3,308 research outputs found
A Linear Belief Function Approach to Portfolio Evaluation
By elaborating on the notion of linear belief functions (Dempster 1990; Liu
1996), we propose an elementary approach to knowledge representation for expert
systems using linear belief functions. We show how to use basic matrices to
represent market information and financial knowledge, including complete
ignorance, statistical observations, subjective speculations, distributional
assumptions, linear relations, and empirical asset pricing models. We then
appeal to Dempster's rule of combination to integrate the knowledge for
assessing an overall belief of portfolio performance, and updating the belief
by incorporating additional information. We use an example of three gold stocks
to illustrate the approach.Comment: Appears in Proceedings of the Nineteenth Conference on Uncertainty in
Artificial Intelligence (UAI2003
Binary Join Trees
The main goal of this paper is to describe a data structure called binary
join trees that are useful in computing multiple marginals efficiently using
the Shenoy-Shafer architecture. We define binary join trees, describe their
utility, and sketch a procedure for constructing them.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in
Artificial Intelligence (UAI1996
Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians
The main goal of this paper is to describe a method for exact inference in
general hybrid Bayesian networks (BNs) (with a mixture of discrete and
continuous chance variables). Our method consists of approximating general
hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a
fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG
Bayesian networks, and there exists a commercial implementation of this
algorithm. However, this algorithm can only be used for MoG BNs. Some
limitations of such networks are as follows. All continuous chance variables
must have conditional linear Gaussian distributions, and discrete chance nodes
cannot have continuous parents. The methods described in this paper will enable
us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This
includes networks with continuous chance nodes with non-Gaussian distributions,
networks with no restrictions on the topology of discrete and continuous
variables, networks with conditionally deterministic variables that are a
nonlinear function of their continuous parents, and networks with continuous
chance variables whose variances are functions of their parents.Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty
in Artificial Intelligence (UAI2006
Valuation Networks and Conditional Independence
Valuation networks have been proposed as graphical representations of
valuation-based systems (VBSs). The VBS framework is able to capture many
uncertainty calculi including probability theory, Dempster-Shafer's
belief-function theory, Spohn's epistemic belief theory, and Zadeh's
possibility theory. In this paper, we show how valuation networks encode
conditional independence relations. For the probabilistic case, the class of
probability models encoded by valuation networks includes undirected graph
models, directed acyclic graph models, directed balloon graph models, and
recursive causal graph models.Comment: Appears in Proceedings of the Ninth Conference on Uncertainty in
Artificial Intelligence (UAI1993
Conditional Independence in Uncertainty Theories
This paper introduces the notions of independence and conditional
independence in valuation-based systems (VBS). VBS is an axiomatic framework
capable of representing many different uncertainty calculi. We define
independence and conditional independence in terms of factorization of the
joint valuation. The definitions of independence and conditional independence
in VBS generalize the corresponding definitions in probability theory. Our
definitions apply not only to probability theory, but also to Dempster-Shafer's
belief-function theory, Spohn's epistemic-belief theory, and Zadeh's
possibility theory. In fact, they apply to any uncertainty calculi that fit in
the framework of valuation-based systems.Comment: Appears in Proceedings of the Eighth Conference on Uncertainty in
Artificial Intelligence (UAI1992
A New Pruning Method for Solving Decision Trees and Game Trees
The main goal of this paper is to describe a new pruning method for solving
decision trees and game trees. The pruning method for decision trees suggests a
slight variant of decision trees that we call scenario trees. In scenario
trees, we do not need a conditional probability for each edge emanating from a
chance node. Instead, we require a joint probability for each path from the
root node to a leaf node. We compare the pruning method to the traditional
rollback method for decision trees and game trees. For problems that require
Bayesian revision of probabilities, a scenario tree representation with the
pruning method is more efficient than a decision tree representation with the
rollback method. For game trees, the pruning method is more efficient than the
rollback method.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in
Artificial Intelligence (UAI1995
A Fusion Algorithm for Solving Bayesian Decision Problems
This paper proposes a new method for solving Bayesian decision problems. The
method consists of representing a Bayesian decision problem as a
valuation-based system and applying a fusion algorithm for solving it. The
fusion algorithm is a hybrid of local computational methods for computation of
marginals of joint probability distributions and the local computational
methods for discrete optimization problems.Comment: Appears in Proceedings of the Seventh Conference on Uncertainty in
Artificial Intelligence (UAI1991
Solving Hybrid Influence Diagrams with Deterministic Variables
We describe a framework and an algorithm for solving hybrid influence
diagrams with discrete, continuous, and deterministic chance variables, and
discrete and continuous decision variables. A continuous chance variable in an
influence diagram is said to be deterministic if its conditional distributions
have zero variances. The solution algorithm is an extension of Shenoy's fusion
algorithm for discrete influence diagrams. We describe an extended
Shenoy-Shafer architecture for propagation of discrete, continuous, and utility
potentials in hybrid influence diagrams that include deterministic chance
variables. The algorithm and framework are illustrated by solving two small
examples.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty
in Artificial Intelligence (UAI2010
Valuation-Based Systems for Discrete Optimization
This paper describes valuation-based systems for representing and solving
discrete optimization problems. In valuation-based systems, we represent
information in an optimization problem using variables, sample spaces of
variables, a set of values, and functions that map sample spaces of sets of
variables to the set of values. The functions, called valuations, represent the
factors of an objective function. Solving the optimization problem involves
using two operations called combination and marginalization. Combination tells
us how to combine the factors of the joint objective function. Marginalization
is either maximization or minimization. Solving an optimization problem can be
simply described as finding the marginal of the joint objective function for
the empty set. We state some simple axioms that combination and marginalization
need to satisfy to enable us to solve an optimization problem using local
computation. For optimization problems, the solution method of valuation-based
systems reduces to non-serial dynamic programming. Thus our solution method for
VBS can be regarded as an abstract description of dynamic programming. And our
axioms can be viewed as conditions that permit the use of dynamic programming.Comment: Appears in Proceedings of the Sixth Conference on Uncertainty in
Artificial Intelligence (UAI1990
Hybrid Influence Diagrams Using Mixtures of Truncated Exponentials
Mixtures of truncated exponentials (MTE) potentials are an alternative to
discretization for representing continuous chance variables in influence
diagrams. Also, MTE potentials can be used to approximate utility functions.
This paper introduces MTE influence diagrams, which can represent decision
problems without restrictions on the relationships between continuous and
discrete chance variables, without limitations on the distributions of
continuous chance variables, and without limitations on the nature of the
utility functions. In MTE influence diagrams, all probability distributions and
the joint utility function (or its multiplicative factors) are represented by
MTE potentials and decision nodes are assumed to have discrete state spaces.
MTE influence diagrams are solved by variable elimination using a fusion
algorithm.Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in
Artificial Intelligence (UAI2004
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