arXiv subjects

Gregory F. Cooper

Publications and source records attributed to Gregory F. Cooper.

33 records · Page 2Linked to original sources

arXiv2013

KNET: Integrating Hypermedia and Bayesian Modeling

KNET is a general-purpose shell for constructing expert systems based on belief networks and decision networks. Such networks serve as graphical representations for decision models, in which the knowledge engineer must define clearly the alternatives, states, preferences, and relationships that constitute a decision basis. KNET contains a knowledge-engineering core written in Object Pascal and an interface that tightly integrates HyperCard, a hypertext authoring tool for the Apple Macintosh computer, into a novel expert-system architecture. Hypertext and hypermedia have become increasingly important in the storage management, and retrieval of information. In broad terms, hypermedia deliver heterogeneous bits of information in dynamic, extensively cross-referenced packages. The resulting KNET system features a coherent probabilistic scheme for managing uncertainty, an objectoriented graphics editor for drawing and manipulating decision networks, and HyperCard's potential for quickly constructing flexible and friendly user interfaces. We envision KNET as a useful prototyping tool for our ongoing research on a variety of Bayesian reasoning problems, including tractable representation, inference, and explanation.

cs.AI↗

arXiv2013

A Method for Using Belief Networks as Influence Diagrams

This paper demonstrates a method for using belief-network algorithms to solve influence diagram problems. In particular, both exact and approximation belief-network algorithms may be applied to solve influence-diagram problems. More generally, knowing the relationship between belief-network and influence-diagram problems may be useful in the design and development of more efficient influence diagram algorithms.

cs.AI↗

arXiv2013

Updating Probabilities in Multiply-Connected Belief Networks

This paper focuses on probability updates in multiply-connected belief networks. Pearl has designed the method of conditioning, which enables us to apply his algorithm for belief updates in singly-connected networks to multiply-connected belief networks by selecting a loop-cutset for the network and instantiating these loop-cutset nodes. We discuss conditions that need to be satisfied by the selected nodes. We present a heuristic algorithm for finding a loop-cutset that satisfies these conditions.

cs.AI↗

arXiv2013

Stochastic Simulation of Bayesian Belief Networks

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling, and a method described by Pearl, called stochastic simulation. We first review the conditions under which logic sampling is computationally infeasible. Such cases motivated the development of the Pearl's stochastic simulation algorithm. We have found that this stochastic simulation algorithm, when applied to certain networks, leads to much slower than expected convergence to the true posterior probabilities. This behavior is a result of the tendency for local areas in the network to become fixed through many simulation cycles. The time required to obtain significant convergence can be made arbitrarily long by strengthening the probabilistic dependency between nodes. We propose the use of several forms of graph modification, such as graph pruning, arc reversal, and node reduction, in order to convert some networks into formats that are computationally more efficient for simulation.

cs.AI↗

arXiv2013

An Algorithm for Computing Probabilistic Propositions

A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In particular, the method allows belief network algorithms to calculate general probabilistic propositions over nodes in the network. Although in the worst case the time complexity of the method is exponential in the size of a query, it is polynomial in the size of a number of common types of queries.

cs.AI↗

arXiv2013

A Bayesian Method for Constructing Bayesian Belief Networks from Databases

This paper presents a Bayesian method for constructing Bayesian belief networks from a database of cases. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. We relate the methods in this paper to previous work, and we discuss open problems.

cs.AI↗

arXiv2013

An Evaluation of an Algorithm for Inductive Learning of Bayesian Belief Networks Usin

Bayesian learning of belief networks (BLN) is a method for automatically constructing belief networks (BNs) from data using search and Bayesian scoring techniques. K2 is a particular instantiation of the method that implements a greedy search strategy. To evaluate the accuracy of K2, we randomly generated a number of BNs and for each of those we simulated data sets. K2 was then used to induce the generating BNs from the simulated data. We examine the performance of the program, and the factors that influence it. We also present a simple BN model, developed from our results, which predicts the accuracy of K2, when given various characteristics of the data set.

cs.AI↗

arXiv2013

A Structurally and Temporally Extended Bayesian Belief Network Model: Definitions, Properties, and Modeling Techniques

We developed the language of Modifiable Temporal Belief Networks (MTBNs) as a structural and temporal extension of Bayesian Belief Networks (BNs) to facilitate normative temporal and causal modeling under uncertainty. In this paper we present definitions of the model, its components, and its fundamental properties. We also discuss how to represent various types of temporal knowledge, with an emphasis on hybrid temporal-explicit time modeling, dynamic structures, avoiding causal temporal inconsistencies, and dealing with models that involve simultaneously actions (decisions) and causal and non-causal associations. We examine the relationships among BNs, Modifiable Belief Networks, and MTBNs with a single temporal granularity, and suggest areas of application suitable to each one of them.

cs.AI↗

arXiv2013

A Multivariate Discretization Method for Learning Bayesian Networks from Mixed Data

In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for multivariate discretization, whereby each continuous variable is discretized while taking into account its interaction with the other variables. The technique is based on the use of a Bayesian scoring metric that scores the discretization policy for a continuous variable given a BN structure and the observed data. Since the metric is relative to the BN structure currently being evaluated, the discretization of a variable needs to be dynamically adjusted as the BN structure changes.

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arXiv2013

Causal Discovery from a Mixture of Experimental and Observational Data

This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced by randomized controlled trials, result from the experimenter manipulating one or more variables (typically randomly) and observing the states of other variables. The paper presents a Bayesian method for learning the causal structure and parameters of the underlying causal process that is generating the data, given that (1) the data contains a mixture of observational and experimental case records, and (2) the causal process is modeled as a causal Bayesian network. This learning method was applied using as input various mixtures of experimental and observational data that were generated from the ALARM causal Bayesian network. In these experiments, the absolute and relative quantities of experimental and observational data were varied systematically. For each of these training datasets, the learning method was applied to predict the causal structure and to estimate the causal parameters that exist among randomly selected pairs of nodes in ALARM that are not confounded. The paper reports how these structure predictions and parameter estimates compare with the true causal structures and parameters as given by the ALARM network.

cs.AI↗

arXiv2013

A Bayesian Network Classifier that Combines a Finite Mixture Model and a Naive Bayes Model

In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two component models are based, in an attempt to improve on their classification performance, both in terms of accuracy and in terms of calibration of the estimated probabilities. The proposed classifier is obtained by superimposing a finite mixture model on the set of feature variables of a naive Bayes model. We present experimental results that compare the predictive performance on real datasets of the new classifier with the predictive performance of the NB classifier and the FM classifier.

cs.LG↗

arXiv2013

A Bayesian Method for Causal Modeling and Discovery Under Selection

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and case-control data in which a fixed number of samples with and without some condition is collected; such data are not uncommon. The paper describes a method for combining data under selection with prior beliefs in order to derive a posterior probability for a model of the causal processes that are generating the data in the population of interest. The priors include beliefs about the nature of the non-random sampling procedure. Although exact application of the method would be computationally intractable for most realistic datasets, efficient special-case and approximation methods are discussed. Finally, the paper describes how to combine learning under selection with previous methods for learning from observational and experimental data that are obtained on random samples of the population of interest. The net result is a Bayesian methodology that supports causal modeling and discovery from a rich mixture of different types of data.

cs.AI↗

arXiv2012

A Bayesian Network Scoring Metric That Is Based On Globally Uniform Parameter Priors

We introduce a new Bayesian network (BN) scoring metric called the Global Uniform (GU) metric. This metric is based on a particular type of default parameter prior. Such priors may be useful when a BN developer is not willing or able to specify domain-specific parameter priors. The GU parameter prior specifies that every prior joint probability distribution P consistent with a BN structure S is considered to be equally likely. Distribution P is consistent with S if P includes just the set of independence relations defined by S. We show that the GU metric addresses some undesirable behavior of the BDeu and K2 Bayesian network scoring metrics, which also use particular forms of default parameter priors. A closed form formula for computing GU for special classes of BNs is derived. Efficiently computing GU for an arbitrary BN remains an open problem.

cs.AI↗

arXiv2012

Bayesian Biosurveillance of Disease Outbreaks

Early, reliable detection of disease outbreaks is a critical problem today. This paper reports an investigation of the use of causal Bayesian networks to model spatio-temporal patterns of a non-contagious disease (respiratory anthrax infection) in a population of people. The number of parameters in such a network can become enormous, if not carefully managed. Also, inference needs to be performed in real time as population data stream in. We describe techniques we have applied to address both the modeling and inference challenges. A key contribution of this paper is the explication of assumptions and techniques that are sufficient to allow the scaling of Bayesian network modeling and inference to millions of nodes for real-time surveillance applications. The results reported here provide a proof-of-concept that Bayesian networks can serve as the foundation of a system that effectively performs Bayesian biosurveillance of disease outbreaks.

stat.AP↗

arXiv2012

A theoretical study of Y structures for causal discovery

There are several existing algorithms that under appropriate assumptions can reliably identify a subset of the underlying causal relationships from observational data. This paper introduces the first computationally feasible score-based algorithm that can reliably identify causal relationships in the large sample limit for discrete models, while allowing for the possibility that there are unobserved common causes. In doing so, the algorithm does not ever need to assign scores to causal structures with unobserved common causes. The algorithm is based on the identification of so called Y substructures within Bayesian network structures that can be learned from observational data. An example of a Y substructure is A -> C, B -> C, C -> D. After providing background on causal discovery, the paper proves the conditions under which the algorithm is reliable in the large sample limit.

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