Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in-and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.

Hierarchical data with multiple observations per group is ubiquitous in empirical sciences and is often analyzed using mixed-effects regression. In such models, Bayesian inference gives an estimate of uncertainty but is analytically intractable and requires costly approximation using Markov Chain Monte Carlo (MCMC) methods. Neural posterior estimation shifts the bulk of computation from inference time to pre-training time, amortizing over simulated datasets with known ground truth targets. We propose metabeta, a transformer-based neural network model for Bayesian mixed-effects regression. Using simulated and real data, we show that it reaches stable and comparable performance to MCMC-based parameter estimation at a fraction of the usually required time.

Estimating uncertainty from deep neural networks is a widely used approach for detecting out-of-distribution (OoD) samples, which typically exhibit high predictive uncertainty. However, conventional methods such as Monte Carlo (MC) Dropout often focus solely on either model or data uncertainty, failing to align with the semantic objective of OoD detection. T o address this, we propose the Free-Energy Posterior Network, a novel framework that jointly models distributional uncertainty and identifying OoD and misclassified regions using free energy. Our method introduces two key contributions: (1) a free-energy-based density estimator parameterized by a Beta distribution, which enables fine-grained uncertainty estimation near ambiguous or unseen regions; and (2) a loss integrated within a posterior network, allowing direct uncertainty estimation from learned parameters without requiring stochastic sampling. By integrating our approach with the residual prediction branch (RPL) framework, the proposed method goes beyond post-hoc energy thresholding and enables the network to learn OoD regions by leveraging the variance of the Beta distribution, resulting in a semantically meaningful and computationally efficient solution for uncertainty-aware segmentation.

We present GO-CBED, a goal-oriented Bayesian framework for sequential causal experimental design. Unlike conventional approaches that select interventions aimed at inferring the full causal model, GO-CBED directly maximizes the expected information gain (EIG) on user-specified causal quantities of interest, enabling more targeted and efficient experimentation. The framework is both non-myopic, optimizing over entire intervention sequences, and goal-oriented, targeting only model aspects relevant to the causal query. To address the intractability of exact EIG computation, we introduce a variational lower bound estimator, optimized jointly through a transformer-based policy network and normalizing flow-based variational posteriors. The resulting policy enables real-time decision-making via an amortized network. We demonstrate that GO-CBED consistently outperforms existing baselines across various causal reasoning and discovery tasks-including synthetic structural causal models and semi-synthetic gene regulatory networks-particularly in settings with limited experimental budgets and complex causal mechanisms. Our results highlight the benefits of aligning experimental design objectives with specific research goals and of forward-looking sequential planning.

Weaknesses: While the paper proposes an interesting solution, I believe it falls short on a range of aspects which greatly affected my score. It is not clear what measures of uncertainty are used for OOD detection. Previous work on Prior Networks and ensemble methods consistently make use of mutual information to obtain a separable set of estimates of total, aleatoric and epistemic uncertainty. However, this work does neither mentions this nor uses these *established* and *theoretically meaningful* measures. Rather perplexingly, this work seems to make use of max alpha_c {I} scores for Prior Network and variance of probability for ensembles.

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample.

In this work, we study the influence of domain-specific characteristics when defining a meaningful notion of predictive uncertainty on graph data. Previously, the so-called Graph Posterior Network (GPN) model has been proposed to quantify uncertainty in node classification tasks. Given a graph, it uses Normalizing Flows (NFs) to estimate class densities for each node independently and converts those densities into Dirichlet pseudo-counts, which are then dispersed through the graph using the personalized Page-Rank algorithm. The architecture of GPNs is motivated by a set of three axioms on the properties of its uncertainty estimates. We show that those axioms are not always satisfied in practice and therefore propose the family of Committe-based Uncertainty Quantification Graph Neural Networks (CUQ-GNNs), which combine standard Graph Neural Networks with the NF-based uncertainty estimation of Posterior Networks (PostNets). This approach adapts more flexibly to domain-specific demands on the properties of uncertainty estimates. We compare CUQ-GNN against GPN and other uncertainty quantification approaches on common node classification benchmarks and show that it is effective at producing useful uncertainty estimates.

Generative models have gained popularity for their potential applications in imaging science, such as image reconstruction, posterior sampling and data sharing. Flow-based generative models are particularly attractive due to their ability to tractably provide exact density estimates along with fast, inexpensive and diverse samples. Training such models, however, requires a large, high quality dataset of objects. In applications such as computed imaging, it is often difficult to acquire such data due to requirements such as long acquisition time or high radiation dose, while acquiring noisy or partially observed measurements of these objects is more feasible. In this work, we propose AmbientFlow, a framework for learning flow-based generative models directly from noisy and incomplete data. Using variational Bayesian methods, a novel framework for establishing flow-based generative models from noisy, incomplete data is proposed. Extensive numerical studies demonstrate the effectiveness of AmbientFlow in learning the object distribution. The utility of AmbientFlow in a downstream inference task of image reconstruction is demonstrated.

This work studies how brain-inspired neural ensembles equipped with local Hebbian plasticity can perform active inference (AIF) in order to control dynamical agents. A generative model capturing the environment dynamics is learned by a network composed of two distinct Hebbian ensembles: a posterior network, which infers latent states given the observations, and a state transition network, which predicts the next expected latent state given current state-action pairs. Experimental studies are conducted using the Mountain Car environment from the OpenAI gym suite, to study the effect of the various Hebbian network parameters on the task performance. It is shown that the proposed Hebbian AIF approach outperforms the use of Q-learning, while not requiring any replay buffer, as in typical reinforcement learning systems. These results motivate further investigations of Hebbian learning for the design of AIF networks that can learn environment dynamics without the need for revisiting past buffered experiences.

Neural networks trained on model simulations enable amortized inference: A pre-trained network can be stored and re-used for Bayesian inference on millions of data sets (von This work proposes "jointly amortized neural Krause et al., 2022). Crucially, most previous neural approaches approximation" (JANA) of intractable likelihood have tackled either SM or SBI in isolation, but little functions and posterior densities arising in attention has been paid to learning both tasks simultaneously. Bayesian surrogate modeling and simulation-based To address this gap, we propose JANA ("Jointly Amortized inference. We train three complementary networks Neural Approximation"), a Bayesian neural framework for in an end-to-end fashion: 1) a summary network simultaneously amortized SM and SBI, and show how it enables to compress individual data points, sets, or time novel solutions to challenging downstream tasks like series into informative embedding vectors; 2) a posterior the estimation of marginal and posterior predictive distributions network to learn an amortized approximate (see Figure 1). JANA also presents a major qualitative posterior; and 3) a likelihood network to learn an upgrade to the BayesFlow framework (Radev et al., 2020), amortized approximate likelihood. Their interaction which was originally designed for amortized SBI alone.