Results 1  10
of
21
Geometric Foundations for IntervalBased Probabilities
 Annals of Mathematics and Artificial Intelligence
, 1998
"... IONBASED PROBABILISTIC PLANNING In the framework of decisiontheoretic planning, uncertainty in the state of the world and in the effects of actions are represented with probabilities, and the planner's goals, as well as tradeoffs among them, are represented with utilities. 9 Given this represent ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
IONBASED PROBABILISTIC PLANNING In the framework of decisiontheoretic planning, uncertainty in the state of the world and in the effects of actions are represented with probabilities, and the planner's goals, as well as tradeoffs among them, are represented with utilities. 9 Given this representation, the objective is to find an optimal plan or policy, where optimality is defined as maximizing expected utility. In most of the existing decisiontheoretic planning approaches, the world is represented with a probability distribution over the state space, and actions are represented as stochastic mappings among the states [14,5,1,26]. Given this framing of the problem, all probabilistic and decisiontheoretic planners face the burden of computational complexity in seeking an optimal or nearoptimal solution. One popular way to address this problem is to use abstraction techniques to guide the search through the plan space and to reduce the cost of plan evaluation. This concept has bee...
Theoretical Foundations for AbstractionBased Probabilistic Planning
 In Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence
, 1996
"... ionBased Probabilistic Planning Vu Ha Peter Haddawy Department of EE & CS University of WisconsinMilwaukee fvu, haddawyg@cs.uwm.edu Abstract Modeling worlds and actions under uncertainty is one of the central problems in the framework of decisiontheoretic planning. The representation must be ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
ionBased Probabilistic Planning Vu Ha Peter Haddawy Department of EE & CS University of WisconsinMilwaukee fvu, haddawyg@cs.uwm.edu Abstract Modeling worlds and actions under uncertainty is one of the central problems in the framework of decisiontheoretic planning. The representation must be general enough to capture realworld problems but at the same time it must provide a basis upon which theoretical results can be derived. The central notion in the framework we propose here is that of the affineoperator, which serves as a tool for constructing (convex) sets of probability distributions, and which can be considered as a generalization of belief functions and interval mass assignments. Uncertainty in the state of the worlds is modeled with sets of probability distributions, represented by affinetrees, while actions are defined as treemanipulators. A small set of key properties of the affineoperator is presented, forming the basis for most existing operatorbased definitio...
Probabilistic logic and probabilistic networks
, 2008
"... While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches ..."
Abstract

Cited by 17 (13 self)
 Add to MetaCart
While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic fit into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. Specifically, we show in Part I that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question: the standard probabilistic semantics (which takes probability functions as models), probabilistic argumentation (which considers the probability of a hypothesis being a logical consequence of the available evidence), evidential probability (which handles reference classes and frequency data), classical statistical inference
A Theory of Satisficing Control
, 1996
"... The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a superlative perspective. These techniques can be of limited value when the global behavior of the system is difficult to characterize, as it may be when the system is nonlinear, when the inpu ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a superlative perspective. These techniques can be of limited value when the global behavior of the system is difficult to characterize, as it may be when the system is nonlinear, when the input is constrained, or when only partial information is available regarding system dynamics or the environment. Satisficing control theory is an alternative approach that is compatible with such systems. This theory is extended by the introduction of the notion of strongly satisficing to provide a rigorous, systematic procedure for the design of satisficing controllers which are consistent with optimal control theory. Because they are often difficult to solve optimally, one application of satisficing control theory is to nonlinear control problems. Of particular interest are the nonlinear quadratic regulator and nonlinear minimum time problems. A controller synthesis procedure and resulting so...
Confidence Intervals and Prediction Intervals for FeedForward Neural Networks
 Clinical Applications of Artificial Neural Networks
, 2001
"... d to feedforward networks. This includes a critique on Bayesian confidence intervals and classification. 1.1 Regression Regression analysis is a common statistical technique for modelling the relationshipb etween a response or dependent) variable y and a set x of regressors x 1 ,... ,x d (also k ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
d to feedforward networks. This includes a critique on Bayesian confidence intervals and classification. 1.1 Regression Regression analysis is a common statistical technique for modelling the relationshipb etween a response or dependent) variable y and a set x of regressors x 1 ,... ,x d (also known as independent or explanatory variables). For example, the relationship couldb eb etween whether a patient has a malig1 2 Dybowski & Roberts nantbq ast tumor (the response variab e) and the patient's age and level of serum albq= n (the regressors). When an article includes a discussion of artificial neural networks, it is customary to refer to response variab les as targets and regressors as inputs. Furthermore, the ordered set {x 1 ,... ,x<F7
Model predictive satisficing fuzzy logic control
 IEEE Transactions on Fuzzy Systems
, 1999
"... Abstract — Modelpredictive control, which is an alternative to conventional optimal control, provides controller solutions to many constrained and nonlinear control problems. However, even when a good model is available, it may be necessary for an expert to specify the relationship between local mo ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
Abstract — Modelpredictive control, which is an alternative to conventional optimal control, provides controller solutions to many constrained and nonlinear control problems. However, even when a good model is available, it may be necessary for an expert to specify the relationship between local model predictions and global system performance. We present a satisficing fuzzy logic controller that is based on a receding control horizon, but which employs a fuzzy description of system consequences via model predictions. This controller considers the gains and losses associated with each control action, is compatible with robust design objectives, and permits flexible defuzzifier design. We demonstrate the controller’s application to representative problems from the control of uncertain nonlinear systems. Index Terms — Decisionmaking, intelligent control, predictive control, satisficing.
Separation Properties of Sets of Probability Measures
 In Conference on Uncertainty in Artificial Intelligence
, 2000
"... This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparati ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to dseparation but still fails to guarantee a belief separation property. To overcome this unsatisfactory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this result implies that (1) separation properties of Bayesian networks do extend to epistemic independence and sets of probability measures, and (2) strong independence has a clear justi cation based on epistemic independence and the strong Markov condition. 1
Robust Bayesianism: Relation to evidence theory
 J. Advances in Information Fusion
"... We are interested in understanding the relationship between Bayesian inference and evidence theory. The concept of a set of probability distributions is central both in robust Bayesian analysis and in some versions of DempsterShafer’s evidence theory. We interpret imprecise probabilities as impreci ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We are interested in understanding the relationship between Bayesian inference and evidence theory. The concept of a set of probability distributions is central both in robust Bayesian analysis and in some versions of DempsterShafer’s evidence theory. We interpret imprecise probabilities as imprecise posteriors obtainable from imprecise likelihoods and priors, both of which are convex sets that can be considered as evidence and represented with, e.g., DSstructures. Likelihoods and prior are in Bayesian analysis combined with Laplace’s parallel composition. The natural and simple robust combination operator makes all pairwise combinations of elements from the two sets representing prior and likelihood. Our proposed combination operator is unique, and it has interesting normative and factual properties. We compare its behavior with other proposed fusion rules, and earlier efforts to reconcile Bayesian analysis and evidence theory. The behavior of the robust rule is consistent with the behavior of Fixsen/Mahler’s modified Dempster’s (MDS) rule, but not with Dempster’s rule. The Bayesian framework is liberal in allowing all significant uncertainty concepts to be modeled and taken care of and is therefore a viable, but probably not the only, unifying structure that can be economically taught and in which alternative solutions can be modeled, compared and explained. Manuscript received April 20, 2006; released for publication April
Dynamics of Beliefs and Strategy of Perception.
 in 12th ECAI
, 1996
"... . An autonomous agent equipped with sensors is expected to efficiently perform a given mission within a dynamic and changing world of which it has an uncertain representation. In order to keep this representation wellgrounded, the agent has to organize the acquisition of information autonomously. A ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
. An autonomous agent equipped with sensors is expected to efficiently perform a given mission within a dynamic and changing world of which it has an uncertain representation. In order to keep this representation wellgrounded, the agent has to organize the acquisition of information autonomously. A key issue is to choose a framework for the representation of beliefs which is adapted to deal both with time and uncertainty. A perception strategy, designed for the purpose of collecting the right information at the right time, should be based on a dynamic evaluation of the relevance of the beliefs of the system. A review of works concerning the problems of belief revision and temporal representation of uncertainty is presented. The differences between the variety of existing formalisms are discussed and the framework of a welladapted approach is recalled. The issue of a robust perception strategy is addressed within this framework ; a first solution, together with the corresponding resul...
A Derivation of QuasiBayesian Theory
, 1997
"... This report presents a concise and complete theory of convex sets of distributions, which extends and unifies previous approaches. Lower expectations and convex sets of probability distributions are derived from axioms of preference; concepts of conditionalization, independence and conditional indep ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This report presents a concise and complete theory of convex sets of distributions, which extends and unifies previous approaches. Lower expectations and convex sets of probability distributions are derived from axioms of preference; concepts of conditionalization, independence and conditional independence are defined based on convex sets of distributions. c fl1996 Carnegie Mellon University This research is supported in part by NASA under Grant NAGW1175. Fabio Cozman was supported under a scholarship from CNPq, Brazil. 1 Introduction A variety of approaches for decisionmaking deal with intervalvalued inferences. Researchers have investigated the properties of inner/outer measures [19, 23, 44, 57], and lower probability [4, 9, 14, 28, 56] for evaluating and selecting courses of action; DempsterShafer theory employs belief and plausibility functions [44, 49] to represent intervalvalued "beliefs" in events. Several authors advocate the use of convex sets of distributions as a fl...