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.

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.

With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the benefit of simplicity, and work reasonably well in low dimensions, but as the number of variables increases, they can lack the required flexibility and scalability. Classical parametric models for angular variables, such as the von Mises-Fisher (vMF) distribution, provide an alternative. Exploiting mixtures of vMF distributions increases their flexibility, but there are cases where even this is not sufficient to capture the intricate features that can arise in data. Owing to their flexibility, generative deep learning methods are able to capture complex data structures; they therefore have the potential to be useful in the simulation of angular variables. In this paper, we explore a range of deep learning approaches for this task, including generative adversarial networks, normalizing flows and flow matching. We assess their performance via a range of metrics and make comparisons to the more classical approach of using a mixture of vMF distributions. The methods are also applied to a metocean data set, demonstrating their applicability to real-world, complex data structures.

Aiming at the group decision - making problem with multi - objective attributes, this study proposes a group decision - making system that integrates fuzzy inference and Bayesian network. A fuzzy rule base is constructed by combining threshold values, membership functions, expert experience, and domain knowledge to address quantitative challenges such as scale differences and expert linguistic variables. A hierarchical Bayesian network is designed, featuring a directed acyclic graph with nodes selected by experts, and maximum likelihood estimation is used to dynamically optimize the conditional probability table, modeling the nonlinear correlations among multidimensional indices for posterior probability aggregation. In a comprehensive student evaluation case, this method is compared with the traditional weighted scoring approach. The results indicate that the proposed method demonstrates effectiveness in both rule criterion construction and ranking consistency, with a classification accuracy of 86.0% and an F1 value improvement of 53.4% over the traditional method. Additionally, computational experiments on real - world datasets across various group decision scenarios assess the method's performance and robustness, providing evidence of its reliability in diverse contexts.

Artificial Intelligence (AI) models deployed in production frequently face challenges in maintaining their performance in non-stationary environments. This issue is particularly noticeable in medical settings, where temporal dataset shifts often occur. These shifts arise when the distributions of training data differ from those of the data encountered during deployment over time. Further, new labeled data to continuously retrain AI is not typically available in a timely manner due to data access limitations. To address these challenges, we propose a proactive self-adaptive AI approach, or pro-adaptive, where we model the temporal trajectory of AI parameters, allowing us to short-term forecast parameter values. To this end, we use polynomial spline bases, within an extensible Functional Data Analysis framework. We validate our methodology with a logistic regression model addressing prior probability shift, covariate shift, and concept shift. This validation is conducted on both a controlled simulated dataset and a publicly available real-world COVID-19 dataset from Mexico, with various shifts occurring between 2020 and 2024. Our results indicate that this approach enhances the performance of AI against shifts compared to baseline stable models trained at different time distances from the present, without requiring updated training data. This work lays the foundation for pro-adaptive AI research against dynamic, non-stationary environments, being compatible with data protection, in resilient AI production environments for health.

Large language models (LLMs) exhibit probabilistic output characteristics, yet conventional evaluation frameworks rely on deterministic scalar metrics. This study introduces a Bayesian approach for LLM capability assessment that integrates prior knowledge through probabilistic inference, addressing limitations under limited-sample regimes. By treating model capabilities as latent variables and leveraging a curated query set to induce discriminative responses, we formalize model ranking as a Bayesian hypothesis testing problem over mutually exclusive capability intervals. Experimental evaluations with GPT-series models demonstrate that the proposed method achieves superior discrimination compared to conventional evaluation methods. Results indicate that even with reduced sample sizes, the approach maintains statistical robustness while providing actionable insights, such as probabilistic statements about a model's likelihood of surpassing specific baselines. This work advances LLM evaluation methodologies by bridging Bayesian inference with practical constraints in real-world deployment scenarios.