Prakash Shenoy | University of Kansas (original) (raw)
Papers by Prakash Shenoy
International Journal of Intelligent Systems, 1995
We describe a simple method for propagating belief functions in AND-trees. We exploit the propert... more We describe a simple method for propagating belief functions in AND-trees. We exploit the properties of AND-trees to make our method simpler than the general method discussed by Shenoy and Shafer, and Dempster and Kong. We illustrate our method for aggregation of evidence in a financial audit.
Information Systems Frontiers, 2000
We are very pleased to serve as guest editors for this special issue of Information Systems Front... more We are very pleased to serve as guest editors for this special issue of Information Systems Frontiers on business applications of uncertain reasoning. We would like to thank the chief editors Raghav Rao and Ram Ramesh for providing this opportunity. We would also like to thank the reviewers,
Abstract. This article discusses a potential application of RFID and collaborative filtering for ... more Abstract. This article discusses a potential application of RFID and collaborative filtering for targeted advertising in grocery stores. Every day hundreds of items in grocery stores are marked down for promotional purposes. Whether these promotions are effective or not depends primarily on whether the customers are aware of them or not, and secondarily whether the customer is interested in the products or not.
In this paper we discuss some practical issues that arise in solving hybrid Bayesian networks tha... more In this paper we discuss some practical issues that arise in solving hybrid Bayesian networks that include deterministic conditionals for continuous variables. We show how exact inference can become intractable even for small networks, due to the difficulty in handling deterministic conditionals (for continuous variables). We propose some strategies for carrying out the inference task using mixtures of polynomials and mixtures of truncated exponentials. Mixtures of polynomials can be defined on hypercubes or hyper-rhombuses. We compare these two methods. A key strategy is to re-approximate large potentials with potentials consisting of fewer pieces and lower degrees/number of terms. We discuss several methods for re-approximating potentials. We illustrate our methods in a practical application consisting of solving a stochastic PERT network.
Uncertainty in Artificial Intelligence, 1988
In this paper, we describe an abstract framework and axioms under which exact local computation o... more In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.
Studies in Fuzziness and Soft Computing, 2008
In this paper, we describe an abstract framework and axioms under which exact local computation o... more In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.
Uncertainty in Artificial Intelligence, 2004
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretiza- tion for re... more Mixtures of truncated exponentials (MTE) potentials are an alternative to discretiza- tion for representing continuous chance variables in influence diagrams. Also, MTE potentials can be used to approximate util- ity functions. This paper introduces MTE influence diagrams, which can represent de- cision problems without restrictions on the relationships between continuous and dis- crete chance variables, without limitations on the distributions
International Journal of Approximate Reasoning, 2000
In this paper, we propose the plausibility transformation method for translating Dempster-Shafer ... more In this paper, we propose the plausibility transformation method for translating Dempster-Shafer (D-S) belief function models to probability models, and describe some of its properties. There are many other transformation methods used in the literature for translating belief function models to probability models. We argue that the plausibility transformation method produces probability models that are consistent with D-S semantics of
This paper extend exacts inference for hybrid Bayesian networks to allow continuous variables wit... more This paper extend exacts inference for hybrid Bayesian networks to allow continuous variables with any conditional density functions, discrete variables with continuous par- ents, and conditionally deterministic continuous variables that are linearly dependent on their continuous parents. We introduce a mixed distribution representation of po- tentials and derive operations from the method of convolutions in probability theory to determine distributions
Uncertainty in Artificial Intelligence, 2005
When a hybrid Bayesian network has con- ditionally deterministic variables with con- tinuous pare... more When a hybrid Bayesian network has con- ditionally deterministic variables with con- tinuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when the continuous vari- ables have a multi-variate normal distribu- tion and the discrete variables do not have continuous parents. In this paper, opera- tions required for
Lecture Notes in Computer Science, 2003
Recently, we proposed a new method called the plausibility transformation method to convert a bel... more Recently, we proposed a new method called the plausibility transformation method to convert a belief function model to an equivalent probability model. In this paper, we compare the plausibility transformation method with the pignistic transformation method. The two transformation methods yield qualitatively different probability models. We argue that the plausibility transformation method is the correct method for translating a belief function model to an equivalent probability model that maintains belief function semantics.
Statistics and Computing, 2006
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for appr... more Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for approximating probability density functions (PDF's). This paper presents MTE potentials that approximate standard PDF's and applications of these potentials for solving inference problems in hybrid Bayesian networks.
Lecture Notes in Computer Science, 2005
In a Bayesian network with continuous variables containing a variable(s) that is a conditionally ... more In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function for the variables in the network does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations required for performing inference with nonlinear conditionally deterministic variables are developed. We perform inference in networks with nonlinear deterministic variables and non-Gaussian continuous variables by using piecewise linear approximations to nonlinear functions and modeling probability distributions with mixtures of truncated exponentials (MTE) potentials.
Annals of Mathematics and Artificial Intelligence, 1990
In this paper we give a simple account of local computation of marginal probabilities when the jo... more In this paper we give a simple account of local computation of marginal probabilities when the joint probability distribution is given in factored form and the sets of variables involved in the factors form a hypertree. Previous expositions of such local computation have emphasized conditional probability. We believe this emphasis is misplaced. What is essential to local computation is a
Machine Intelligence and Pattern Recognition, 1988
International Journal of Intelligent Systems, 1995
We describe a simple method for propagating belief functions in AND-trees. We exploit the propert... more We describe a simple method for propagating belief functions in AND-trees. We exploit the properties of AND-trees to make our method simpler than the general method discussed by Shenoy and Shafer, and Dempster and Kong. We illustrate our method for aggregation of evidence in a financial audit.
Information Systems Frontiers, 2000
We are very pleased to serve as guest editors for this special issue of Information Systems Front... more We are very pleased to serve as guest editors for this special issue of Information Systems Frontiers on business applications of uncertain reasoning. We would like to thank the chief editors Raghav Rao and Ram Ramesh for providing this opportunity. We would also like to thank the reviewers,
Abstract. This article discusses a potential application of RFID and collaborative filtering for ... more Abstract. This article discusses a potential application of RFID and collaborative filtering for targeted advertising in grocery stores. Every day hundreds of items in grocery stores are marked down for promotional purposes. Whether these promotions are effective or not depends primarily on whether the customers are aware of them or not, and secondarily whether the customer is interested in the products or not.
In this paper we discuss some practical issues that arise in solving hybrid Bayesian networks tha... more In this paper we discuss some practical issues that arise in solving hybrid Bayesian networks that include deterministic conditionals for continuous variables. We show how exact inference can become intractable even for small networks, due to the difficulty in handling deterministic conditionals (for continuous variables). We propose some strategies for carrying out the inference task using mixtures of polynomials and mixtures of truncated exponentials. Mixtures of polynomials can be defined on hypercubes or hyper-rhombuses. We compare these two methods. A key strategy is to re-approximate large potentials with potentials consisting of fewer pieces and lower degrees/number of terms. We discuss several methods for re-approximating potentials. We illustrate our methods in a practical application consisting of solving a stochastic PERT network.
Uncertainty in Artificial Intelligence, 1988
In this paper, we describe an abstract framework and axioms under which exact local computation o... more In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.
Studies in Fuzziness and Soft Computing, 2008
In this paper, we describe an abstract framework and axioms under which exact local computation o... more In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework.
Uncertainty in Artificial Intelligence, 2004
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretiza- tion for re... more Mixtures of truncated exponentials (MTE) potentials are an alternative to discretiza- tion for representing continuous chance variables in influence diagrams. Also, MTE potentials can be used to approximate util- ity functions. This paper introduces MTE influence diagrams, which can represent de- cision problems without restrictions on the relationships between continuous and dis- crete chance variables, without limitations on the distributions
International Journal of Approximate Reasoning, 2000
In this paper, we propose the plausibility transformation method for translating Dempster-Shafer ... more In this paper, we propose the plausibility transformation method for translating Dempster-Shafer (D-S) belief function models to probability models, and describe some of its properties. There are many other transformation methods used in the literature for translating belief function models to probability models. We argue that the plausibility transformation method produces probability models that are consistent with D-S semantics of
This paper extend exacts inference for hybrid Bayesian networks to allow continuous variables wit... more This paper extend exacts inference for hybrid Bayesian networks to allow continuous variables with any conditional density functions, discrete variables with continuous par- ents, and conditionally deterministic continuous variables that are linearly dependent on their continuous parents. We introduce a mixed distribution representation of po- tentials and derive operations from the method of convolutions in probability theory to determine distributions
Uncertainty in Artificial Intelligence, 2005
When a hybrid Bayesian network has con- ditionally deterministic variables with con- tinuous pare... more When a hybrid Bayesian network has con- ditionally deterministic variables with con- tinuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when the continuous vari- ables have a multi-variate normal distribu- tion and the discrete variables do not have continuous parents. In this paper, opera- tions required for
Lecture Notes in Computer Science, 2003
Recently, we proposed a new method called the plausibility transformation method to convert a bel... more Recently, we proposed a new method called the plausibility transformation method to convert a belief function model to an equivalent probability model. In this paper, we compare the plausibility transformation method with the pignistic transformation method. The two transformation methods yield qualitatively different probability models. We argue that the plausibility transformation method is the correct method for translating a belief function model to an equivalent probability model that maintains belief function semantics.
Statistics and Computing, 2006
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for appr... more Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for approximating probability density functions (PDF's). This paper presents MTE potentials that approximate standard PDF's and applications of these potentials for solving inference problems in hybrid Bayesian networks.
Lecture Notes in Computer Science, 2005
In a Bayesian network with continuous variables containing a variable(s) that is a conditionally ... more In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function for the variables in the network does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations required for performing inference with nonlinear conditionally deterministic variables are developed. We perform inference in networks with nonlinear deterministic variables and non-Gaussian continuous variables by using piecewise linear approximations to nonlinear functions and modeling probability distributions with mixtures of truncated exponentials (MTE) potentials.
Annals of Mathematics and Artificial Intelligence, 1990
In this paper we give a simple account of local computation of marginal probabilities when the jo... more In this paper we give a simple account of local computation of marginal probabilities when the joint probability distribution is given in factored form and the sets of variables involved in the factors form a hypertree. Previous expositions of such local computation have emphasized conditional probability. We believe this emphasis is misplaced. What is essential to local computation is a
Machine Intelligence and Pattern Recognition, 1988