Prakash P. Shenoy

Prakash P. Shenoy
University of Kansas | KU · School of Business

PhD, Cornell University, 1977

About

178
Publications
40,538
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7,049
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Introduction
Prakash P. Shenoy is a Distinguished Professor Emeritus in the School of Business, University of Kansas, Lawrence, KS, US. He received a B.Tech. in Mechanical Engineering from the Indian Institute of Technology, Bombay, India, in 1973 and an M.S. and a Ph.D. in Operations Research from Cornell University in 1975 and 1977, respectively. He was appointed as Ronald G. Harper Distinguished Professor of Artificial Intelligence in the School of Business, University of Kansas, in 1994.
Additional affiliations
January 2019 - May 2019
University of Technology of Compiègne
Position
  • Professor
Description
  • Worked with Thierry Denœux on an axiomatic framework for decision-making with Dempster-Shafer belief functions.
August 1978 - July 1982
University of Kansas
Position
  • Research Assistant
August 1977 - July 1978
University of Wisconsin–Madison
Position
  • Researcher
Education
August 1973 - May 1977
Cornell University
Field of study
  • Operations Research and Information Engineering
August 1968 - May 1973
Indian Institute of Technology Bombay
Field of study
  • Mechanical Engineering

Publications

Publications (178)
Article
Full-text available
We define entropy of belief functions in the Dempster-Shafer (D-S) theory that satisfies a compound distributions property that is analogous to the property that characterizes Shannon's definitions of entropy and conditional entropy for probability mass functions. None of the existing definitions of entropy for belief functions in the D-S theory sa...
Article
Full-text available
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utili...
Preprint
Full-text available
In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy(d-entropy). This paper provides an algorithm for computing the d-entropy of directed graphical D-S belief function models. We illustrate the algorithm using Almond’s Captain’s Problem example. For belief function undi...
Article
Full-text available
How do you make inferences from a Bayesian network (BN) model with missing information? For example, we may not have priors for some variables or may not have conditionals for some states of the parent variables. It is well-known that the Dempster-Shafer (D-S) belief function theory is a generalization of probability theory. So, a solution is to em...
Article
Full-text available
In 2018, Jiroušek and Shenoy proposed a definition of entropy for Dempster-Shafer (D-S) belief functions called decomposable entropy (d-entropy). This paper provides an algorithm for computing the d-entropy of directed graphical D-S belief function models. We illustrate the algorithm using Almond's Captain's Problem example. For belief function und...
Code
Appendices A. Additional Simulation Results This appendix presents the detailed results for simulation 3 & 4, and the core-sponding bias-variance analysis. A.1. Simulation Setting 3: Continuous Predictor The third simulation setting is the same as the first one, but with all predic-tors being generated directly from the multivariate normal distribu...
Chapter
Full-text available
In probability theory, the mutual information between two discrete random variables, X and Y, measures the average reduction in uncertainty about Y when we learn the value of X. It is defined using the Shannon entropy of probability distributions. This paper defines a corresponding concept of mutual information between two variables in the Dempster...
Article
To reduce the estimator’s variance and prevent overfitting, regularization techniques have attracted great interest from the statistics and machine learning communities. Most existing regularized methods rely on the sparsity assumption that a model with fewer parameters predicts better than one with many parameters. This assumption works particular...
Article
Full-text available
The prediction of posttraumatic stress disorder (PTSD) has gained a lot of interest in clinical studies. Identifying patients with a high risk of PTSD can guide mental healthcare workers when making treatment decisions. The main goal of this paper is to propose several Bayesian network (BN) models to assess the probability that a veteran has PTSD w...
Article
The goal of this repository is to share a synthetic data and R codes for the empirical analysis of our paper. Our motivation is to present our code and results in a reproducible way and facilitate the coding effort of those who want to improve our model.
Article
Full-text available
The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similarly to probability theory's notion of conditional probability tables. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables are necessary for con...
Technical Report
Full-text available
The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similarly to probability theory's notion of conditional probability tables. Conditional belief functions are necessary for constructing directed graph-ical belief function models in the same sense as conditional probability tables are necessary for co...
Chapter
Full-text available
The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similar to the notion of conditional probability tables in probability theory. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables for constructing B...
Article
Full-text available
Applications of Dempster-Shafer (D-S) belief functions to practical problems involve difficulties arising from their high computational complexity. One can use space-saving factored approximations such as graphical belief function models to solve them. Using an analogy with probability distributions, we represent these approximations in the form of...
Article
This editorial article is a biography of Glenn Shafer, briefly covering his early years, his education, and his contributions as an academic to research, teaching, and administration.
Chapter
We investigate learning of belief function compositional models from data using information content and mutual information based on two different definitions of entropy proposed by Jiroušek and Shenoy in 2018 and 2020, respectively. The data consists of 2,310 randomly generated basic assignments of 26 binary variables from a pairwise consistent and...
Preprint
Full-text available
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utili...
Article
Full-text available
Discriminative classifiers tend to have lower asymptotic classification errors, while generative classifiers can be more accurate when the training set size is small. In this paper, we examine the construction of hybrid models from categorical data, where we use logistic regression (LR) as a discriminative component, and na¨ıvena¨ıve Bayes (NB) as...
Article
Full-text available
The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expec...
Conference Paper
Full-text available
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for proba-bilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued util...
Article
Full-text available
Feature selection is a dimensionality reduction technique that helps to improve data visualization, simplify learning, and enhance the efficiency of learning algorithms. The existing redundancy-based approach, which relies on relevance and redundancy criteria, does not account for feature complementarity. Complementarity implies information synergy...
Article
Realistic decision-making often occurs with insufficient time to gather all possible evidence before a decision must be rendered, requiring an efficient process for prioritizing between potential action sequences. This work aims to develop a rigorous framework for gathering evidence to resolve hypotheses notwithstanding ambiguous, incomplete, and u...
Chapter
Full-text available
In probability theory, as well as in other alternative uncertainty theories, the existence of efficient processes for the multidimensional model construction is a basic assumption making the application of the respective theory to practical problems possible. Most of the approaches are based on the idea that a multidimensional model is set up from...
Article
Full-text available
We propose a new definition of entropy of basic probability assignments (BPAs) in the Dempster–Shafer (DS) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our definition is different from those proposed by Höhle, Smets, Yager, Nguyen, Dubois–Prade, Lamata–Moral, Klir–Ramer, Klir–Parviz, Pal et al., Mae...
Article
Full-text available
To enable inference in hybrid Bayesian networks containing nonlinear deterministic conditional distributions, Cobb and Shenoy in 2005 propose approximating nonlinear deterministic functions by piecewise linear ones. In this paper, we describe a method for finding piecewise linear approximations of nonlinear functions based on a penalized MSE heuris...
Article
Full-text available
The main goal of this paper is to propose a probability model for computing probabilities of dismissal of 10b-5 securities class-action cases filed in United States Federal district courts. By dismissal, we mean dismissal with prejudice in response to the motion to dismiss filed by the defendants, and not eventual dismissal after the discovery proc...
Conference Paper
We propose a new definition of entropy of basic probability assignments (BPA) in the Dempster-Shafer (D-S) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. We state a list of five desired properties of entropy for D-S belief functions theory that are motivated by Shannon’s definition of entropy of proba...
Article
Bayesian networks (BNs) are a useful tool for applications where dynamic decision-making is involved. However, it is not easy to learn the structure and conditional probability tables of BNs from small datasets. There are many algorithms and heuristics for learning BNs from sparse datasets, but most of these are not concerned with the quality of th...
Technical Report
Full-text available
We propose a new definition of entropy for basic probability assignments (BPA) in the Dempster-Shafer (D-S) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our definition is different from the definitions proposed by Hohle, Smets, Yager, Nguyen, Dubois-Prade, Lamata-Moral, Klir-Ramer, Klir-Parviz, Pal...
Article
Full-text available
We show that Pearl's causal networks can be described using causal compositional models (CCMs) in the valuation-based systems (VBS) framework. One major advantage of using the VBS framework is that as VBS is a generalization of several uncertainty theories (e.g., probability theory, a version of possibility theory where combination is the product t...
Article
Full-text available
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 strategie...
Conference Paper
Full-text available
Valuation-based systems (VBS) can be considered as a generic uncertainty framework that has many uncertainty calculi, such as probability theory, a version of possibility theory where combination is the product t-norm, Spohn's epistemic belief theory, and Dempster-Shafer belief function theory, as special cases. In this paper, we focus our attentio...
Article
Compositional models were initially described for discrete probability theory, and later extended for possibility theory and for belief functions in Dempster–Shafer (D–S) theory of evidence. Valuation-based system (VBS) is an unifying theoretical framework generalizing some of the well known and frequently used uncertainty calculi. This generalizat...
Preprint
Full-text available
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 condition...
Conference Paper
Full-text available
In this paper we study the problem of inference in hybrid Bayesian networks containing deterministic conditionals. The difficulties in handling deterministic conditionals for con-tinuous variables can make inference intractable even for small networks. We describe the use of re-approximations to reduce the complexity of the potentials that arise in...
Conference Paper
Full-text available
Valuation-based systems (VBS) can be considered as a generic uncertainty framework that has many uncertainty calculi, such as probability theory, a version of possibility theory where combination is the product t-norm, Spohn's epistemic belief theory, and Dempster-Shafer belief function theory, as special cases. In this paper, we focus our attentio...
Article
We discuss two issues in using mixtures of polynomials (MOPs) for inference in hybrid Bayesian networks. MOPs were proposed by Shenoy and West for mitigating the problem of integration in inference in hybrid Bayesian networks. First, in defining MOP for multidimensional functions, one requirement is that the pieces where the polynomials are defined...
Conference Paper
Full-text available
To enable inference in continuous Bayesian networks containing nonlinear deterministic conditional distributions, Cobb and Shenoy (2005) have proposed approximating nonlinear deterministic functions by piecewise linear ones. In this paper, we describe two princi-ples and a heuristic for finding piecewise linear approximations of nonlinear functions...
Article
Full-text available
We describe a framework and an algorithm for approximately solving a class of hybrid influence diagrams (IDs) containing discrete and continuous chance variables, discrete and continuous decision variables, and deterministic conditional distributions for chance variables. A conditional distribution for a chance variable is said to be deterministic...
Article
Full-text available
In this paper we analyze the use of hybrid Bayesian networks in domains that include deterministic conditionals for continuous variables. We show how exact inference can become infeasible even for small networks, due to the difficulty in handling functional relationships. We compare two strategies for carrying out the inference task, using mixtures...
Article
The main goal of this paper is to describe an architecture for solving large general hybrid Bayesian networks (BNs) with deterministic conditionals for continuous variables using local computation. In the presence of deterministic conditionals for continuous variables, we have to deal with the non-existence of the joint density function for the con...
Article
The main goal of this paper is to describe inference in hybrid Bayesian networks (BNs) using mixture of polynomials (MOP) approximations of probability density functions (PDFs). Hybrid BNs contain a mix of discrete, continuous, and conditionally deterministic random variables. The conditionals for continuous variables are typically described by con...
Conference Paper
Full-text available
We discuss some issues in using mixtures of polynomials (MOPs) for inference in hybrid Bayesian networks. MOPs were proposed by Shenoy and West for mitigating the problem of integration in inference in hybrid Bayesian networks. In defining MOP for multi-dimensional functions, one requirement is that the pieces where the polynomials are defined are...
Article
Full-text available
Since their introduction in the mid 1970s, influence diagrams have become a de facto standard for representing Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology designed to increase the ability to represent complex problems. In this paper, we review the representation issue...
Article
Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster–Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability funct...
Article
Influence diagrams have become a popular tool for representing and solving complex decision-making problems under uncertainty. In this paper, we focus on the task of building probability models from expert knowledge, and also on the challenging and less known task of constructing utility models in influence diagrams. Our goal is to review the state...
Chapter
Full-text available
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...
Chapter
Full-text available
The main goal of this paper is to describe inference in hybrid Bayesian networks (BNs) using mixtures of polynomials (MOP) approximations of probability density functions (PDFs). Hybrid BNs contain a mix of dis-crete, continuous, and conditionally deterministic random variables. The conditionals for continuous variables are typically described by c...
Conference Paper
Full-text available
In this paper, we transform a PERT network into a mixtures of truncated exponentials Bayesian network. We use the Shenoy-Shafer architecture to propagate the MTE potentials in the resulting MTE PERT Bayes net and thus to find the marginal distribution of the project completion time. Finding the distribution of the project completion time is importa...
Conference Paper
Full-text available
The main goal of this paper is to describe an architecture for solving large general hybrid Bayesian networks (BNs) with deterministic variables using local computation. In the presence of deterministic variables, we have to deal with non-existence of joint densities. We represent deterministic conditional distributions using Dirac delta functions....
Article
This article discusses arc reversals in hybrid Bayesian networks with deterministic variables. Hybrid Bayesian networks contain a mix of discrete and continuous chance variables. In a Bayesian network representation, a continuous chance variable is said to be deterministic if its conditional distributions have zero variances. Arc reversals are used...
Article
Full-text available
Since their introduction in the mid 70s, influence diagrams have become a de facto standard for representation of Bayesian decision problems. The need to represent complex problems has led to extensions of the influence diagram methodology to increase their representation power. In this paper, we review the representation issues associated with inf...
Article
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...
Conference Paper
Full-text available
This article discusses a potential application of radio frequency identification (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...
Article
Full-text available
This paper extend exacts inference for hybrid Bayesian networks to allow condition-ally deterministic continuous variables and discrete variables with continuous parents. We introduce a mixed distribution representation of potentials and derive operations from the method of convolutions in probability theory to determine distributions for determini...
Article
This study provides operational guidance for building naïve Bayes Bayesian network (BN) models for bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors. Based on the correlations and partial correlations among variables, the method aims at eliminating redundant and less relevant variables. A...
Conference Paper
Full-text available
In this paper, we describe how a stochastic PERT network can be formulated as a Bayesian network. We approximate such PERT Bayesian network by mixtures of Gaussians hybrid Bayesian networks. Since there exists algorithms for solving mixtures of Gaussians hybrid Bayesian networks exactly, we can use these algorithms to make inferences in PERT Bayesi...
Article
Full-text available
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always be marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer arc...
Article
Full-text available
This paper proposes a linear belief function (LBF) approach to evaluate portfolio performance. By drawing on the notion of LBFs, an elementary approach to knowledge representation in expert systems is proposed. It is shown how to use basic matrices to represent market information and financial knowledge, including complete ignorance, statistical ob...
Conference Paper
Full-text available
Dempster’s rule of combination is the commonly used rule for combining independent belief functions. In 1987, Peter Walley proposed an alternative rule for combining belief function representations of independent statistical evidence that result in partially consonant belief functions. In this paper, we examine in detail Walley’s combination rule a...
Chapter
Full-text available
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 e...
Article
Full-text available
An important class of continuous Bayesian networks are those that have linear conditionally deterministic variables (a variable that is a linear deterministic function of its parents). In this case, the joint density function for the variables in the network does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when...
Article
Full-text available
We describe a new graphical language for specifying asymmetric decision problems. The language is based on a filtered merge of several existing languages including sequential valuation networks, asymmetric influence diagrams, and unconstrained influence diagrams. Asymmetry is encoded using a structure resembling a clustered decision tree, whereas t...
Article
Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated with an MTE potential, which can always be marginalized in closed form. This allows propagation to be done exactly using the Shenoy–Shafer architecture for computin...
Article
Full-text available
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 tran...
Article
This paper deals with representation and solution of asymmetric decision problems. We describe a new representation called sequential valuation networks that is a hybrid of Covaliu and Oliver’s sequential decision diagrams and Shenoy’s valuation networks. The solution algorithm is based on the idea of decomposing a large asymmetric problem into sma...
Article
Full-text available
This paper presents a new axiomatic decision theory for choice under uncertainty. Unlike Bayesian decision theory where uncertainty is represented by a probability function, in our theory, uncertainty is given in the form of a likelihood function extracted from statistical evidence. The likelihood principle in statistics stipulates that likelihood...
Conference Paper
Full-text available
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 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 norm...
Chapter
Full-text available
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when the continuous variables have a multi-variate normal distribution and the discrete variables do not have contin...
Conference Paper
Full-text available
The main goal of this paper is to describe a new semantic for conditional independence in terms of no double counting of uncertain evidence. For ease of exposition, we use probability calculus to state all results. But the results generalize easily to any calculus that fits in the framework of valuation-based systems. Thus, the results described in...
Article
Full-text available
This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are su...
Article
Full-text available
This paper describes a systematic procedure for constructing Bayesian networks (BNs) from domain knowledge of experts using the causal mapping approach. We outline how causal knowledge of experts can be represented as causal maps, and how the graphical structure of causal maps can be modified to construct Bayes nets. Probability encoding techniques...
Chapter
Full-text available
An important class of hybrid Bayesian networks are those that have conditionally deterministic variables (a variable that is a deterministic function of its parents). In this case, if some of the parents are continuous, then the joint density function does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when the det...
Conference Paper
Full-text available
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 relation...