Raphaël Trésor

Marco Hidalgo-Araya, Raphaël Trésor, Bart Van Erp et al.

Speech enhancement in hearing aids remains a difficult task in nonstationary acoustic environments, mainly because current signal processing algorithms rely on fixed, manually tuned parameters that cannot adapt in situ to different users or listening contexts. This paper introduces a unified modular framework that formulates signal processing, learning, and personalization as Bayesian inference with explicit uncertainty tracking. The proposed framework replaces ad hoc algorithm design with a single probabilistic generative model that continuously adapts to changing acoustic conditions and user preferences. It extends spectral subtraction with principled mechanisms for in-situ personalization and adaptation to acoustic context. The system is implemented as an interconnected probabilistic state-space model, and inference is performed via variational message passing in the \texttt{RxInfer.jl} probabilistic programming environment, enabling real-time Bayesian processing under hearing-aid constraints. Proof-of-concept experiments on the \emph{VoiceBank+DEMAND} corpus show competitive speech quality and noise reduction with 85 effective parameters. The framework provides an interpretable, data-efficient foundation for uncertainty-aware, adaptive hearing-aid processing and points toward devices that learn continuously through probabilistic inference.

Raphaël Trésor, Thijs van de Laar, Bert de Vries

Maximum entropy, Bayesian updating, and exponential-family estimation are all instances of a common inference principle: selecting the measure or distribution that minimizes a divergence subject to the available constraints. Which divergence to use is usually decided by analytic convenience, by empirical performance, or by a set of axioms chosen to single it out, leaving open a basic question: why one divergence and not another? We answer it from a single requirement: an inference method should return the same answer whenever the same problem is presented in an equivalent form, for instance, after simply renaming its parts. This requirement alone forces inference to be the minimisation of a classical divergence, and each further reformulation it must respect tightens the admissible family one notch, narrowing the broad f-divergences to the α-divergences and finally to the single Kullback-Leibler (KL) divergence. Mathematically, inference is recast from minimising a numerical functional to selecting a least element under a preorder on positive measures, a divergence being merely one numerical scale that reproduces that preorder. The reformulations are the morphisms of a category of inference problems, and the invariance requirement says the inference operator is a covariant functor into the category of statistical models of Cencov, mirroring his characterisation of the Fisher metric. The representation is proved on finite spaces and lifted to general measurable spaces by an elementary closure, covering discrete and continuous spaces alike. Earlier axiomatisations, such as those of Shore-Johnson and Csiszar, postulate their consistency axioms directly and only on finite alphabets; here the axioms follow from reformulation invariance alone.