationality: To be rational is to reason according to rules (Brown, 1989). Logic and mathematics provide the normative rules that tell us how we should reason. Rationality therefore seems to demand that the human cognitive system embodies the rules of logic and mathematics. However, results in the psychology of reasoning appear to show that people do not reason according to these rules. In both deductive (Evans, 1982, 1989;
Stochastic simulation algorithms for dynamic probabilistic networks
, 1995
"... Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special characteristics of dynamic probabilistic networks (DPNs), whi ..."
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Cited by 175 (10 self)
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Stochastic simulation algorithms such as likelihood weighting often give fast, accurate approximations to posterior probabilities in probabilistic networks, and are the methods of choice for very large networks. Unfortunately, the special characteristics of dynamic probabilistic networks (DPNs), which are used to represent stochastic temporal processes, mean that standard simulation algorithms perform very poorly. In essence, the simulation trials diverge further and further from reality as the process is observed over time. In this paper, we present simulation algorithms that use the evidence observed at each time step to push the set of trials back towards reality. The first algorithm, &quot;evidence reversal &quot; (ER) restructures each time slice of the DPN so that the evidence nodes for the slice become ancestors of the state variables. The second algorithm, called &quot;survival of the fittest &quot; sampling (SOF), &quot;repopulates &quot; the set of trials at each time step using a stochastic reproduction rate weighted by the likelihood of the evidence according to each trial. We compare the performance of each algorithm with likelihood weighting on the original network, and also investigate the benefits of combining the ER and SOF methods. The ER/SOF combination appears to maintain bounded error independent of the number of time steps in the simulation.