Dynamic diagnostic and decision procedures under uncertainty

Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 87–104, May–June, 1994.     

A hyperparameter consensus method for agreement under uncertainty

This paper addresses the problem of information consensus in a team of networked agents by presenting a generic consensus method that permits agreement to a Bayesian fusion of uncertain local parameter estimates. In particular, the method utilizes the concept of conjugacy of probability distributions to achieve a steady-state estimate consistent with a Bayesian combination of each agent’s local knowledge, without requiring complex channel filters or being limited to normally distributed uncertainties. It is shown that this algorithm, termed hyperparameter consensus, is adaptable to many local uncertainty distributions within the exponential family, and will converge to a Bayesian fusion of local estimates with some standard assumptions on the network topology.     

Inference rules for proving the equivalence of recursive procedures

Inspired by Hoare’s rule for recursive procedures, we present three proof rules for the equivalence between recursive programs. The first rule can be used for proving partial equivalence of programs; the second can be used for proving their mutual termination; the third rule can be used for proving the equivalence of reactive programs. There are various applications to such rules, such as proving equivalence of programs after refactoring and proving backward compatibility.     

Maximum compatibility method for data fitting under interval uncertainty

For the linear regression model, the data-fitting problem under the interval uncertainty of the data is studied. As an estimate of the linear function parameters, it is proposed to take their values that deliver the maximum for the so-called recognizing functional of the parameter set compatible with the data (the maximum compatibility method). The properties of the recognizing functional, its interpretation, and the properties of the estimates obtained using the maximum compatibility method are investigated. The relationships to other data analysis methods are discussed, and a practical electrochemistry problem is solved.     

Inference procedures for the Birnbaum–Saunders distribution and its generalizations

Goodness-of-fit tests are constructed for the two-parameter Birnbaum–Saunders distribution in the case where the parameters are unknown and are therefore estimated from the data. With each test the procedure starts by computing efficient estimators of the parameters. Then the data are transformed to normality and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Two classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function. All methods are extended to cover the case of generalized three-parameter Birnbaum–Saunders distributions.     

A modified Benders decomposition method for efficient robust optimization under interval uncertainty

The goal of robust optimization problems is to find an optimal solution that is minimally sensitive to uncertain factors. Uncertain factors can include inputs to the problem such as parameters, decision variables, or both. Given any combination of possible uncertain factors, a solution is said to be robust if it is feasible and the variation in its objective function value is acceptable within a given user-specified range. Previous approaches for general nonlinear robust optimization problems under interval uncertainty involve nested optimization and are not computationally tractable. The overall objective in this paper is to develop an efficient robust optimization method that is scalable and does not contain nested optimization. The proposed method is applied to a variety of numerical and engineering examples to test its applicability. Current results show that the approach is able to numerically obtain a locally optimal robust solution to problems with quasi-convex constraints (≤ type) and an approximate locally optimal robust solution to general nonlinear optimization problems.     

Sequential probabilistic analytical target cascading method for hierarchical multilevel optimization under uncertainty

Probabilistic Analytical Target Cascading (PATC) is a methodology for hierarchical multilevel optimization under uncertainty. In PATC, the statisticalmoments of the stochastic interrelated responses are matched between neighbouring levels to ensure the consistency of the solution. When the interrelated response is far from normal distribution, high order moments may need to be matched in the PATC formulation, which results in great computational difficulty. To overcome this disadvantage, a sequential PATC (SPATC) approach is proposed in this paper. SPATC firstly decouples the original probabilistic design problem into deterministic optimization problem and probabilistic analysis, and then hierarchically decomposes them into subproblems. The statistical information matching between neighbouring levels in the existing PATC framework is eliminated in SPATC. All in one probabilistic analysis and hierarchical probabilistic analysis are established to calculate the probabilistic characteristic of the interrelated responses and linking variables. Three examples are used to demonstrate the effectiveness and efficiency of the proposed SPATC approach. The results show that the SPATC approach is more efficient and accurate than PATC, especially for the multilevel design problem with non-normal interrelated responses.     

Inference for Weibull distribution under generalized order statistics

Based on generalized order statistics from Weibull distribution the approach of Bayesian and non-Bayesian estimation are discussed. We present a simple and efficient simulational algorithm for generating a generalized order statistics sample from any continuous distribution. Specializations to Bayesian and non-Bayesian estimators, some lifetime parameters and confidence intervals of progressive II censoring and record values are obtained and compared with the existing results. Two examples are given to illustrate the proposed estimators and the simulation algorithm.     

A framework for building knowledge-bases under uncertainty

Managing uncertainty during the knowledge engineering process from elicitation to validation and verification requires a flexible, intuitive, and semantically sound knowledge representation. This is especially important since this process is typically highly interactive with the human user to add, update, and maintain knowledge. In this paper, we present a model of knowledge representation called Bayesian Knowledge-Bases (BKBs). It unifies a ‘if-then’ style rules with probability theory. We also consider the computational efficiency of reasoning over BKBs. We can show that through careful construction of the knowledge-base, reasoning is computationally tractable and can in fact be polynomial-time. BKBs are currently fielded in the PESKI intelligent system development environment.     

Inference under imprecise probability assessments

Under partial knowledge, the use of the precise probability might be misleading. However, it is possible to process imprecise assessments, such as comparative previsions or grades of previsions. Rules for checking their coherence with the theoretical model and for making inference are given. Sometimes the derived conclusions might provide us with a complete answer for a given problem. In any case, technical tools can measure the imprecision of the answer and reveal if the analysis is thorough enough.     

Semimyopic measurement selection for optimization under uncertainty

The following sequential decision problem is considered: given a set of items of unknown utility, an item with as high a utility as possible must be selected ("the selection problem"). Measurements (possibly noisy) of item features prior to selection are allowed at known costs. The goal is to optimize the overall sequential decision process of measurements and selection. Value of information (VOI) is a well-known scheme for selecting measurements, but the intractability of the problem typically leads to using myopic VOI estimates. In the selection problem, myopic VOI frequently badly underestimates the VOI, leading to inferior measurement policies. In this paper, the strict myopic assumption is relaxed into a scheme termed semimyopic, providing a spectrum of methods that can improve the performance of measurement policies. In particular, the efficiently computable method of "blinkered" VOI is proposed, and theoretical bounds for important special cases are examined. Empirical evaluation of "blinkered" VOI in the selection problem with normally distributed item values shows that it performs much better than pure myopic VOI.     

Bayesian optimization for learning gaits under uncertainty

Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal parameters can be daunting. Typically, this kind of parameter optimization requires specific expert knowledge and extensive robot experiments. Automatic black-box gait optimization methods greatly reduce the need for human expertise and time-consuming design processes. Many different approaches for automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this article, we thoroughly discuss multiple automatic optimization methods in the context of gait optimization. We extensively evaluate Bayesian optimization, a model-based approach to black-box optimization under uncertainty, on both simulated problems and real robots. This evaluation demonstrates that Bayesian optimization is particularly suited for robotic applications, where it is crucial to find a good set of gait parameters in a small number of experiments.     

Combinatorial optimization under uncertainty

In this paper, the general problem of Euclidean combinatorial optimization under uncertainty is formulated for the first time and the concepts of a stochastic multiset, a multiset of fuzzy numbers, a stochastic Euclidean combinatorial set, and general Euclidean combinatorial set of fuzzy stochastic numbers that combines the properties of both types of uncertainty are introduced. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 35–44, September–October 2008.     

Time-constrained reasoning under uncertainty

Dynamic classification problems present unique challenges beyond those of more traditionalstatic knowledge-based systems. Uncertain and incomplete input data, unpredictable event sequences, and critical time and resource constraints require new approaches and techniques for automated reasoning. Our work toward addressing these complex requirements has concentrated on developing an integrated software architecture which supports the knowledge engineering process from development to deployment. The approach we are using to deal with real-time issues in the deployment environment involves the use of a fast knowledge representation scheme, efficient forward and backward chaining mechanisms, and a meta-controller which handles asynchronous inputs, prioritized task requests, and hard performance deadlines.     

A survey of techniques for inference under uncertainty

The field of automated inference under uncertainty is too large and too young for elegant, unified presentation. We present, rather, a discussion of the principal techniques under some broad classifications. For the most important or least known techniques, we present, as appendices, introductory tutorials in order to give the reader some idea of the basic methods involved; other techniques we describe more briefly. First, after this introduction, we must cover some basic terms and philosophical ideas.     

Correspondence identification for collaborative multi-robot perception under uncertainty

Autonomous Robots - Correspondence identification is a critical capability for multi-robot collaborative perception, which allows a group of robots to consistently refer to the same objects in...     

Fuzzy modeling for intelligent decision making under uncertainty

We consider here the problem of decision making under uncertainty. We suggest an approach for the construction of decision functions which allow for the inclusion of probabilistic information as well as for the inclusion of information about the decision maker's attitude and preferences. Use is made of the fuzzy modeling technology to construct these functions from specifications provided by the decision maker.     

Pareto surface construction for multi-objective optimization under uncertainty

Structural and Multidisciplinary Optimization - This paper presents a novel approach for multi-objective optimization under both aleatory and epistemic sources of uncertainty. Given paired samples...     

Methods for minimax estimation under elementwise covariance uncertainty

We consider the minimax estimation problem in the linear regression model under elementwise constraints imposed on the covariance matrix of the random parameters vector. Minimax estimates are designed using several approaches to the numerical solution of the dual problem, namely, the semidefinite programming method, the conditional gradient method and its modification with the Lagrange multipliers and regularization. The efficiency of the suggested methods is illustrated by the example of path restoration for a maneuvering target with a statistically uncertain acceleration.     

A methodology for missile countermeasures optimization under uncertainty

The missile countermeasures optimization problem is a complex strategy optimization problem that combines aircraft maneuvers with additional countermeasures in an attempt to survive attack from a single surface-launched, anti-aircraft missile. Classic solutions require the evading aircraft to execute specific sequences of maneuvers at precise distances from the pursuing missile and do not effectively account for uncertainty about the type and/or current state of the missile. This paper defines a new methodology for solving the missile countermeasures optimization problem under conditions of uncertainty. The resulting genetic programming system evolves programs that combine maneuvers with such countermeasures as chaff, flares, and jamming to optimize aircraft survivability. This methodology may be generalized to solve strategy optimization problems for intelligent, autonomous agents operating under conditions of uncertainty.