Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis (Bürkner et al., 2022; Gelman et al., 2020; Schad et al., 2021). Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. However, despite their theoretical appeal and utility, the practical execution of Bayesian workflows is often limited by computational bottlenecks: Obtaining even a single posterior may already take a long time, such that repeated estimation for the purpose of model validation or calibration becomes completely infeasible. BayesFlow provides a framework for simulation-based training of established neural network architectures, such as transformers (Vaswani et al., 2017) and normalizing flows (Papamakarios et al., 2021), for amortized data compression and inference. Amortized Bayesian inference (ABI), as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously (typically well below one second), the upfront neural network training is quickly amortized. For instance, amortized inference allows us to test a model's ability to recover its parameters (Schad et al., 2021) or assess its simulation-based calibration (Säilynoja et al., 2022; Talts et al., 2018) for different data set sizes in a matter of seconds, even though this may require the estimation of thousands of posterior distributions. BayesFlow offers a user-friendly API, which encapsulates the details of neural network architectures and training procedures that are less relevant for the practitioner and provides robust default implementations that work well across many applications. At the same time, BayesFlow implements a modular software architecture, allowing machine learning scientists to modify every component of the pipeline for custom applications as well as research at the frontier of Bayesian inference.

Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to expectations of well-known distributions. We can then directly write the update by simply ``reading-off'' the terms in front of those expectations. The recipe makes the derivation easier, faster, shorter, and more general.

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a tree-structured Ising model whose leaf node distribution is close in Total Variation Distance, improving on the results of prior work. On the testing side, we provide an efficient algorithm with fewer samples for testing whether two latent-tree Ising models have leaf-node distributions that are close or far in Total Variation distance. We obtain our algorithms by showing novel localization results for the total variation distance between the leaf-node distributions of tree-structured Ising models, in terms of their marginals on pairs of leaves.

We consider the problem of routing a team of energy-constrained Unmanned Aerial Vehicles (UAVs) to drop unmovable sensors for monitoring a task area in the presence of stochastic wind disturbances. In prior work on mobile sensor routing problems, sensors and their carrier are one integrated platform, and sensors are assumed to be able to take measurements at exactly desired locations. By contrast, airdropping the sensors onto the ground can introduce stochasticity in the landing locations of the sensors. We focus on addressing this stochasticity in sensor locations from the path-planning perspective. Specifically, we formulate the problem (Multi-UAV Sensor Drop) as a variant of the Submodular Team Orienteering Problem with one additional constraint on the number of sensors on each UAV. The objective is to maximize the Mutual Information between the phenomenon at Points of Interest (PoIs) and the measurements that sensors will take at stochastic locations. We show that such an objective is computationally expensive to evaluate. To tackle this challenge, we propose a surrogate objective with a closed-form expression based on the expected mean and expected covariance of the Gaussian Process. We propose a heuristic algorithm to solve the optimization problem with the surrogate objective. The formulation and the algorithms are validated through extensive simulations.

Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a transport map that pushes forward a simple reference (e.g., a standard Gaussian) to a target distribution. While these approaches successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn these transformations. This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a two dimensional example and on a parameter inference problem involving nonlinear ODEs.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

Collision avoidance in the presence of dynamic obstacles in unknown environments is one of the most critical challenges for unmanned systems. In this paper, we present a method that identifies obstacles in terms of ellipsoids to estimate linear and angular obstacle velocities. Our proposed method is based on the idea of any object can be approximately expressed by ellipsoids. To achieve this, we propose a method based on variational Bayesian estimation of Gaussian mixture model, the Kyachiyan algorithm, and a refinement algorithm. Our proposed method does not require knowledge of the number of clusters and can operate in real-time, unlike existing optimization-based methods. In addition, we define an ellipsoid-based feature vector to match obstacles given two timely close point frames. Our method can be applied to any environment with static and dynamic obstacles, including the ones with rotating obstacles. We compare our algorithm with other clustering methods and show that when coupled with a trajectory planner, the overall system can efficiently traverse unknown environments in the presence of dynamic obstacles.

While recent machine learning research has revealed connections between deep generative models such as VAEs and rate-distortion losses used in learned compression, most of this work has focused on images. In a similar spirit, we view recently proposed neural video coding algorithms through the lens of deep autoregressive and latent variable modeling. We present these codecs as instances of a generalized stochastic temporal autoregressive transform, and propose new avenues for further improvements inspired by normalizing flows and structured priors. We propose several architectures that yield state-of-the-art video compression performance on high-resolution video and discuss their tradeoffs and ablations. In particular, we propose (i) improved temporal autoregressive transforms, (ii) improved entropy models with structured and temporal dependencies, and (iii) variable bitrate versions of our algorithms. Since our improvements are compatible with a large class of existing models, we provide further evidence that the generative modeling viewpoint can advance the neural video coding field.

Data-driven soft sensors are essential for achieving accurate perception through reliable state inference. However, developing representative soft sensor models is challenged by issues such as missing labels, domain adaptability, and temporal coherence in data. To address these challenges, we propose a deep Particle Flow Bayes (DPFB) framework for cross-domain soft sensor modeling in the absence of target state labels. In particular, a sequential Bayes objective is first formulated to perform the maximum likelihood estimation underlying the cross-domain soft sensing problem. At the core of the framework, we incorporate a physics-inspired particle flow that optimizes the sequential Bayes objective to perform an exact Bayes update of the model extracted latent and hidden features. As a result, these contributions enable the proposed framework to learn a rich approximate posterior feature representation capable of characterizing complex cross-domain system dynamics and performing effective time series unsupervised domain adaptation (UDA). Finally, we validate the framework on a complex industrial multiphase flow process system with complex dynamics and multiple operating conditions. The results demonstrate that the DPFB framework achieves superior cross-domain soft sensing performance, outperforming state-of-the-art deep UDA and normalizing flow approaches.