arXiv subjects

Wouter W. L. Nuijten

Publications and source records attributed to Wouter W. L. Nuijten.

10 recordsLinked to original sources

arXiv2026

A Factor Graph Approach to Scalable Multi-Output Gaussian Process Regression

Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs. We express multi-output Gaussian process regression as a Forney-style factor graph in which a nearest-neighbor chain orders a fixed candidate set of $C$ inputs into a one-dimensional sequence. Along this chain, latent Matérn processes evolve through linear-Gaussian transition factors, while the linear model of coregionalization mixes $L$ latent processes into $D$ outputs through a deterministic mixing factor and per-output scalar observation factors. Posterior computation reduces to exact Gaussian message passing on the chain at cost $\mathcal{O}(C(DL^2 + L^3))$ after chain construction, and missing observations omit their local factor without any covariance-matrix restructuring. The formulation therefore scales in the number of data samples and in the rate of missing observations, while remaining best suited to candidate sets in low input dimension. We compare the factor-graph formulation against an exact kernel-matrix baseline, a sparse-variational inducing-point baseline, and a nearest-neighbor baseline on a synthetic input-dimension sweep and on electricity time series forecasting. At low input dimension the factor-graph posterior tracks the exact kernel-matrix posterior closely, and the gap grows gradually as input dimension increases while staying competitive with both approximate baselines. On the electricity time series our factor-graph formulation matches all three baselines in forecast accuracy while scaling linearly in the number of data points, where the exact kernel-matrix method becomes infeasible and the inducing-point baseline remains substantially slower.

cs.LG↗

arXiv2026

Sophisticated Policies from Epistemic Priors

Sophisticated Inference is a variant of active inference often associated with recursive belief modeling and tree search. We argue that its central computational role is simpler: within a planning horizon, it makes active inference closed-loop by allowing future actions to depend on future states and observations. This closed-loop structure can be represented in the epistemic-prior variational free energy framework. Epistemic priors supply the active-inference objective, while a joint posterior over future states and actions supplies the state-contingent control structure. We evaluate this decomposition in the Reactivity Maze, a stochastic benchmark designed to separate epistemic incentive from inner-horizon closed-loop control. The comparison includes three variational objectives with the same state-action posterior family, an action-state factorized active inference objective, Sophisticated Inference, and standard Expected Free Energy planning. The results show that neither ingredient is sufficient on its own. Methods without an epistemic component do not seek information, while methods that prevent future actions from depending on future states cannot turn information into reliable goal-reaching. By contrast, both Sophisticated Inference and full-joint epistemic-prior active inference solve the environment by combining epistemic drive with closed-loop inference. These results show that the advantage associated with Sophisticated Inference need not be specific to tree search itself. It arises from the closed-loop form of active inference, and this form can be represented in epistemic-prior variational inference when the posterior keeps future actions dependent on future states.

cs.AI↗

arXiv2026

What Type of Inference is Active Inference?

Active inference casts decision-making as inference, with the Expected Free Energy (EFE) unifying goal-directed and information-seeking behavior. Recent work showed that EFE minimization can be written as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors. We prove that the VFE of the augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent. We then show that proper EFE-based planning requires combining these epistemic corrections with a planning correction that turns marginal inference into policy optimization, yielding a full variational characterization of EFE-based planning. This clarifies which corrections are needed for cross-entropy planning and for full EFE-based planning. The same entropy-corrected formulation leads to a detailed message-passing scheme for EFE-based planning together with simpler ablations. Experiments on three grid-world environments show that full EFE-based planning outperforms ablations that omit either the planning correction or the epistemic corrections.

cs.AI↗

arXiv2026

Expected Free Energy-based Planning as Variational Inference

Planning under uncertainty requires agents to balance goal achievement with information gathering. Active inference addresses this through the Expected Free Energy (EFE), a cost function that unifies instrumental and epistemic objectives. However, existing EFE-based methods typically employ specialized optimization procedures that are difficult to extend or analyze. In this paper, we show that EFE-based planning can be formulated as Variational Free Energy minimization on a generative model augmented with epistemic priors. Our main result demonstrates that minimizing a Variational Free Energy functional with appropriately chosen priors yields a decomposition into expected plan costs (the EFE) plus a complexity term. This formulation reinforces theoretical consistency with the Free Energy Principle by casting planning as the same inferential process that governs perception and learning. We validate our approach on three environments of increasing complexity: a deterministic T-maze, a stochastic Reactivity Maze, and a partially observable MiniGrid DoorKey-8x8 environment. The experiments demonstrate that the epistemic priors induce information-seeking behavior, that the variational formulation yields policy-based inference outperforming plan-based methods under stochastic transitions, and that temporal factorization enables scalability to environments where existing tabular active inference methods cannot operate.

cs.AI↗

arXiv2026

A Probabilistic Generative Model for Spectral Speech Enhancement

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.

cs.SD↗

arXiv2026

A Message Passing Realization of Expected Free Energy Minimization

We present a message passing approach to Expected Free Energy (EFE) minimization on factor graphs, based on the theory introduced in arXiv:2504.14898. By reformulating EFE minimization as Variational Free Energy minimization with epistemic priors, we transform a combinatorial search problem into a tractable inference problem solvable through standard variational techniques. Applying our message passing method to factorized state-space models enables efficient policy inference. We evaluate our method on environments with epistemic uncertainty: a stochastic gridworld and a partially observable Minigrid task. Agents using our approach consistently outperform conventional KL-control agents on these tasks, showing more robust planning and efficient exploration under uncertainty. In the stochastic gridworld environment, EFE-minimizing agents avoid risky paths, while in the partially observable minigrid setting, they conduct more systematic information-seeking. This approach bridges active inference theory with practical implementations, providing empirical evidence for the efficiency of epistemic priors in artificial agents.

cs.AI↗

arXiv2025

Active Inference is a Subtype of Variational Inference

Automated decision-making under uncertainty requires balancing exploitation and exploration. Classical methods treat these separately using heuristics, while Active Inference unifies them through Expected Free Energy (EFE) minimization. However, EFE minimization is computationally expensive, limiting scalability. We build on recent theory recasting EFE minimization as variational inference, formally unifying it with Planning-as-Inference and showing the epistemic drive as a unique entropic contribution. Our main contribution is a novel message-passing scheme for this unified objective, enabling scalable Active Inference in factored-state MDPs and overcoming high-dimensional planning intractability.

cs.AI↗

arXiv2024

Reactive Environments for Active Inference Agents with RxEnvironments.jl

Active Inference is a framework that emphasizes the interaction between agents and their environment. While the framework has seen significant advancements in the development of agents, the environmental models are often borrowed from reinforcement learning problems, which may not fully capture the complexity of multi-agent interactions or allow complex, conditional communication. This paper introduces Reactive Environments, a comprehensive paradigm that facilitates complex multi-agent communication. In this paradigm, both agents and environments are defined as entities encapsulated by boundaries with interfaces. This setup facilitates a robust framework for communication in nonequilibrium-Steady-State systems, allowing for complex interactions and information exchange. We present a Julia package RxEnvironments.jl, which is a specific implementation of Reactive Environments, where we utilize a Reactive Programming style for efficient implementation. The flexibility of this paradigm is demonstrated through its application to several complex, multi-agent environments. These case studies highlight the potential of Reactive Environments in modeling sophisticated systems of interacting agents.

eess.SY↗

arXiv2024

Node Classification in Random Trees

We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes (typically high dimensional embeddings). The tree topology is not predetermined and none of the label assignments are present during inference. Other methods that produce a distribution over node label assignment in trees (or more generally in graphs) either assume conditional independence of the label assignment, operate on a fixed graph topology, or require part of the node labels to be observed. Our method defines a Markov Network with the corresponding topology of the random tree and an associated Gibbs distribution. We parameterize the Gibbs distribution with a Graph Neural Network that operates on the random tree and the node embeddings. This allows us to estimate the likelihood of node assignments for a given random tree and use MCMC to sample from the distribution of node assignments. We evaluate our method on the tasks of node classification in trees on the Stanford Sentiment Treebank dataset. Our method outperforms the baselines on this dataset, demonstrating its effectiveness for modeling joint distributions of node labels in random trees.

cs.LG↗

arXiv2023

Automating Model Comparison in Factor Graphs

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.

cs.LG↗