Federated learning methods enable model training across distributed data sources without data leaving their original locations and have gained increasing interest in various fields. However, existing approaches are limited, excluding many structured probabilistic models. We present a general and elegant solution based on structured variational inference, widely used in Bayesian machine learning, adapted for the federated setting. Additionally, we provide a communication-efficient variant analogous to the canonical FedAvg algorithm. The proposed algorithms' effectiveness is demonstrated, and their performance is compared with hierarchical Bayesian neural networks and topic models.

Understanding differences between sub-stellar spectral data and models has proven to be a major challenge, especially for self-consistent model grids that are necessary for a thorough investigation of brown dwarf atmospheres. Using the supervised machine learning method of the random forest, we study the information content of 14 previously published model grids of brown dwarfs (from 1997 to 2021). The random forest method allows us to analyze the predictive power of these model grids, as well as interpret data within the framework of Approximate Bayesian Computation (ABC). Our curated dataset includes 3 benchmark brown dwarfs (Gl 570D, {\epsilon} Indi Ba and Bb) as well as a sample of 19 L and T dwarfs; this sample was previously analyzed in Lueber et al. (2022) using traditional Bayesian methods (nested sampling). We find that the effective temperature of a brown dwarf can be robustly predicted independent of the model grid chosen for the interpretation. However, inference of the surface gravity is model-dependent. Specifically, the BT-Settl, Sonora Bobcat and Sonora Cholla model grids tend to predict logg ~3-4 (cgs units) even after data blueward of 1.2 {\mu}m have been disregarded to mitigate for our incomplete knowledge of the shapes of alkali lines. Two major, longstanding challenges associated with understanding the influence of clouds in brown dwarf atmospheres remain: our inability to model them from first principles and also to robustly validate these models.

We consider the problem of unfair discrimination between two groups and propose a pre-processing method to achieve fairness. Corrective methods like statistical parity usually lead to bad accuracy and do not really achieve fairness in situations where there is a correlation between the sensitive attribute S and the legitimate attribute E (explanatory variable) that should determine the decision. To overcome these drawbacks, other notions of fairness have been proposed, in particular, conditional statistical parity and equal opportunity. However, E is often not directly observable in the data, i.e., it is a latent variable. We may observe some other variable Z representing E, but the problem is that Z may also be affected by S, hence Z itself can be biased. To deal with this problem, we propose BaBE (Bayesian Bias Elimination), an approach based on a combination of Bayes inference and the Expectation-Maximization method, to estimate the most likely value of E for a given Z for each group. The decision can then be based directly on the estimated E. We show, by experiments on synthetic and real data sets, that our approach provides a good level of fairness as well as high accuracy.

The proposed work focuses on the path planning for Unmanned Surface Vehicles (USVs) in the ocean enviroment, taking into account various spatiotemporal factors such as ocean currents and other energy consumption factors. The paper proposes the use of Gaussian Process Motion Planning (GPMP2), a Bayesian optimization method that has shown promising results in continuous and nonlinear path planning algorithms. The proposed work improves GPMP2 by incorporating a new spatiotemporal factor for tracking and predicting ocean currents using a spatiotemporal Bayesian inference. The algorithm is applied to the USV path planning and is shown to optimize for smoothness, obstacle avoidance, and ocean currents in a challenging environment. The work is relevant for practical applications in ocean scenarios where an optimal path planning for USVs is essential for minimizing costs and optimizing performance.

Time-series datasets are central in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs), which are powerful mathematical tools that allow for probabilistic and interpretable learning on time series. Estimating the model parameters in SSMs is arguably one of the most complicated tasks, and the inclusion of prior knowledge is known to both ease the interpretation but also to complicate the inferential tasks. Very recent works have attempted to incorporate a graphical perspective on some of those model parameters, but they present notable limitations that this work addresses. More generally, existing graphical modeling tools are designed to incorporate either static information, focusing on statistical dependencies among independent random variables (e.g., graphical Lasso approach), or dynamic information, emphasizing causal relationships among time series samples (e.g., graphical Granger approaches). However, there are no joint approaches combining static and dynamic graphical modeling within the context of SSMs. This work proposes a novel approach to fill this gap by introducing a joint graphical modeling framework that bridges the static graphical Lasso model and a causal-based graphical approach for the linear-Gaussian SSM. We present DGLASSO (Dynamic Graphical Lasso), a new inference method within this framework that implements an efficient block alternating majorization-minimization algorithm. The algorithm's convergence is established by departing from modern tools from nonlinear analysis. Experimental validation on synthetic and real weather variability data showcases the effectiveness of the proposed model and inference algorithm.

In this paper, we consider a general observation model for restless multi-armed bandit problems. The operation of the player needs to be based on certain feedback mechanism that is error-prone due to resource constraints or environmental or intrinsic noises. By establishing a general probabilistic model for dynamics of feedback/observation, we formulate the problem as a restless bandit with a countable belief state space starting from an arbitrary initial belief (a priori information). We apply the achievable region method with partial conservation law (PCL) to the infinite-state problem and analyze its indexability and priority index (Whittle index). Finally, we propose an approximation process to transform the problem into which the AG algorithm of Ni\~no-Mora and Bertsimas for finite-state problems can be applied to. Numerical experiments show that our algorithm has an excellent performance.

We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed, neural-network-based tensor basis functions dependent on the rate of strain and rotation tensor invariants. This is complemented by latent, random variables which account for aleatoric model errors. A fully Bayesian formulation is proposed, combined with a sparsity-inducing prior in order to identify regions in the problem domain where the parametric closure is insufficient and where stochastic corrections to the Reynolds stress tensor are needed. Training is performed using sparse, indirect data, such as mean velocities and pressures, in contrast to the majority of alternatives that require direct Reynolds stress data. For inference and learning, a Stochastic Variational Inference scheme is employed, which is based on Monte Carlo estimates of the pertinent objective in conjunction with the reparametrization trick. This necessitates derivatives of the output of the RANS solver, for which we developed an adjoint-based formulation. In this manner, the parametric sensitivities from the differentiable solver can be combined with the built-in, automatic differentiation capability of the neural network library in order to enable an end-to-end differentiable framework. We demonstrate the capability of the proposed model to produce accurate, probabilistic, predictive estimates for all flow quantities, even in regions where model errors are present, on a separated flow in the backward-facing step benchmark problem.

Database alignment is a variant of the graph alignment problem: Given a pair of anonymized databases containing separate yet correlated features for a set of users, the problem is to identify the correspondence between the features and align the anonymized user sets based on correlation alone. This closely relates to planted matching, where given a bigraph with random weights, the goal is to identify the underlying matching that generated the given weights. We study an instance of the database alignment problem with multivariate Gaussian features and derive results that apply both for database alignment and for planted matching, demonstrating the connection between them. The performance thresholds for database alignment converge to that for planted matching when the dimensionality of the database features is \(\omega(\log n)\), where \(n\) is the size of the alignment, and no individual feature is too strong. The maximum likelihood algorithms for both planted matching and database alignment take the form of a linear program and we study relaxations to better understand the significance of various constraints under various conditions and present achievability and converse bounds. Our results show that the almost-exact alignment threshold for the relaxed algorithms coincide with that of maximum likelihood, while there is a gap between the exact alignment thresholds. Our analysis and results extend to the unbalanced case where one user set is not fully covered by the alignment.

Understanding the causal relationships that underlie a system is a fundamental prerequisite to accurate decision-making. In this work, we explore how expert knowledge can be used to improve the data-driven identification of causal graphs, beyond Markov equivalence classes. In doing so, we consider a setting where we can query an expert about the orientation of causal relationships between variables, but where the expert may provide erroneous information. We propose strategies for amending such expert knowledge based on consistency properties, e.g., acyclicity and conditional independencies in the equivalence class. We then report a case study, on real data, where a large language model is used as an imperfect expert.

Federated learning is a decentralized and privacy-preserving technique that enables multiple clients to collaborate with a server to learn a global model without exposing their private data. However, the presence of statistical heterogeneity among clients poses a challenge, as the global model may struggle to perform well on each client's specific task. To address this issue, we introduce a new perspective on personalized federated learning through Amortized Bayesian Meta-Learning. Specifically, we propose a novel algorithm called \emph{FedABML}, which employs hierarchical variational inference across clients. The global prior aims to capture representations of common intrinsic structures from heterogeneous clients, which can then be transferred to their respective tasks and aid in the generation of accurate client-specific approximate posteriors through a few local updates. Our theoretical analysis provides an upper bound on the average generalization error and guarantees the generalization performance on unseen data. Finally, several empirical results are implemented to demonstrate that \emph{FedABML} outperforms several competitive baselines.