arXiv subjects

Ross D. Shachter

Publications and source records attributed to Ross D. Shachter.

At least 19 recordsLinked to original sources

arXiv2015

A Definition and Graphical Representation for Causality

We present a precise definition of cause and effect in terms of a fundamental notion called unresponsiveness. Our definition is based on Savage's (1954) formulation of decision theory and departs from the traditional view of causation in that our causal assertions are made relative to a set of decisions. An important consequence of this departure is that we can reason about cause locally, not requiring a causal explanation for every dependency. Such local reasoning can be beneficial because it may not be necessary to determine whether a particular dependency is causal to make a decision. Also in this paper, we examine the graphical encoding of causal relationships. We show that influence diagrams in canonical form are an accurate and efficient representation of causal relationships. In addition, we establish a correspondence between canonical form and Pearl's causal theory.

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arXiv2015

A Decision-Based View of Causality

Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able to predict the effects of actions. In this paper, we attempt to unite two branches of research that address such predictions: causal modeling and decision analysis. First, we provide a definition of causal dependence in decision-analytic terms, which we derive from consequences of causal dependence cited in the literature. Using this definition, we show how causal dependence can be represented within an influence diagram. In particular, we identify two inadequacies of an ordinary influence diagram as a representation for cause. We introduce a special class of influence diagrams, called causal influence diagrams, which corrects one of these problems, and identify situations where the other inadequacy can be eliminated. In addition, we describe the relationships between Howard Canonical Form and existing graphical representations of cause.

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arXiv2013

Approximate Kalman Filter Q-Learning for Continuous State-Space MDPs

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that outperforms the current state of the art projected TD-Learning methods on several standard benchmark problems.

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arXiv2013

Directed Reduction Algorithms and Decomposable Graphs

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on undirected graph structures, and that those methods are inherently superior to those based on node reduction operations on the influence diagram. We show here that these two approaches are essentially the same, since they are explicitly or implicity building and operating on the same underlying graphical structures. In this paper we examine those graphical structures and show how this insight can lead to an improved class of directed reduction methods.

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arXiv2013

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.

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arXiv2013

Simulation Approaches to General Probabilistic Inference on Belief Networks

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the graph structure is relatively sparse, and probabilistic sampling techniques which exploit the "conductance" of an embedded Markov chain when the conditional probabilities have non-extreme values. In this paper, we investigate a family of "forward" Monte Carlo sampling techniques similar to Logic Sampling [Henrion, 1988] which appear to perform well even in some multiply connected networks with extreme conditional probabilities, and thus would be generally applicable. We consider several enhancements which reduce the posterior variance using this approach and propose a framework and criteria for choosing when to use those enhancements.

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arXiv2013

A Linear Approximation Method for Probabilistic Inference

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on the Gaussian influence diagram, iterates over linear approximations to the inference problem.

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arXiv2013

A Heuristic Bayesian Approach to Knowledge Acquisition: Application to Analysis of Tissue-Type Plasminogen Activator

This paper describes a heuristic Bayesian method for computing probability distributions from experimental data, based upon the multivariate normal form of the influence diagram. An example illustrates its use in medical technology assessment. This approach facilitates the integration of results from different studies, and permits a medical expert to make proper assessments without considerable statistical training.

cs.AI↗

arXiv2013

Efficient Inference on Generalized Fault Diagrams

The generalized fault diagram, a data structure for failure analysis based on the influence diagram, is defined. Unlike the fault tree, this structure allows for dependence among the basic events and replicated logical elements. A heuristic procedure is developed for efficient processing of these structures.

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arXiv2013

A Backwards View for Assessment

Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the relationship between evidence and hypothesis in a directed manner. Moreover, the direction in which evidence is stored is typically from evidence to hypothesis.

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arXiv2013

DAVID: Influence Diagram Processing System for the Macintosh

Influence diagrams are a directed graph representation for uncertainties as probabilities. The graph distinguishes between those variables which are under the control of a decision maker (decisions, shown as rectangles) and those which are not (chances, shown as ovals), as well as explicitly denoting a goal for solution (value, shown as a rounded rectangle.

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arXiv2013

Intelligent Probabilistic Inference

The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network that makes explicit the random variables in a model and their probabilistic dependencies. Recent advances have developed solution procedures based on the influence diagram. In this paper, we examine the fundamental properties that underlie those techniques, and the information about the probabilistic structure that is available in the influence diagram representation. The influence diagram is a convenient representation for computer processing while also being clear and non-mathematical. It displays probabilistic dependence precisely, in a way that is intuitive for decision makers and experts to understand and communicate. As a result, the same influence diagram can be used to build, assess and analyze a model, facilitating changes in the formulation and feedback from sensitivity analysis. The goal in this paper is to determine arbitrary conditional probability distributions from a given probabilistic model. Given qualitative information about the dependence of the random variables in the model we can, for a specific conditional expression, specify precisely what quantitative information we need to be able to determine the desired conditional probability distribution. It is also shown how we can find that probability distribution by performing operations locally, that is, over subspaces of the joint distribution. In this way, we can exploit the conditional independence present in the model to avoid having to construct or manipulate the full joint distribution. These results are extended to include maximal processing when the information available is incomplete, and optimal decision making in an uncertain environment. Influence diagrams as a computer-aided modeling tool were developed by Miller, Merkofer, and Howard [5] and extended by Howard and Matheson [2]. Good descriptions of how to use them in modeling are in Owen [7] and Howard and Matheson [2]. The notion of solving a decision problem through influence diagrams was examined by Olmsted [6] and such an algorithm was developed by Shachter [8]. The latter paper also shows how influence diagrams can be used to perform a variety of sensitivity analyses. This paper extends those results by developing a theory of the properties of the diagram that are used by the algorithm, and the information needed to solve arbitrary probability inference problems. Section 2 develops the notation and the framework for the paper and the relationship between influence diagrams and joint probability distributions. The general probabilistic inference problem is posed in Section 3. In Section 4 the transformations on the diagram are developed and then put together into a solution procedure in Section 5. In Section 6, this procedure is used to calculate the information requirement to solve an inference problem and the maximal processing that can be performed with incomplete information. Section 7 contains a summary of results.

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arXiv2013

A Graph-Based Inference Method for Conditional Independence

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without resorting to their numerical definition. This paper explores a representation for independence statements using multiple undirected graphs and some simple graphical transformations. The independence statements derivable in this system are equivalent to those obtainable by the graphoid axioms. Therefore, this is a purely graphical proof technique for conditional independence.

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arXiv2013

Structural Controllability and Observability in Influence Diagrams

Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability analyzes the inferability of its variables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowledge of the values of its elements (tin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional dependence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intuitions and detecting inconsistency in a model. This type of qualitative reasoning can sometimes provide insight even when there is insufficient numerical information in a model.

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arXiv2013

Decision Making Using Probabilistic Inference Methods

The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the fundamental normative arguments of decision theory. In this paper we show how the developments underlying those efficient methods can be applied immediately to decision problems. In addition to general approaches which need know nothing about the actual probabilistic inference method, we suggest some simple modifications to the clustering family of algorithms in order to efficiently incorporate decision making capabilities.

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arXiv2013

End-User Construction of Influence Diagrams for Bayesian Statistics

Influence diagrams are ideal knowledge representations for Bayesian statistical models. However, these diagrams are difficult for end users to interpret and to manipulate. We present a user-based architecture that enables end users to create and to manipulate the knowledge representation. We use the problem of physicians' interpretation of two-arm parallel randomized clinical trials (TAPRCT) to illustrate the architecture and its use. There are three primary data structures. Elements of statistical models are encoded as subgraphs of a restricted class of influence diagram. The interpretations of those elements are mapped into users' language in a domain-specific, user-based semantic interface, called a patient-flow diagram, in the TAPRCT problem. Pennitted transformations of the statistical model that maintain the semantic relationships of the model are encoded in a metadata-state diagram, called the cohort-state diagram, in the TAPRCT problem. The algorithm that runs the system uses modular actions called construction steps. This framework has been implemented in a system called THOMAS, that allows physicians to interpret the data reported from a TAPRCT.

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arXiv2013

Mixtures of Gaussians and Minimum Relative Entropy Techniques for Modeling Continuous Uncertainties

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is to fit analytically tractable continuous probability distributions. This approach has potential simplicity and accuracy advantages, especially if variables can be transformed first. This paper shows how a minimum relative entropy criterion can drive both transformation and fitting, illustrating with a power and logarithm family of transformations and mixtures of Gaussian (normal) distributions, which allow use of efficient influence diagram methods. The fitting procedure in this case is the well-known EM algorithm. The selection of the number of components in a fitted mixture distribution is automated with an objective that trades off accuracy and computational cost.

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arXiv2013

Using Potential Influence Diagrams for Probabilistic Inference and Decision Making

The potential influence diagram is a generalization of the standard "conditional" influence diagram, a directed network representation for probabilistic inference and decision analysis [Ndilikilikesha, 1991]. It allows efficient inference calculations corresponding exactly to those on undirected graphs. In this paper, we explore the relationship between potential and conditional influence diagrams and provide insight into the properties of the potential influence diagram. In particular, we show how to convert a potential influence diagram into a conditional influence diagram, and how to view the potential influence diagram operations in terms of the conditional influence diagram.

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