Understanding how humans adapt to streaky performance under uncertainty is central to research on belief updating, attention, and decision-making. Professional basketball provides a naturalistic setting in which these processes can be observed under real incentives and time pressure. Using NBA player-tracking data, we examine how defenders adjust their behavior in response to offensive shooting outcomes, shifting focus from shooter performance to defensive adaptation. We conduct three complementary studies relating multiple spatial defensive metrics to recent shooting history, including asymmetric responses to makes versus misses, cumulative success over short memory windows, and escalation during extended streaks. Across analyses, we estimate regression-based models with appropriate clustering and controls to isolate behavioral updating from contextual factors. The results show clear evidence of asymmetric updating: defenders tighten coverage more after made shots than they relax following misses, with effects strongest for the closest defender. Defensive adjustments are driven primarily by short recency windows of approximately three to five shots. Escalation during long hot streaks is limited, with defensive responses stabilizing rather than increasing indefinitely. Together, these findings suggest that defensive behavior reflects psychologically structured but bounded belief updating rather than full rational inference or indiscriminate overreaction to streaks.

We propose a multidimensional tensor clustering approach for studying how professional basketball players’ shooting patterns vary over court locations and game time. Unlike most existing methods that only study continuous-valued tensors or have to assume the same cluster structure along different tensor directions, we propose a Bayesian nonparametric model that deals with count-valued tensors and projects the heterogeneity among players onto tensor dimensions while allowing cluster structures to be different over directions. Our method is fully probabilistic; hence allows simultaneous inference on both the number of clusters and the cluster configurations. We present an efficient posterior sampling method and establish the large-sample convergence properties for the posterior distribution. Simulation studies have demonstrated an excellent empirical performance of the proposed method. Finally, an application to shot chart data collected from 191 NBA players during the 2017–2018 regular season is conducted and reveals several interesting insights for basketball analytics.

Gene therapies aim to address the root causes of diseases, particularly those stemming from rare genetic defects that can be life-threatening or severely debilitating. Although an increasing number of gene therapies have received regulatory approvals in recent years, understanding their long-term efficacy in trials with limited follow-up time remains challenging. To address this critical question, we propose a novel Bayesian framework designed to selectively integrate relevant external data with internal trial data to improve the inference of the durability of long-term efficacy. We proved that the proposed method has desired theoretical properties, such as identifying and favoring external subsets deemed relevant, where the relevance is defined as the similarity, induced by the marginal likelihood, between the generating mechanisms of the internal data and the selected external data. We also conducted comprehensive simulations to evaluate its performance under various scenarios. Furthermore, we apply this method to predict and infer the endogenous factor IX (FIX) levels of patients who receive Etranacogene dezaparvovec over the long-term. Our estimated long-term FIX levels, validated by recent trial data, indicate that Etranacogene dezaparvovec induces sustained FIX production. Together, the theoretical findings, simulation results, and successful application of this framework underscore its potential to address similar long-term effectiveness estimation and inference questions in real world applications.

Long-form video understanding remains challenging for Vision-Language Models (VLMs) due to the inherent tension between computational constraints and the need to capture information distributed across thousands of frames. Existing approaches either sample frames uniformly (risking information loss) or select keyframes in a single pass (with no recovery from poor choices). We propose VideoBrain, an end-to-end framework that enables VLMs to adaptively acquire visual information through learned sampling policies. Our approach features dual complementary agents: a CLIP-based agent for semantic retrieval across the video and a Uniform agent for dense temporal sampling within intervals. Unlike prior agent-based methods that rely on text-only LLMs orchestrating visual tools, our VLM directly perceives frames and reasons about information sufficiency. To prevent models from invoking agents indiscriminately to maximize rewards, we introduce a behavior-aware reward function coupled with a data classification pipeline that teaches the model when agent invocation is genuinely beneficial. Experiments on four long video benchmarks demonstrate that VideoBrain achieves +3.5\% to +9.0\% improvement over the baseline while using 30-40\% fewer frames, with strong zero-shot generalization to short video benchmarks.

Artificial Intelligence brings powerful new tools to sports, from automated officiating to tactical analysis, but these applications all depend on a core reasoning capability. Deeply understanding sports requires an intricate blend of fine-grained visual perception and rule-based reasoning—a challenge that pushes the limits of current multimodal models. To succeed, models must master three critical capabilities: perceiving nuanced visual details, applying abstract sport rule knowledge, and grounding that knowledge in specific visual evidence. Current sports benchmarks either cover single sports or lack the detailed reasoning chains and precise visual grounding needed to robustly evaluate these core capabilities in a multi-sport context. To address this gap, we introduce SportR, the first multi-sports large-scale benchmark designed to train and evaluate MLLMs on the fundamental reasoning required for sports intelligence. Our benchmark provides a dataset of 5,017 images and 2,101 videos. To enable granular evaluation, we structure our benchmark around a progressive hierarchy of question-answer (QA) pairs designed to probe reasoning at increasing depths—from simple infraction identification to complex penalty prediction. For the most advanced tasks requiring multi-step reasoning, such as determining penalties or explaining tactics, we provide 7,118 high-quality, human-authored Chain-of-Thought (CoT) annotations. In addition, our benchmark incorporates both image and video modalities and provides manual bounding box annotations to directly test visual grounding in the image part. Extensive experiments demonstrate the profound difficulty of our benchmark. State-of-the-art baseline models perform poorly on our most challenging tasks. While training on our data via Supervised Fine-Tuning and Reinforcement Learning improves these scores, they remain relatively low, highlighting a significant gap in current model capabilities. SportR presents a new challenge for the community, providing a critical resource to drive future research in multimodal sports reasoning. The dataset is available at https://anonymous.4open.science/r/ICLR2026-E071/.

In this paper our objective is to identify the risk factors associated with adolescent marijuana use in Washington State, utilizing data from the 2018 and 2021 Healthy Youth Survey (HYS). Despite the survey's assurance of anonymity, the possibility of over-or underreporting exists due to various reasons, such as fear of being exposed, social stigma, and peer pressure. We are also interested in identifying factors that are associated with the occurrence of misreport. To achieve these goals, we develop a full Bayesian framework with a two-level latent linear regression model. The top level is for the true marijuana use response, and the second level is for the occurrence of misreporting. An informative prior is designed to seamlessly incorporate the domain knowledge or prior information while minimizing the risk of prior misspecification. We propose a partially collapsed Gibbs sampling algorithm with a Metropolis-Hastings step to sample the regression coefficients. Simulation studies have been conducted to demonstrate the superior performance of the proposed method over alternative approaches. Our analysis of HYS data discovers multiple factors for identifying at-risk adolescents and informing future prevention efforts.

With the rapid advancement of large language models (LLMs), Multi-agent Systems (MAS) have achieved significant progress in various application scenarios. However, substantial challenges remain in designing versatile, robust, and efficient platforms for agent deployment. To address these limitations, we propose \textbf{LightAgent}, a lightweight yet powerful agentic framework, effectively resolving the trade-off between flexibility and simplicity found in existing frameworks. LightAgent integrates core functionalities such as Memory (mem0), Tools, and Tree of Thought (ToT), while maintaining an extremely lightweight structure. As a fully open-source solution, it seamlessly integrates with mainstream chat platforms, enabling developers to easily build self-learning agents. We have released LightAgent at \href{https://github.com/wxai-space/LightAgent}{https://github.com/wxai-space/LightAgent}

Current literature on transfer learning has been focused on improving the predictive performance corresponding to a small dataset by transferring information to it from a larger but possibly biassed dataset. However, the transfer learning methods currently available do not allow the computation of prediction intervals, and hence, one has to rely on using either the small dataset alone or combining it with the possibly biassed dataset to obtain prediction intervals using traditional linear regression methods. In this article, we propose an Empirical Bayes approach for Prediction Interval Transfer Learning (EB-PITL), to compute prediction intervals for transfer learning in linear regression tasks. We have proved that the Gibbs sampler associated with EB-PITL is geometrically ergodic, so EB-PITL can also quantify the Monte Carlo uncertainty associated with its predicted value. The efficiency of EB-PITL against currently available methods is demonstrated using simulation studies and by analysing the Tetouan City power consumption dataset.

Bloodstain Pattern Analysis (BPA) helps us understand how bloodstains form, with a focus on their size, shape, and distributions. This aids in crime scene reconstruction and provides insight into victim positions and crime investigation. One challenge in BPA is distinguishing between different types of bloodstains, such as those from firearms, impacts, or other mechanisms. Our study focuses on differentiating impact spatter bloodstain patterns from gunshot backward spatter bloodstain patterns. We distinguish patterns by extracting well-designed individual stain features, applying effective data consolidation methods, and selecting boosting classifiers. As a result, our model exhibits competitive accuracy and efficiency on the tested dataset, suggesting its potential in similar scenarios.

In many scientific domains, clustering aims to reveal interpretable latent structure that reflects relevant subpopulations or processes. Widely used Bayesian mixture models for model-based clustering often produce overlapping or redundant components because priors on cluster locations are specified independently, hindering interpretability. To mitigate this, repulsive priors have been proposed to encourage well-separated components, yet existing approaches face both computational and theoretical challenges. We introduce a fully tractable Bayesian repulsive mixture model by assigning a projection Determinantal Point Process (DPP) prior to the component locations. Projection DPPs induce strong repulsion and allow exact sampling, enabling parsimonious and interpretable posterior clustering. Leveraging their analytical tractability, we derive closed-form posterior and predictive distributions. These results, in turn, enable two efficient inference algorithms: a conditional Gibbs sampler and the first fully implementable marginal sampler for DPP-based mixtures. We also provide strong frequentist guarantees, including posterior consistency for density estimation, elimination of redundant components, and contraction of the mixing measure. Simulation studies confirm superior mixing and clustering performance compared to alternatives in misspecified settings. Finally, we demonstrate the utility of our method on event-related potential functional data, where it uncovers interpretable neuro-cognitive subgroups. Our results support the projection DPP mixtures as a theoretically sound and practically effective solution for Bayesian clustering.

Deeply understanding sports requires an intricate blend of fine-grained visual perception and rule-based reasoning - a challenge that pushes the limits of current multimodal models. To succeed, models must master three critical capabilities: perceiving nuanced visual details, applying abstract sport rule knowledge, and grounding that knowledge in specific visual evidence. Current sports benchmarks either cover single sports or lack the detailed reasoning chains and precise visual grounding needed to robustly evaluate these core capabilities in a multi-sport context. To address this gap, we introduce SportR, the first multi-sports large-scale benchmark designed to train and evaluate MLLMs on the fundamental reasoning required for sports intelligence. Our benchmark provides a dataset of 5,017 images and 2,101 videos. To enable granular evaluation, we structure our benchmark around a progressive hierarchy of question-answer (QA) pairs designed to probe reasoning at increasing depths - from simple infraction identification to complex penalty prediction. For the most advanced tasks requiring multi-step reasoning, such as determining penalties or explaining tactics, we provide 7,118 high-quality, human-authored Chain of Thought (CoT) annotations. In addition, our benchmark incorporates both image and video modalities and provides manual bounding box annotations to test visual grounding in the image part directly. Extensive experiments demonstrate the profound difficulty of our benchmark. State-of-the-art baseline models perform poorly on our most challenging tasks. While training on our data via Supervised Fine-Tuning and Reinforcement Learning improves these scores, they remain relatively low, highlighting a significant gap in current model capabilities. SportR presents a new challenge for the community, providing a critical resource to drive future research in multimodal sports reasoning.

Inference on high-dimensional parameters in structured linear models is an important statistical problem.This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that enjoys adaptive minimax posterior concentration rates and improved structure learning properties compared to existing methods.Moreover, thanks to the conjugate form of the empirical prior, posterior computations are fast and easy.Numerical examples also highlight the method's strong finite-sample performance compared to existing methods across a range of different scenarios.

Understanding sports presents a fascinating challenge for Natural Language Processing (NLP) due to its intricate and ever-changing nature. Current NLP technologies struggle with the advanced cognitive demands required to reason over complex sports scenarios. To explore the current boundaries of this field, we extensively evaluated mainstream and emerging large models on various sports tasks and addressed the limitations of previous benchmarks. Our study ranges from answering simple queries about basic rules and historical facts to engaging in complex, context-specific reasoning using strategies like few-shot learning and chain-of-thought techniques. Beyond text-based analysis, we also explored the sports reasoning capabilities of mainstream video language models to bridge the gap in benchmarking multimodal sports understanding. Based on a comprehensive overview of main-stream large models on diverse sports understanding tasks, we presented a new benchmark, which highlighted the critical challenges of sports understanding for NLP and the varying capabilities of state-of-the-art large models on sports understanding. We also provided an extensive set of error analyses that pointed to detailed reasoning defects of large model reasoning which model-based error analysis failed to reveal. We hope the benchmark and the error analysis set will help identify future research priorities in this field.

In sports analytics, home field advantage is a robust phenomenon where the home team wins more games than the away team. However, discovering the causal factors behind home field advantage presents unique challenges due to the non-stationary, time-varying environment of sports matches. In response, we propose a novel causal discovery method, DYnamic Non-stAtionary local M-estimatOrs (DYNAMO), to learn the time-varying causal structures of home field advantage. DYNAMO offers flexibility by integrating various loss functions, making it practical for learning linear and non-linear causal structures from a general class of non-stationary causal processes. By leveraging local information, we provide theoretical guarantees for the identifiability and estimation consistency of non-stationary causal structures without imposing additional assumptions. Simulation studies validate the efficacy of DYNAMO in recovering time-varying causal structures. We apply our method to high-resolution event data from the 2020-2021 and 2021-2022 English Premier League seasons, during which the former season had no audience presence. Our results reveal intriguing, time-varying, team-specific field advantages influenced by referee bias, which differ significantly with and without crowd support. Furthermore, the time-varying causal structures learned by our method improve goal prediction accuracy compared to existing methods.

Sports video understanding presents unique challenges, requiring models to perceive high-speed dynamics, comprehend complex rules, and reason over long temporal contexts. While Multimodal Large Language Models (MLLMs) have shown promise in genral domains, the current state of research in sports remains narrowly focused: existing approaches are either single-sport centric, limited to specific tasks, or rely on training-free paradigms that lack robust, learned reasoning process. To address this gap, we introduce DeepSport, the first end-to-end trained MLLM framework designed for multi-task, multi-sport video understanding. DeepSport shifts the paradigm from passive frame processing to active, iterative reasoning, empowering the model to “think with videos” by dynamically interrogating content via a specialized frame-extraction tool. To enable this, we propose a data distillation pipeline that synthesizes high-quality Chain-of-Thought (CoT) trajectories from 10 diverse data source, creating a unified resource of 78k training data. We then employ a two-stage training strategy, Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) with a novel gated tool-use reward, to optimize the model's reasoning process. Extensive experiments on the testing benchmark of 6.7k questions demonstrate that DeepSport achieves state-of-the-art performance, significantly outperforming baselines of both proprietary model and open-source models. Our work establishes a new foundation for domain-specific video reasoning to address the complexities of diverse sports.

Multimodal Large Language Models (MLLMs) are advancing the ability to reason about complex sports scenarios by integrating textual and visual information. To comprehensively evaluate their capabilities, we introduce SPORTU, a benchmark designed to assess MLLMs across multi-level sports reasoning tasks. SPORTU comprises two key components: SPORTU-text, featuring 900 multiple-choice questions with human-annotated explanations for rule comprehension and strategy understanding. This component focuses on testing models' ability to reason about sports solely through question-answering (QA), without requiring visual inputs; SPORTU-video, consisting of 1,701 slow-motion video clips across 7 different sports and 12,048 QA pairs, designed to assess multi-level reasoning, from simple sports recognition to complex tasks like foul detection and rule application. We evaluated four prevalent LLMs mainly utilizing few-shot learning paradigms supplemented by chain-of-thought (CoT) prompting on the SPORTU-text part. GPT-4o achieves the highest accuracy of 71\%, but still falls short of human-level performance, highlighting room for improvement in rule comprehension and reasoning. The evaluation for the SPORTU-video part includes 6 proprietary and 8 open-source MLLMs. Experiments show that models fall short on hard tasks that require deep reasoning and rule-based understanding. GPT-4o performs the best with only 57.8\% accuracy on the hard task, showing large room for improvement. We hope that SPORTU will serve as a critical step toward evaluating models' capabilities in sports understanding and reasoning. The dataset is available at [https://github.com/chili-lab/SPORTU](https://github.com/chili-lab/SPORTU).

Large language models have demonstrated outstanding performance in various natural language processing tasks, but their security capabilities in the financial domain have not been explored, and their performance on complex tasks like financial agent remains unknown. This paper presents FinEval, a benchmark designed to evaluate LLMs' financial domain knowledge and practical abilities. The dataset contains 8,351 questions categorized into four different key areas: Financial Academic Knowledge, Financial Industry Knowledge, Financial Security Knowledge, and Financial Agent. Financial Academic Knowledge comprises 4,661 multiple-choice questions spanning 34 subjects such as finance and economics. Financial Industry Knowledge contains 1,434 questions covering practical scenarios like investment research. Financial Security Knowledge assesses models through 1,640 questions on topics like application security and cryptography. Financial Agent evaluates tool usage and complex reasoning with 616 questions. FinEval has multiple evaluation settings, including zero-shot, five-shot with chain-of-thought, and assesses model performance using objective and subjective criteria. Our results show that Claude 3.5-Sonnet achieves the highest weighted average score of 72.9 across all financial domain categories under zero-shot setting. Our work provides a comprehensive benchmark closely aligned with Chinese financial domain.