Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

Incorporating PGMs into a BDI Architecture

In this paper, we present a hybrid BDI-PGM framework, in which PGMs (Probabilistic Graphical Models) are incorporated into a BDI (belief-desire-intention) architecture. This work is motivated by the need to address the scalability and noisy sensing issues in SCADA (Supervisory Control And Data Acquisition) systems. Our approach uses the incorporated PGMs to model the uncertainty reasoning and decision making processes of agents situated in a stochastic environment. In particular, we use Bayesian networks to reason about an agent’s beliefs about the environment based on its sensory observations, and select optimal plans according to the utilities of actions defined in influence diagrams. This approach takes the advantage of the scalability of the BDI architecture and the uncertainty reasoning capability of PGMs. We present a prototype of the proposed approach using a transit scenario to validate its effectiveness.

A belief revision framework for revising epistemic states with partial epistemic states

Belief revision performs belief change on an agent’s beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey’s rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey’s rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey’s rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl’s postulates C1 and C2.