ARO PECASE: Credal Information Theory

Information Exchange Under Epistemic Uncertainty

Information theory provides the mathematical foundation for optimizing communication systems across bandwidth, latency, power consumption and reliability. Since Shannon’s seminal 1948 work, its foundational quantities have been defined relative to a single, precisely known probability distribution. While this framework rigorously characterizes aleatoric uncertainty, which is the irreducible randomness intrinsic to communication, it does not characterize epistemic uncertainty, which is our ignorance about the true source and channel distributions. In practice, epistemic uncertainty arises from partial sensor calibration, incompletely characterized fading and interference, adversarial perturbations and online learning algorithms that couple encoding and decoding to adaptive behavior. Existing approaches reduce this model uncertainty to a single worst-case scalar, discarding the structure of the uncertainty itself and providing no principled way to distinguish irreducible noise from model ignorance.

This project addresses the limitations described above by developing a new mathematical framework for information fusion and exchange under epistemic uncertainty, where entropy, mutual information and channel capacity become intervals that expand and contract with the degree of epistemic uncertainty. Thrust 1 develops a rigorous theory of credal information fusion for heterogeneous, partially dependent, and dynamically evolving sources, including certified conditions distinguishing when fusion genuinely reduces task-relevant epistemic uncertainty and regret guarantees under adversarial sensor contamination and drift. Thrust 2 establishes the information-theoretic limits of communication and compression under credal uncertainty, introducing a robust rate–distortion theory, probing-assisted channel coding with explicit rate-recovery guarantees, and a task-aware coding framework that makes downstream decision risk an explicit design objective. Thrust 3 validates these theories end-to-end on multi-view image benchmarks, real multimodal perception datasets, and experimental wireless testbeds at Northeastern, under explicit bandwidth, latency, and energy constraints.