The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Time series analysis has emerged as an important tool for improving patient diagnosis and management in healthcare applications. However, these applications commonly face two critical challenges: time misalignment and data sparsity. Traditional approaches address these issues through a two-step process of imputation followed by prediction. We propose MAGIC (Multi-tAsk Gaussian Process for Imputation and Classification), a novel unified framework that simultaneously performs class-informed missing value imputation and label prediction within a hierarchical multi-task Gaussian process coupled with functional logistic regression. To handle intractable likelihood components, MAGIC employs Taylor expansion approximations with bounded error analysis, and parameter estimation is performed using EM algorithm with block coordinate optimization supported by convergence analysis. We validate MAGIC through two healthcare applications: prediction of post-traumatic headache improvement following mild traumatic brain injury and prediction of in-hospital mortality within 48 hours after ICU admission. In both applications, MAGIC achieves superior predictive accuracy compared to existing methods. The ability to generate real-time and accurate predictions with limited samples facilitates early clinical assessment and treatment planning, enabling healthcare providers to make more informed treatment decisions.

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard baseline methods such as model logits and elicited probabilities produce overconfident and poorly calibrated estimates. In this work, we propose Approximate Bayesian Computation (ABC), a likelihood-free Bayesian inference, based approach that treats LLMs as a stochastic simulator to infer posterior distributions over predictive probabilities. We evaluate our ABC approach on two clinically relevant benchmarks: a synthetic oral lesion diagnosis dataset and the publicly available GretelAI symptom-to-diagnosis dataset. Compared to standard baselines, our approach improves accuracy by up to 46.9\%, reduces Brier scores by 74.4\%, and enhances calibration as measured by Expected Calibration Error (ECE) and predictive entropy.

Traffic accidents remain a major global concern, with lane-change maneuvers recognized as one of the significant contributors to collision risk. Anticipating these maneuvers has become an important research focus, supporting both traffic safety and the safe integration of autonomous and assisted driving technologies. Over the past decade, numerous models have been developed for lane-change prediction. However, most existing works have been designed and validated using simulation environments or pre-recorded datasets. While these settings allow for benchmarking and controlled evaluation, they often rely on simplified assumptions about sensing, communication, and vehicle behavior that do not fully capture the complexity of real-world operation. Real-world deployments of lane-change prediction systems are relatively rare, and when they are reported, their practical challenges, limitations, and insights remain under-documented. To illustrate the setting more concretely, consider the left lane change scenario shown in Figure 1. The Ego Vehicle (EV) is driving in the left lane, while the Target Vehicle (TV) is moving in the right lane behind a Preceding Vehicle (PV). When the PV suddenly brakes, the TV must change lanes to avoid a collision.

Advanced reasoning models with agentic capabilities (AI agents) are deployed to interact with humans and to solve sequential decision-making problems under (approximate) utility functions and internal models. When such problems have resource or failure constraints where action sequences may be forcibly terminated once resources are exhausted, agents face implicit trade-offs that reshape their utility-driven (rational) behaviour. Additionally, since these agents are typically commissioned by a human principal to act on their behalf, asymmetries in constraint exposure can give rise to previously unanticipated misalignment between human objectives and agent incentives. We formalise this setting through a survival bandit framework, provide theoretical and empirical results that quantify the impact of survival-driven preference shifts, identify conditions under which misalignment emerges and propose mechanisms to mitigate the emergence of risk-seeking or risk-averse behaviours. As a result, this work aims to increase understanding and interpretability of emergent behaviours of AI agents operating under such survival pressure, and offer guidelines for safely deploying such AI systems in critical resource-limited environments.

This paper presents a lidar-only state estimation and tracking framework, along with a roadside sensing unit for integration with existing urban infrastructure. Urban deployments demand scalable, real-time tracking solutions, yet traditional remote sensing remains costly and computationally intensive, especially under perceptually degraded conditions. Our sensor node couples a single lidar with an edge computing unit and runs a computationally efficient, GPU-free observer that simultaneously estimates object state, class, dimensions, and existence probability. The pipeline performs: (i) state updates via an extended Kalman filter, (ii) dimension estimation using a 1D grid-map/Bayesian update, (iii) class updates via a lookup table driven by the most probable footprint, and (iv) existence estimation from track age and bounding-box consistency. Experiments in dynamic urban-like scenes with diverse traffic participants demonstrate real-time performance and high precision: The complete end-to-end pipeline finishes within \SI{100}{\milli\second} for \SI{99.88}{\%} of messages, with an excellent detection rate. Robustness is further confirmed under simulated wind and sensor vibration. These results indicate that reliable, real-time roadside tracking is feasible on CPU-only edge hardware, enabling scalable, privacy-friendly deployments within existing city infrastructure. The framework integrates with existing poles, traffic lights, and buildings, reducing deployment costs and simplifying large-scale urban rollouts and maintenance efforts.

We introduce GuessingGame, a protocol for evaluating large language models (LLMs) as strategic question-askers in open-ended, open-domain settings. A Guesser LLM identifies a hidden object by posing free-form questions to an Oracle without predefined choices or candidate lists. To measure question quality, we propose two information gain (IG) metrics: a Bayesian method that tracks belief updates over semantic concepts using LLM-scored relevance, and an entropy-based method that filters candidates via ConceptNet. Both metrics are model-agnostic and support post hoc analysis. Across 858 games with multiple models and prompting strategies, higher IG strongly predicts efficiency: a one-standard-deviation IG increase reduces expected game length by 43\%. Prompting constraints guided by IG, such as enforcing question diversity, enable weaker models to significantly improve performance. These results show that question-asking in LLMs is both measurable and improvable, and crucial for interactive reasoning.

The spreading dynamics in social networks are often studied under the assumption that individuals' statuses, whether informed or infected, are fully observable. However, in many real-world situations, such statuses remain unobservable, which is crucial for determining an individual's potential to further spread the infection. While final statuses are hidden, intermediate indicators such as symptoms of infection are observable and provide useful representations of the underlying diffusion process. We propose a partial observability-aware Machine Learning framework to learn the characteristics of the spreading model. We term the method Distribution Classification, which utilizes the power of classifiers to infer the underlying transmission dynamics. Through extensive benchmarking against Approximate Bayesian Computation and GNN-based baselines, our framework consistently outperforms these state-of-the-art methods, delivering accurate parameter estimates across diverse diffusion settings while scaling efficiently to large networks. We validate the method on synthetic networks and extend the study to a real-world insider trading network, demonstrating its effectiveness in analyzing spreading phenomena where direct observation of individual statuses is not possible.

This paper studies how insurers can chose which claims to investigate for fraud. Given a prediction model, typically only claims with the highest predicted propability of being fraudulent are investigated. We argue that this can lead to inconsistent learning and propose a randomized alternative. More generally, we draw a parallel with the multi-arm bandit literature and argue that, in the presence of selection, the obtained observations are not iid. Hence, dependence on past observations should be accounted for when updating parameter estimates. We formalize selection in a binary regression framework and show that model updating and maximum-likelihood estimation can be implemented as if claims were investigated at random. Then, we define consistency of selection strategies and conjecture sufficient conditions for consistency. Our simulations suggest that the often-used selection strategy can be inconsistent while the proposed randomized alternative is consistent. Finally, we compare our randomized selection strategy with Thompson sampling, a standard multi-arm bandit heuristic. Our simulations suggest that the latter can be inefficient in learning low fraud probabilities.

In recent years, there has been significant interest in designing machine learning algorithms that enable robust and sample-efficient knowledge transfer across tasks to facilitate rapid and accurate estimation and prediction. Traditional machine learning methods have largely followed a single-task or "isolated learning" framework, where each task is learned independently, ignoring knowledge from prior tasks (Upadhyay et al., 2024). However, unlike such isolated approaches, human learning relies on prior experiences to accelerate new learning. Inspired by this, recent prominent "knowledge-transfer" approaches include meta-learning (Finn et al., 2017; Bouchattaoui, 2024), transfer learning (Zhu et al., 2023; Zhuang et al., 2020), multi-task learning (Crawshaw, 2020; Zhang and Yang, 2022), and lifelong learning (Liu, 2017), all of which aim to leverage shared structure across tasks to improve generalization and aim to replicate this human-like knowledge transfer. Meta-learning focuses on learning a learning algorithm that can quickly adapt to new tasks using limited data. Transfer learning reuses knowledge from related source tasks to improve performance on a target task with few labeled examples.