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Horvitz, Eric J., Heckerman, David
Over the last decade, there has been growing interest in the use or measures or change in belief for reasoning with uncertainty in artificial intelligence research. An important characteristic of several methodologies that reason with changes in belief or belief updates, is a property that we term modularity. We call updates that satisfy this property modular updates. Whereas probabilistic measures of belief update - which satisfy the modularity property were first discovered in the nineteenth century, knowledge and discussion of these quantities remains obscure in artificial intelligence research. We define modular updates and discuss their inappropriate use in two influential expert systems.
Horvitz, Eric J.
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete normative analysis impossible. We attempt to move discussion beyond the debate over the scope of problems that can be handled effectively to cases where it is clear that there are insufficient computational resources to perform an analysis deemed as complete. Under these conditions, we stress the importance of considering the expected costs and benefits of applying alternative approximation procedures and heuristics for computation and knowledge acquisition. We discuss how knowledge about the structure of user utility can be used to control value tradeoffs for tailoring inference to alternative contexts. We address the notion of real-time rationality, focusing on the application of knowledge about the expected timewise-refinement abilities of reasoning strategies to balance the benefits of additional computation with the costs of acting with a partial result. We discuss the benefits of applying decision theory to control the solution of difficult problems given limitations and uncertainty in reasoning resources.
Breese, John S., Horvitz, Eric J.
The intelligent reformulation or restructuring of a belief network can greatly increase the efficiency of inference. However, time expended for reformulation is not available for performing inference. Thus, under time pressure, there is a tradeoff between the time dedicated to reformulating the network and the time applied to the implementation of a solution. We investigate this partition of resources into time applied to reformulation and time used for inference. We shall describe first general principles for computing the ideal partition of resources under uncertainty. These principles have applicability to a wide variety of problems that can be divided into interdependent phases of problem solving. After, we shall present results of our empirical study of the problem of determining the ideal amount of time to devote to searching for clusters in belief networks. In this work, we acquired and made use of probability distributions that characterize (1) the performance of alternative heuristic search methods for reformulating a network instance into a set of cliques, and (2) the time for executing inference procedures on various belief networks. Given a preference model describing the value of a solution as a function of the delay required for its computation, the system selects an ideal time to devote to reformulation.
We introduce and analyze the problem of the compilation of decision models from a decision-theoretic perspective. The techniques described allow us to evaluate various configurations of compiled knowledge given the nature of evidential relationships in a domain, the utilities associated with alternative actions, the costs of run-time delays, and the costs of memory. We describe procedures for selecting a subset of the total observations available to be incorporated into a compiled situation-action mapping, in the context of a binary decision with conditional independence of evidence. The methods allow us to incrementally select the best pieces of evidence to add to the set of compiled knowledge in an engineering setting. After presenting several approaches to compilation, we exercise one of the methods to provide insight into the relationship between the distribution over weights of evidence and the preferred degree of compilation.
Heckerman, David, Horvitz, Eric J.
In this paper, we examine the concept of modularity, an often cited advantage of the ruled-based representation methodology. We argue that the notion of modularity consists of two distinct concepts which we call syntactic modularity and semantic modularity. We argue that when reasoning under certainty, it is reasonable to regard the rule-based approach as both syntactically and semantically modular. However, we argue that in the case of plausible reasoning, rules are syntactically modular but are rarely semantically modular. To illustrate this point, we examine a particular approach for managing uncertainty in rule-based systems called the MYCIN certainty factor model. We formally define the concept of semantic modularity with respect to the certainty factor model and discuss logical consequences of the definition. We show that the assumption of semantic modularity imposes strong restrictions on rules in a knowledge base. We argue that such restrictions are rarely valid in practical applications. Finally, we suggest how the concept of semantic modularity can be relaxed in a manner that makes it appropriate for plausible reasoning.
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final probabilities of interest with the allocation of a complete resource fraction. The approach allows a reasoner to exchange arbitrary quantities of computational resource for incremental gains in inference quality. As such, bounded conditioning holds promise as a useful inference technique for reasoning under the general conditions of uncertain and varying reasoning resources. The algorithm solves a probabilistic bounding problem in complex belief networks by breaking the problem into a set of mutually exclusive, tractable subproblems and ordering their solution by the expected effect that each subproblem will have on the final answer. We introduce the algorithm, discuss its characterization, and present its performance on several belief networks, including a complex model for reasoning about problems in intensive-care medicine.
Horvitz, Eric J., Rutledge, Geoffrey
We discuss representing and reasoning with knowledge about the time-dependent utility of an agent's actions. Time-dependent utility plays a crucial role in the interaction between computation and action under bounded resources. We present a semantics for time-dependent utility and describe the use of time-dependent information in decision contexts. We illustrate our discussion with examples of time-pressured reasoning in Protos, a system constructed to explore the ideal control of inference by reasoners with limit abilities.
Dagum, Paul, Horvitz, Eric J.
We describe how we selectively reformulate portions of a belief network that pose difficulties for solution with a stochastic-simulation algorithm. With employ the selective conditioning approach to target specific nodes in a belief network for decomposition, based on the contribution the nodes make to the tractability of stochastic simulation. We review previous work on BNRAS algorithms- randomized approximation algorithms for probabilistic inference. We show how selective conditioning can be employed to reformulate a single BNRAS problem into multiple tractable BNRAS simulation problems. We discuss how we can use another simulation algorithm-logic sampling-to solve a component of the inference problem that provides a means for knitting the solutions of individual subproblems into a final result. Finally, we analyze tradeoffs among the computational subtasks associated with the selective conditioning approach to reformulation.
Poh, Kim-Leng, Horvitz, Eric J.
We investigate the value of extending the completeness of a decision model along different dimensions of refinement. Specifically, we analyze the expected value of quantitative, conceptual, and structural refinement of decision models. We illustrate the key dimensions of refinement with examples. The analyses of value of model refinement can be used to focus the attention of an analyst or an automated reasoning system on extensions of a decision model associated with the greatest expected value.
Burnell, Lisa J., Horvitz, Eric J.
We describe the integration of logical and uncertain reasoning methods to identify the likely source and location of software problems. To date, software engineers have had few tools for identifying the sources of error in complex software packages. We describe a method for diagnosing software problems through combining logical and uncertain reasoning analyses. Our preliminary results suggest that such methods can be of value in directing the attention of software engineers to paths of an algorithm that have the highest likelihood of harboring a programming error.