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.

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.

The famous aphorism of George Box states: "all models are wrong, but some are useful" [1]. It is the task of statisticians and data analysts to find a model which is most useful for a given problem. The build, compute, critique and repeat cycle [2], also known as Box's loop [3], is an iterative approach for finding the most useful model. Any efforts in shortening this design cycle increase the chances of developing more useful models, which in turn might yield more reliable predictions, more profitable returns or more efficient operations for the problem at hand. In this paper we choose to adopt the Bayesian formalism and therefore we will specify all tasks in Box's loop as principled probabilistic inference tasks. In addition to the well-known parameter and state inference tasks, the critique step in the design cycle is also phrased as an inference task, known as Bayesian model comparison, which automatically embodies Occam's razor [4, Ch. 28.1]. Opposed to just selecting a single model in the critique step, for different models we better quantify our confidence about which model is best, especially when data is limited [5, Ch. 18.5.1]. The uncertainty arising from prior beliefs p(m) over a set of models m and limited observations can be naturally included through the use of Bayes' theorem

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.

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.