Eugene Santos

A linear constraint satisfaction approach to cost-based abduction

Santos Jr, E., A linear constraint satisfaction approach to cost-based abduction, Artificial Intelligence 65 (1994) 1-27. Abduction is the problem of finding the best explanation for a given set of observations. Within AI, this has been modeled as proving the observation by assuming some set of hypotheses. Cost-based abduction associates a cost with each hypothesis. The best proof is the one which assumes the least costly set. Previous approaches to finding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, efficient admissible heuristics have proven difficult to find. In this paper, we present a new technique for finding least cost sets by using linear constraints to represent causal relationships. In particular, we are able to recast the problem as a 0-1 integer linear programming problem. We can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost-based abduction problems. Experiments comparing our linear constraint satisfaction approach to standard graph searching methodologies suggest that our approach is superior to existing search techniques in that our approach exhibits an expected-case polynomial run-time growth rate.

Polynomial solvability of cost-based abduction

Abstract In recent empirical studies we have shown that many interesting cost-based abduction problems can be solved efficiently by considering the linear program relaxation of their integer program formulation. We tie this to the concept of total unimodularity from network flow analysis, a fundamental result in polynomial solvability. From this, we can determine the polynomial solvability of abduction problems and, in addition, present a new heuristic for branch and bound in the non-polynomial cases.

Belief updating by enumerating high-probabilityindependence-based assignments

Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially supported variables. We use IB assignments to approximate marginal probabilities in Bayesian belief networks. Recent work in belief updating for Bayes networks attempts to approximate posterior probabilities by finding a small number of the highest probability complete (or perhaps evidentially supported) assignments. Under certain assumptions, the probability mass in the union of these assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly-connected networks, where the maximum clique size or the cutset size make the standard algorithms intractable. Since IB assignments contain fewer assigned variables, the probability mass in each assignment is greater than in the respective complete assignment. Thus, fewer IB assignments are sufficient, and a good approximation can be obtained more efficiently. IB assignments can be used for efficiently approximating posterior node probabilities even in cases which do not obey the rather strict skewness assumptions used in previous research. Two algorithms for finding the high probability IB assignments are suggested: one by doing a best-first heuristic search, and another by special-purpose integer linear programming. Experimental results show that this approach is feasible for highly connected belief networks.

Exploiting case-based independence for approximating marginal probabilities

Abstract Computing marginal probabilities in Bayes networks is a hard problem. Deterministic anytime approximation schemes accumulate the probability mass in a small number of value assignments to the network variables. Under certain assumptions, the probability mass in the assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly connected networks, where the topology makes the exact algorithms intractable. Bayes networks often possess a fine independence structure not evident from the topology, but apparent in local conditional distributions. Independence-based (IB) assignments, originally proposed as a theory of abduction, take advantage of such independence, and thus contain fewer assigned variables-and more probability mass. We present several algorithms that use IB assignments for approximating marginal probabilities. Experimental results suggest that this approach is feasible for highly connected belief networks.

Hybrid algorithms for approximate belief updating in Bayes nets

Abstract Belief updating in Bayes nets, a well-known computationally hard problem, has recently been approximated by several deterministic algorithms and by various randomized approximation algorithms. Deterministic algorithms usually provide probability bounds, but have an exponential runtime. Some randomized schemes have a polynomial runtime, but provide only probability estimates. Randomized algorithms that accumulate high-probability partial instantiations, resulting in probability bounds, are presented. Some of these algorithms are also sampling algorithms. Specifically, a variant of backward sampling, used both as a sampling algorithm and as a randomized enumeration algorithm, is introduced and evaluated. An implicit assumption made in prior work, for both sampling and accumulation algorithms, that query nodes must be instantiated in all the samples, is relaxed. Genetic algorithms can be used as an alternate search component for high-probability instantiations; several methods of applying them to belief updating are presented.

Deterministic approximation of marginal probabilities in Bayes nets

Computation of marginal probabilities in Bayes nets is central to numerous reasoning and automatic decision-making systems. This paper presents a deterministic approximation scheme for this hard problem that supplies provably correct bounds by aggregating probability mass in independence-based (IB) assignments. It refines belief updating methods. It approximates posterior probabilities by finding a small number of the highest probability complete (or evidentially supported) assignments. Under certain assumptions, the probability mass in the union of these assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly connected networks. Since IB assignments contain fewer assigned variables, the probability mass in each assignment is greater than in the respective complete assignment. Thus, fewer assignments are sufficient, and a good approximation can be obtained efficiently. Two classes of algorithms for finding high-probability assignments are suggested: best-first heuristic search and a special integer linear program (ILP). Since IB assignments may be overlapping events in probability space, accumulating the mass in a set of assignments may be hard. In the ILP variant, it is easy to avoid the problem by adding equations that prohibit overlap. In the best-first search algorithm, other schemes are necessary, but experimental results suggest that using inclusion-exclusion (potentially exponential-time in the worst case) in the overlap cases is not too expensive for most problem instances.

Adversarial inferencing for generating dynamic adversary behavior

In the current world environment, the rapidly changing dynamics of organizational adversaries are increasing the difficulty for Military Analysts and Planners to accurately predict potential actions. As an integral part of the planning process, we need to assess our planning strategies against the range of potential adversarial actions. This dynamic world environment has established a necessity to develop tools to assist in establishing hypotheses for future adversary actions. Our research investigated the feasibility to utilize an adversarial tool as the core element within a predictive simulation to establish emergent adversarial behavior. It is our desire to use this intelligent adversary to generate alternative futures in performing Course of Action (COA) analysis. Such a system will allow planners to gauge and evaluate the effectiveness of alternative plans under varying actions and reactions. This research focuses on one of many possible techniques required to address the technical challenge of generating intelligent adversary behaviors. This development activity addresses two research components. First, establish an environment in which to perform the feasibility experiment and analysis. The proof of concept performed to analyze and assess this feasibility of utilizing an adversarial inferencing system to provide emergent adversary behavior is discussed. Second, determine if the appropriate interfaces can be reasonably established to provide integration with an existing force structure simulation framework. The authors also describe the envisioned simulation system and the software development performed to extend the inferencing engine and system interface toward that goal. The experimental results of observing emergent adversary behavior by applying the simulated COAs to the adversary model will be discussed. The research addresses numerous technological challenges in developing the necessary methodologies and tools for a software-based COA analysis framework utilizing intelligent adversarial intent.

GESIA: uncertainty-based reasoning for a generic expert system intelligent user interface

Generic expert systems are reasoning systems that can be used in many application domains, thus requiring domain independence. The user interface for a generic expert system must contain intelligence in order to maintain this domain independence and manage the complex interactions between the user and the expert system. This paper explores the uncertainty-based reasoning contained in an intelligent user interface called GESIA. GESIAs interface architecture and dynamically constructed Bayesian network are examined in detail to show how uncertainty-based reasoning enhances the capabilities of this user interface.

On linear potential functions for approximating Bayesian computations

Probabilistic reasoning suffers from NP-hard implementations. In particular, the amount of probabilistic information necessary to the computations is often overwhelming. For example, the size of conditional probability tables in Bayesian networks has long been a limiting factor in the general use of these networks. We present a new approach for manipulating the probabilistic information given. This approach avoids being overwhelmed by essentially compressing the information using approximation functions called linear potential functions. We can potentially reduce the information from a combinatorial amount to roughly linear in the number of random variable assigments. Furthermore, we can compute these functions through closed form equations. As it turns out, our approximation method is quite general and may be applied to other data compression problems.

Towards an adaptive man-machine interface for virtual environments

We describe an approach to developing an adaptive virtual environment user interface to enable the user to perform a wide variety of tasks while immersed in the virtual environment. Currently, virtual environment operation places an unmanageable cognitive burden upon the user. While some advances in user interface design can alleviate some of this problem, the basic problem of information overload can not be adequately addressed solely through development of a better interface or provision of ad hoc decision support tools. We contend that a comprehensive design approach to the interface can improve user access to the virtual environment display parameters, analysis reports, conferencing and collaboration capabilities, intelligent agents for user assistance, motion and orientation controls, recording devices, and situation awareness aids. Our intelligent interface research effort, called Symbiotic Information Reasoning and Decision Support (SIRDS), addresses the issues related to the design and development of an adaptive, intelligent, learning man machine interface. Construction of the interface requires a mix of traditional human computer interaction, data visualization, and intelligent agents within a software engineering framework. The framework supports the symbiosis of human cognition and computational power that is required to deal with complex virtual environments.