Bart van Erp

Bart van Erp, Wouter W. L. Nuijten, Thijs van de Laar et al.

Bayesian state and parameter estimation have been automated effectively in a variety of probabilistic programming languages. The process of model comparison on the other hand, which still requires error-prone and time-consuming manual derivations, is often overlooked despite its importance. This paper efficiently automates Bayesian model averaging, selection, and combination by message passing on a Forney-style factor graph with a custom mixture node. Parameter and state inference, and model comparison can then be executed simultaneously using message passing with scale factors. This approach shortens the model design cycle and allows for the straightforward extension to hierarchical and temporal model priors to accommodate for modeling complicated time-varying processes.

Jim Beckers, Bart van Erp, Ziyue Zhao et al.

Bayesian model reduction provides an efficient approach for comparing the performance of all nested sub-models of a model, without re-evaluating any of these sub-models. Until now, Bayesian model reduction has been applied mainly in the computational neuroscience community on simple models. In this paper, we formulate and apply Bayesian model reduction to perform principled pruning of Bayesian neural networks, based on variational free energy minimization. Direct application of Bayesian model reduction, however, gives rise to approximation errors. Therefore, a novel iterative pruning algorithm is presented to alleviate the problems arising with naive Bayesian model reduction, as supported experimentally on the publicly available UCI datasets for different inference algorithms. This novel parameter pruning scheme solves the shortcomings of current state-of-the-art pruning methods that are used by the signal processing community. The proposed approach has a clear stopping criterion and minimizes the same objective that is used during training. Next to these benefits, our experiments indicate better model performance in comparison to state-of-the-art pruning schemes.

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.

Bert de Vries, Wouter Nuijten, Thijs van de Laar et al.

We address the problem of planning under uncertainty, where an agent must choose actions that not only achieve desired outcomes but also reduce uncertainty. Traditional methods often treat exploration and exploitation as separate objectives, lacking a unified inferential foundation. Active inference, grounded in the Free Energy Principle, provides such a foundation by minimizing Expected Free Energy (EFE), a cost function that combines utility with epistemic drives, such as ambiguity resolution and novelty seeking. However, the computational burden of EFE minimization had remained a significant obstacle to its scalability. In this paper, we show that EFE-based planning arises naturally from minimizing a variational free energy functional on a generative model augmented with preference and epistemic priors. This result reinforces theoretical consistency with the Free Energy Principle by casting planning under uncertainty itself as a form of variational inference. Our formulation yields policies that jointly support goal achievement and information gain, while incorporating a complexity term that accounts for bounded computational resources. This unifying framework connects and extends existing methods, enabling scalable, resource-aware implementations of active inference agents.

Bart van Erp, Bert de Vries

This paper proposes improvements over earlier work by Nazareth and Blei (2022) for estimating the depth of Bayesian neural networks. Here, we propose a discrete truncated normal distribution over the network depth to independently learn its mean and variance. Posterior distributions are inferred by minimizing the variational free energy, which balances the model complexity and accuracy. Our method improves test accuracy on the spiral data set and reduces the variance in posterior depth estimates.

Albert Podusenko, Bart van Erp, Magnus Koudahl et al.

In this paper we present AIDA, which is an active inference-based agent that iteratively designs a personalized audio processing algorithm through situated interactions with a human client. The target application of AIDA is to propose on-the-spot the most interesting alternative values for the tuning parameters of a hearing aid (HA) algorithm, whenever a HA client is not satisfied with their HA performance. AIDA interprets searching for the "most interesting alternative" as an issue of optimal (acoustic) context-aware Bayesian trial design. In computational terms, AIDA is realized as an active inference-based agent with an Expected Free Energy criterion for trial design. This type of architecture is inspired by neuro-economic models on efficient (Bayesian) trial design in brains and implies that AIDA comprises generative probabilistic models for acoustic signals and user responses. We propose a novel generative model for acoustic signals as a sum of time-varying auto-regressive filters and a user response model based on a Gaussian Process Classifier. The full AIDA agent has been implemented in a factor graph for the generative model and all tasks (parameter learning, acoustic context classification, trial design, etc.) are realized by variational message passing on the factor graph. All verification and validation experiments and demonstrations are freely accessible at our GitHub repository.

Thijs van de Laar, Magnus Koudahl, Bart van Erp et al.

The Free Energy Principle (FEP) postulates that biological agents perceive and interact with their environment in order to minimize a Variational Free Energy (VFE) with respect to a generative model of their environment. The inference of a policy (future control sequence) according to the FEP is known as Active Inference (AIF). The AIF literature describes multiple VFE objectives for policy planning that lead to epistemic (information-seeking) behavior. However, most objectives have limited modeling flexibility. This paper approaches epistemic behavior from a constrained Bethe Free Energy (CBFE) perspective. Crucially, variational optimization of the CBFE can be expressed in terms of message passing on free-form generative models. The key intuition behind the CBFE is that we impose a point-mass constraint on predicted outcomes, which explicitly encodes the assumption that the agent will make observations in the future. We interpret the CBFE objective in terms of its constituent behavioral drives. We then illustrate resulting behavior of the CBFE by planning and interacting with a simulated T-maze environment. Simulations for the T-maze task illustrate how the CBFE agent exhibits an epistemic drive, and actively plans ahead to account for the impact of predicted outcomes. Compared to an EFE agent, the CBFE agent incurs expected reward in significantly more environmental scenarios. We conclude that CBFE optimization by message passing suggests a general mechanism for epistemic-aware AIF in free-form generative models.