579 research outputs found
Logarithmic Time Parallel Bayesian Inference
I present a parallel algorithm for exact probabilistic inference in Bayesian
networks. For polytree networks with n variables, the worst-case time
complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write
parallel random-access machine) with n processors, for any constant number of
evidence variables. For arbitrary networks, the time complexity is O(r^{3w}*log
n) for n processors, or O(w*log n) for r^{3w}*n processors, where r is the
maximum range of any variable, and w is the induced width (the maximum clique
size), after moralizing and triangulating the network.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in
Artificial Intelligence (UAI1998
Global Conditioning for Probabilistic Inference in Belief Networks
In this paper we propose a new approach to probabilistic inference on belief
networks, global conditioning, which is a simple generalization of Pearl's
(1986b) method of loopcutset conditioning. We show that global conditioning, as
well as loop-cutset conditioning, can be thought of as a special case of the
method of Lauritzen and Spiegelhalter (1988) as refined by Jensen et al (199Oa;
1990b). Nonetheless, this approach provides new opportunities for parallel
processing and, in the case of sequential processing, a tradeoff of time for
memory. We also show how a hybrid method (Suermondt and others 1990) combining
loop-cutset conditioning with Jensen's method can be viewed within our
framework. By exploring the relationships between these methods, we develop a
unifying framework in which the advantages of each approach can be combined
successfully.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in
Artificial Intelligence (UAI1994
Optimal Decomposition of Belief Networks
In this paper, optimum decomposition of belief networks is discussed. Some
methods of decomposition are examined and a new method - the method of Minimum
Total Number of States (MTNS) - is proposed. The problem of optimum belief
network decomposition under our framework, as under all the other frameworks,
is shown to be NP-hard. According to the computational complexity analysis, an
algorithm of belief network decomposition is proposed in (Wee, 1990a) based on
simulated annealing.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in
Artificial Intelligence (UAI1990
Logarithmic-Time Updates and Queries in Probabilistic Networks
Traditional databases commonly support efficient query and update procedures
that operate in time which is sublinear in the size of the database. Our goal
in this paper is to take a first step toward dynamic reasoning in probabilistic
databases with comparable efficiency. We propose a dynamic data structure that
supports efficient algorithms for updating and querying singly connected
Bayesian networks. In the conventional algorithm, new evidence is absorbed in
O(1) time and queries are processed in time O(N), where N is the size of the
network. We propose an algorithm which, after a preprocessing phase, allows us
to answer queries in time O(log N) at the expense of O(log N) time per evidence
absorption. The usefulness of sub-linear processing time manifests itself in
applications requiring (near) real-time response over large probabilistic
databases. We briefly discuss a potential application of dynamic probabilistic
reasoning in computational biology.Comment: See http://www.jair.org/ for any accompanying file
Computational Advantages of Relevance Reasoning in Bayesian Belief Networks
This paper introduces a computational framework for reasoning in Bayesian
belief networks that derives significant advantages from focused inference and
relevance reasoning. This framework is based on d -separation and other simple
and computationally efficient techniques for pruning irrelevant parts of a
network. Our main contribution is a technique that we call relevance-based
decomposition. Relevance-based decomposition approaches belief updating in
large networks by focusing on their parts and decomposing them into partially
overlapping subnetworks. This makes reasoning in some intractable networks
possible and, in addition, often results in significant speedup, as the total
time taken to update all subnetworks is in practice often considerably less
than the time taken to update the network as a whole. We report results of
empirical tests that demonstrate practical significance of our approach.Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in
Artificial Intelligence (UAI1997
An Algorithm for the Construction of Bayesian Network Structures from Data
Previous algorithms for the construction of Bayesian belief network
structures from data have been either highly dependent on conditional
independence (CI) tests, or have required an ordering on the nodes to be
supplied by the user. We present an algorithm that integrates these two
approaches - CI tests are used to generate an ordering on the nodes from the
database which is then used to recover the underlying Bayesian network
structure using a non CI based method. Results of preliminary evaluation of the
algorithm on two networks (ALARM and LED) are presented. We also discuss some
algorithm performance issues and open problems.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in
Artificial Intelligence (UAI1993
Ergo: A Graphical Environment for Constructing Bayesian
We describe an environment that considerably simplifies the process of
generating Bayesian belief networks. The system has been implemented on readily
available, inexpensive hardware, and provides clarity and high performance. We
present an introduction to Bayesian belief networks, discuss algorithms for
inference with these networks, and delineate the classes of problems that can
be solved with this paradigm. We then describe the hardware and software that
constitute the system, and illustrate Ergo's use with several exampleComment: Appears in Proceedings of the Sixth Conference on Uncertainty in
Artificial Intelligence (UAI1990
Evidence Absorption and Propagation through Evidence Reversals
The arc reversal/node reduction approach to probabilistic inference is
extended to include the case of instantiated evidence by an operation called
"evidence reversal." This not only provides a technique for computing posterior
joint distributions on general belief networks, but also provides insight into
the methods of Pearl [1986b] and Lauritzen and Spiegelhalter [1988]. Although
it is well understood that the latter two algorithms are closely related, in
fact all three algorithms are identical whenever the belief network is a
forest.Comment: Appears in Proceedings of the Fifth Conference on Uncertainty in
Artificial Intelligence (UAI1989
Anytime Inference in Valuation Algebras
Anytime inference is inference performed incrementally, with the accuracy of
the inference being controlled by a tunable parameter, usually time. Such
anytime inference algorithms are also usually interruptible, gradually
converging to the exact inference value until terminated. While anytime
inference algorithms for specific domains like probability potentials exist in
the literature, our objective in this article is to obtain an anytime inference
algorithm which is sufficiently generic to cover a wide range of domains. For
this we utilise the theory of generic inference as a basis for constructing an
anytime inference algorithm, and in particular, extending work done on ordered
valuation algebras. The novel contribution of this work is the construction of
anytime algorithms in a generic framework, which automatically gives us
instantiations in various useful domains. We also show how to apply this
generic framework for anytime inference in semiring induced valuation algebras,
an important subclass of valuation algebras, which includes instances like
probability potentials, disjunctive normal forms and distributive lattices.
Keywords: Approximation; Anytime algorithms; Resource-bounded computation;
Generic inference; Valuation algebras; Local computation; Binary join trees.Comment: 9 pages, 1 figur
Tutorial on Exact Belief Propagation in Bayesian Networks: from Messages to Algorithms
In Bayesian networks, exact belief propagation is achieved through message
passing algorithms. These algorithms (ex: inward and outward) provide only a
recursive definition of the corresponding messages. In contrast, when working
on hidden Markov models and variants, one classically first defines explicitly
these messages (forward and backward quantities), and then derive all results
and algorithms. In this paper, we generalize the hidden Markov model approach
by introducing an explicit definition of the messages in Bayesian networks,
from which we derive all the relevant properties and results including the
recursive algorithms that allow to compute these messages. Two didactic
examples (the precipitation hidden Markov model and the pedigree Bayesian
network) are considered along the paper to illustrate the new formalism and
standalone R source code is provided in the appendix
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