Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inference
This work addresses the problem of robust and interpretable inference under sparse or imprecise information for researchers in Bayesian learning and uncertainty modeling, representing an incremental adaptation of existing methods to a new framework.
The paper tackled the challenge of adapting variational inference to possibility theory, which models epistemic uncertainty without relying on additive probabilities, by developing a principled formulation for possibilistic variational inference and applying it to exponential-family functions.
Variational inference (VI) is a cornerstone of modern Bayesian learning, enabling approximate inference in complex models that would otherwise be intractable. However, its formulation depends on expectations and divergences defined through high-dimensional integrals, often rendering analytical treatment impossible and necessitating heavy reliance on approximate learning and inference techniques. Possibility theory, an imprecise probability framework, allows to directly model epistemic uncertainty instead of leveraging subjective probabilities. While this framework provides robustness and interpretability under sparse or imprecise information, adapting VI to the possibilistic setting requires rethinking core concepts such as entropy and divergence, which presuppose additivity. In this work, we develop a principled formulation of possibilistic variational inference and apply it to a special class of exponential-family functions, highlighting parallels with their probabilistic counterparts and revealing the distinctive mathematical structures of possibility theory.