In the rapidly evolving educational landscape, the unbiased assessment of soft skills is a significant challenge, particularly in higher education. This paper presents a fuzzy logic approach that employs a Granular Linguistic Model of Phenomena integrated with multimodal analysis to evaluate soft skills in undergraduate students. By leveraging computational perceptions, this approach enables a structured breakdown of complex soft skill expressions, capturing nuanced behaviours with high granularity and addressing their inherent uncertainties, thereby enhancing interpretability and reliability. Experiments were conducted with undergraduate students using a developed tool that assesses soft skills such as decision-making, communication, and creativity. This tool identifies and quantifies subtle aspects of human interaction, such as facial expressions and gesture recognition. The findings reveal that the framework effectively consolidates multiple data inputs to produce meaningful and consistent assessments of soft skills, showing that integrating multiple modalities into the evaluation process significantly improves the quality of soft skills scores, making the assessment work transparent and understandable to educational stakeholders.

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.

In the near future, Structural Health Monitoring (SHM) technologies will be capable of overcoming the drawbacks in the current maintenance and life-cycle management paradigms, namely: cost, increased downtime, less-than-optimal safety management paradigm and the limited applicability of fully-autonomous operations. In the context of SHM, one of the most challenging tasks is damage quantification. Current methods face accuracy and/or robustness issues when it comes to varying operating and environmental conditions. In addition, the damage/no-damage paradigm of current frameworks does not offer much information to maintainers on the ground for proper decision-making. In this study, a novel structural damage quantification framework is proposed based on widely-used Damage Indices (DIs) and Gaussian Process Regression Models (GPRMs). The novelty lies in calculating the probability of an incoming test DI point originating from a specific state, which allows for probability-educated decision-making. This framework is applied to three test cases: a Carbon Fiber-Reinforced Plastic (CFRP) coupon with attached weights as simulated damage, an aluminum coupon with a notch, and an aluminum coupon with attached weights as simulated damage under varying loading states. The state prediction method presented herein is applied to single-state quantification in the first two test cases, as well as the third one assuming the loading state is known. Finally, the proposed method is applied to the third test case assuming neither the damage size nor the load is known in order to predict both simultaneously from incoming DI test points. In applying this framework, two forms of GPRMs (standard and variational heteroscedastic) are used in order to critically assess their performances with respect to the three test cases.

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.

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.

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.

Human behavioural data in psychophysics has been used to elucidate the underlying mechanisms of many cognitive processes, such as attention, sensorimotor integration, and perceptual decision making. Visual working memory has particularly benefited from this approach: analyses of VWM errors have proven crucial for understanding VWM capacity and coding schemes, in turn constraining neural models of both. One poorly understood class of VWM errors are swap errors, whereby participants recall an uncued item from memory. Swap errors could arise from erroneous memory encoding, noisy storage, or errors at retrieval time - previous research has mostly implicated the latter two. However, these studies made strong a priori assumptions on the detailed mechanisms and/or parametric form of errors contributed by these sources. Here, we pursue a data-driven approach instead, introducing a Bayesian non-parametric mixture model of swap errors (BNS) which provides a flexible descriptive model of swapping behaviour, such that swaps are allowed to depend on both the probed and reported features of every stimulus item. We fit BNS to the trial-by-trial behaviour of human participants and show that it recapitulates the strong dependence of swaps on cue similarity in multiple datasets. Critically, BNS reveals that this dependence coexists with a non-monotonic modulation in the report feature dimension for a random dot motion direction-cued, location-reported dataset. The form of the modulation inferred by BNS opens new questions about the importance of memory encoding in causing swap errors in VWM, a distinct source to the previously suggested binding and cueing errors. Our analyses, combining qualitative comparisons of the highly interpretable BNS parameter structure with rigorous quantitative model comparison and recovery methods, show that previous interpretations of swap errors may have been incomplete.

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then, we show that an estimator of a parameter for each edge in a directed acyclic graph (DAG) is distributed normally. We end this paper with computational experiments with the expectation and maximization (EM) algorithm and quadratic optimization.