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 $\mathcal{P}_d$.

Federated Learning enables collaborative training of machine learning models on decentralized data. This scheme, however, is vulnerable to adversarial attacks, when some of the clients submit corrupted model updates. In real-world scenarios, the total number of compromised clients is typically unknown, with the extent of attacks potentially varying over time. To address these challenges, we propose an adaptive approach for robust aggregation of model updates based on Bayesian inference. The mean update is defined by the maximum of the likelihood marginalized over probabilities of each client to be `honest'. As a result, the method shares the simplicity of the classical average estimators (e.g., sample mean or geometric median), being independent of the number of compromised clients. At the same time, it is as effective against attacks as methods specifically tailored to Federated Learning, such as Krum. We compare our approach with other aggregation schemes in federated setting on three benchmark image classification data sets. The proposed method consistently achieves state-of-the-art performance across various attack types with static and varying number of malicious clients.

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.

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.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Many learning problems involve multiple patterns and varying degrees of uncertainty dependent on the covariates. Advances in Deep Learning (DL) have addressed these issues by learning highly nonlinear input-output dependencies. However, model interpretability and Uncertainty Quantification (UQ) have often straggled behind. In this context, we introduce the Competitive/Collaborative Fusion of Experts (CoCoAFusE), a novel, Bayesian Covariates-Dependent Modeling technique. CoCoAFusE builds on the very philosophy behind Mixtures of Experts (MoEs), blending predictions from several simple sub-models (or "experts") to achieve high levels of expressiveness while retaining a substantial degree of local interpretability. Our formulation extends that of a classical Mixture of Experts by contemplating the fusion of the experts' distributions in addition to their more usual mixing (i.e., superimposition). Through this additional feature, CoCoAFusE better accommodates different scenarios for the intermediate behavior between generating mechanisms, resulting in tighter credible bounds on the response variable. Indeed, only resorting to mixing, as in classical MoEs, may lead to multimodality artifacts, especially over smooth transitions. Instead, CoCoAFusE can avoid these artifacts even under the same structure and priors for the experts, leading to greater expressiveness and flexibility in modeling. This new approach is showcased extensively on a suite of motivating numerical examples and a collection of real-data ones, demonstrating its efficacy in tackling complex regression problems where uncertainty is a key quantity of interest.

Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only focus on case studies, where the distribution conditioned on each class is either isotropic Gaussian or supported on a one-dimensional interval with some extra conditions. How to analyze the guidance effect beyond these case studies remains an open question. Towards closing this gap, we make an attempt to analyze diffusion guidance under general data distributions. Rather than demonstrating uniform sample quality improvement, which does not hold in some distributions, we prove that guidance can improve the whole sample quality, in the sense that the average reciprocal of the classifier probability decreases with the existence of guidance. This aligns with the motivation of introducing guidance.