We revisit the Bayesian Black-Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor "view": a forecast vector $q$ and its uncertainty matrix $Ω$ that describe how much a chosen portfolio should outperform the market. Our key idea is to treat $(q,Ω)$ as latent variables and learn them from market data within a single Bayesian network. Consequently, the resulting posterior estimation admits closed-form expression, enabling fast inference and stable portfolio weights. Building on these, we propose two mechanisms to capture how features interact with returns: shared-latent parametrization and feature-influenced views; both recover classical BL and Markowitz portfolios as special cases. Empirically, on 30-year Dow-Jones and 20-year sector-ETF data, we improve Sharpe ratios by 50% and cut turnover by 55% relative to Markowitz and the index baselines. This work turns BL into a fully data-driven, view-free, and coherent Bayesian framework for portfolio optimization.

World modelling, i.e. building a representation of the rules that govern the world so as to predict its evolution, is an essential ability for any agent interacting with the physical world. Despite their impressive performance, many solutions fail to learn a causal representation of the environment they are trying to model, which would be necessary to gain a deep enough understanding of the world to perform complex tasks. With this work, we aim to broaden the research in the intersection of causality theory and neural world modelling by assessing the potential for causal discovery of the State Space Model (SSM) architecture, which has been shown to have several advantages over the widespread Transformer. We show empirically that, compared to an equivalent Transformer, a SSM can model the dynamics of a simple environment and learn a causal model at the same time with equivalent or better performance, thus paving the way for further experiments that lean into the strength of SSMs and further enhance them with causal awareness.

Artificial neural networks (ANNs) are widely used in modeling sentence processing but often exhibit deterministic behavior, contrasting with human sentence comprehension, which manages uncertainty during ambiguous or unexpected inputs. This is exemplified by reversal anomalies--sentences with unexpected role reversals that challenge syntax and semantics--highlighting the limitations of traditional ANN models, such as the Sentence Gestalt (SG) Model. To address these limitations, we propose a Bayesian framework for sentence comprehension, applying an extention of the ensemble Kalman filter (EnKF) for Bayesian inference to quantify uncertainty. By framing language comprehension as a Bayesian inverse problem, this approach enhances the SG model's ability to reflect human sentence processing with respect to the representation of uncertainty. Numerical experiments and comparisons with maximum likelihood estimation (MLE) demonstrate that Bayesian methods improve uncertainty representation, enabling the model to better approximate human cognitive processing when dealing with linguistic ambiguities. Introduction Artificial neural networks (ANNs) have become indispensable tools in modeling sentence processing within the field of natural language processing and cognitive science. These models are capable of handling complex linguistic structures, making accurate predictions, and resolving ambiguities with a notable degree of certainty, even when they are wrong Guo et al. (2017); Hein et al. (2019). However, this behavior stands in contrast to human sentence comprehension, which often involves managing uncertainty, especially when faced with ambiguous or unexpected language inputs. The research has been funded by the Deutsche Forschungsgemeinschaft (DFG)- Project-ID 318763901 - SFB1294.

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean variance estimation (MVE) networks can learn this type of uncertainty but require ad-hoc regularization strategies to avoid overfitting and are unable to predict epistemic uncertainty (model uncertainty). Conversely, Bayesian neural networks predict epistemic uncertainty but are notoriously difficult to train due to the approximate nature of Bayesian inference. We propose to cooperatively train a variance network with a Bayesian neural network and demonstrate that the resulting model disentangles aleatoric and epistemic uncertainties while improving the mean estimation. We demonstrate the effectiveness and scalability of this method across a diverse range of datasets, including a time-dependent heteroscedastic regression dataset we created where the aleatoric uncertainty is known. The proposed method is straightforward to implement, robust, and adaptable to various model architectures.

The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several Gaussian distributions defined on $\mathcal{P}_d$. We will show how popular classifiers on $\mathcal{P}_d$ can be reinterpreted as Bayes Classifiers using these Gaussian distributions. These distributions will also be used for outlier detection and dimension reduction. By showing that those distributions are pervasive in the tools used on $\mathcal{P}_d$, we allow for other machine learning tools to be extended to $\mathcal{P}_d$.

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep neural networks are used to model the treatment and control effect functions, while an additional neural network is employed to estimate their parameters. The universal approximation capability of deep neural networks ensures the broad applicability of this method. Numerical results highlight the superior performance of the proposed Double-NN method compared to the conformal quantile regression (CQR) method in individual treatment effect estimation. From the perspective of statistical inference, this work advances the theory and methodology for statistical inference of large models. Specifically, it is theoretically proven that the proposed method permits the model size to increase with the sample size $n$ at a rate of $O(n^ζ)$ for some $0 \leq ζ<1$, while still maintaining proper quantification of uncertainty in the model parameters. This result marks a significant improvement compared to the range $0\leq ζ< \frac{1}{2}$ required by the classical central limit theorem. Furthermore, this work provides a rigorous framework for quantifying the uncertainty of deep neural networks under the neural scaling law, representing a substantial contribution to the statistical understanding of large-scale neural network models.

In regions lacking medically certified causes of death, verbal autopsy (VA) is a critical and widely used tool to ascertain the cause of death through interviews with caregivers. Data collected by VAs are often analyzed using probabilistic algorithms. The performance of these algorithms often degrades due to distributional shift across populations. Most existing VA algorithms rely on centralized training, requiring full access to training data for joint modeling. This is often infeasible due to privacy and logistical constraints. In this paper, we propose a novel Bayesian Federated Learning (BFL) framework that avoids data sharing across multiple training sources. Our method enables reliable individual-level cause-of-death classification and population-level quantification of cause-specific mortality fractions (CSMFs), in a target domain with limited or no local labeled data. The proposed framework is modular, computationally efficient, and compatible with a wide range of existing VA algorithms as candidate models, facilitating flexible deployment in real-world mortality surveillance systems. We validate the performance of BFL through extensive experiments on two real-world VA datasets under varying levels of distribution shift. Our results show that BFL significantly outperforms the base models built on a single domain and achieves comparable or better performance compared to joint modeling.

--Cut-in maneuvers in high-speed traffic pose critical challenges that can lead to abrupt braking and collisions, necessitating safe and efficient lane change strategies. We propose a Dynamic Bayesian Network (DBN) framework to integrate lateral evidence with safety assessment models, thereby predicting lane changes and ensuring safe cut-in maneuvers effectively. Our proposed framework comprises three key probabilistic hypotheses (lateral evidence, lateral safety, and longitudinal safety) that facilitate the decision-making process through dynamic data processing and assessments of vehicle positions, lateral velocities, relative distance, and Time-to-Collision (TTC) computations. The DBN model's performance compared with other conventional approaches demonstrates superior performance in crash reduction, especially in critical high-speed scenarios, while maintaining a competitive performance in low-speed scenarios. This paves the way for robust, scalable, and efficient safety validation in automated driving systems. I NTRODUCTION The presence of advanced autonomous vehicles(A Vs) in real-world traffic is increasing daily, necessitating the need for robust models that can estimate risks and plan maneuvers proactively to ensure safety. Accurate detection and prediction of lane change maneuvers are crucial for collision avoidance, traffic flow optimization, and safety enhancement [2].

The widespread integration of face recognition technologies into various applications (e.g., access control and personalized advertising) necessitates a critical emphasis on fairness. While previous efforts have focused on demographic fairness, the fairness of individual biological face components remains unexplored. In this paper, we focus on face component fairness, a fairness notion defined by biological face features. To our best knowledge, our work is the first work to mitigate bias of face attribute prediction at the biological feature level. In this work, we identify two key challenges in optimizing face component fairness: attribute label scarcity and attribute inter-dependencies, both of which limit the effectiveness of bias mitigation from previous approaches. To address these issues, we propose \textbf{B}ayesian \textbf{N}etwork-informed \textbf{M}eta \textbf{R}eweighting (BNMR), which incorporates a Bayesian Network calibrator to guide an adaptive meta-learning-based sample reweighting process. During the training process of our approach, the Bayesian Network calibrator dynamically tracks model bias and encodes prior probabilities for face component attributes to overcome the above challenges. To demonstrate the efficacy of our approach, we conduct extensive experiments on a large-scale real-world human face dataset. Our results show that BNMR is able to consistently outperform recent face bias mitigation baselines. Moreover, our results suggest a positive impact of face component fairness on the commonly considered demographic fairness (e.g., \textit{gender}). Our findings pave the way for new research avenues on face component fairness, suggesting that face component fairness could serve as a potential surrogate objective for demographic fairness. The code for our work is publicly available~\footnote{https://github.com/yliuaa/BNMR-FairCompFace.git}.

Manual scoring of the Action Research Arm Test (ARAT) for upper extremity assessment in stroke rehabilitation is time-intensive and variable. We propose an automated ARAT scoring system integrating multimodal video analysis with SlowFast, I3D, and Transformer-based models using OpenPose keypoints and object locations. Our approach employs multi-view data (ipsilateral, contralateral, and top perspectives), applying early and late fusion to combine features across views and models. Hierarchical Bayesian Models (HBMs) infer movement quality components, enhancing interpretability. A clinician dashboard displays task scores, execution times, and quality assessments. We conducted a study with five clinicians who reviewed 500 video ratings generated by our system, providing feedback on its accuracy and usability. Evaluated on a stroke rehabilitation dataset, our framework achieves 89.0% validation accuracy with late fusion, with HBMs aligning closely with manual assessments. This work advances automated rehabilitation by offering a scalable, interpretable solution with clinical validation.