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.

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.

Large language models(LLMs) have demonstrated remarkable performance on many natural language processing(NLP) tasks and have been employed in phishing email detection research. However, in current studies, well-performing LLMs typically contain billions or even tens of billions of parameters, requiring enormous computational resources. To reduce computational costs, we investigated the effectiveness of small-parameter LLMs for phishing email detection. These LLMs have around 3 billion parameters and can run on consumer-grade GPUs. However, small LLMs often perform poorly in phishing email detection task. To address these issues, we designed a set of methods including Prompt Engineering, Explanation Augmented Fine-tuning, and Model Ensemble to improve phishing email detection capabilities of small LLMs. We validated the effectiveness of our approach through experiments, significantly improving both accuracy and F1 score on the SpamAssassin and CEAS\_08 datasets. Furthermore, the fine-tuned models demonstrated strong transferability, achieving robust performance across multiple unseen phishing datasets, outperforming traditional baselines and approaching standard-sized LLMs.

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.