Probabilistic Reasoning

Under contract with DARPA, GCAS has designed a Knowledge Acquisition Tool. The result of this effort is a System for Probabilistic and Logical Reasoning (SPLORE) that integrates state-of-the-art techniques in both logical and probabilistic reasoning through the complement of the Knowledge Machine (KM) and Probabilistic Relational Models (PRMs) languages. KM is a full First-Order Logic reasoning system operating on Knowledge Bases (KBs). PRMs are the object-oriented and relational extension of Bayesian Networks (BNs) and are compatible with Ontology and KB systems. SPLORE allows modeling any complex system starting from structured building blocks (classes). Each class represents both logical predicates through KM concepts and probabilistic knowledge via PRMs constructs. These classes are arranged in a KB and related in both logical and probabilistic fashions. A Graphical User Interface allows the user to express both logical and probabilistic knowledge with a uniform graphical paradigm. SPLORE is also the first system that integrates the novel technique for decision-making in multi-agent games represented by Networks of Influence Diagrams (NIDs). NIDs model the behavior of several agents in an interactive domain and introduce a "naturalistic" approach to BN reasoning. The original goal of SPLORE was to allow Subject-Matter Experts (SMEs) to directly encode complex real-world battle space scenarios for Courses of Action (COA) generation. This COA synthesis exploits Predictive Battlespace Awareness at both Level II (Situation Assessment) and Level III (Impact Assessment) data fusion. Level II/III data fusion has widespread importance in military, intelligence, and civilian organizations.

Under the Missile Defense Agency contract, GCAS has performed research on Interval Propagation in BNs and PRMs. This effort continues now under a Phase II contract for devising techniques for decision-making under Probability Intervals, with prospected integration inside the MDA decision architecture. The algorithms we are developing are useful for propagating the effects of intervals and second-order uncertainty specified for both evidence and Conditional Probability Table (CPT) parameters. Our propagation algorithm also gives support for tracking back to the evidence and CPT parameters that largely contribute to a belief interval in a variable of interest. In the CPT case, if a belief interval in a node is deemed too large, we can pinpoint the parameters responsible for the result and ask the SME to refine their description. In this way, we also know what parameters are relevant and what are secondary in order to have a reliable outcome from the model. This is indeed an alternative approach to Sensitivity Analysis. It is much more powerful than the classical formulations, in that it takes into account the combined effects of all the intervals in all the evidence and CPT parameters in a model. And it is also able to exactly track back and pinpoint the more influencing factors. Of special interest is the use of interval propagation for assessing the robustness of Courses of Action (COAs). We are currently studying how intervals in evidence and CPT parameters affect the synthesis of COAs, and how COAs change because of those intervals. Finally, we are building an Application Programming Interface and a graphical development environment that allow Subject-Matter Experts to create and assess complex probabilistic models featuring decision-making under second-order uncertainty.

GCAS is currently under a Missile Defense Agency contract to study Interval Propagation in BNs and PRMs. The techniques we are developing are useful for propagating the effects of intervals specified for both evidence and Conditional Probability Table (CPT) parameters. Our interval propagation system possesses a backtracking algorithm that identifies the evidence and CPT parameters that largely contribute to a belief interval in a variable of interest. In the CPT case, if a belief interval in a node is deemed too large, we can pinpoint the parameters responsible for the result and ask the SME to refine their description. In this way, we also know what parameters are relevant and what are secondary, in order to have a reliable outcome from the model. This is indeed an alternative approach to Sensitivity Analysis. It is much more powerful than the classical formulations, in that it takes into account the combined effects of all the intervals in all the evidence and CPT parameters in a model. And it is also able to exactly backtrack and pinpoint the more influencing factors. Of special interest is the use of interval propagation for assessing the robustness of Courses of Action (COAs). We are, in fact, studying how intervals in evidence and CPT parameters affect the synthesis of COAs, and how COAs change because of those intervals.