Objective: This study investigates the potential of Large Language Models (LLMs) as an alternative to human expert elicitation for extracting structured causal knowledge and facilitating causal modeling in biometric and healthcare applications. Material and Methods: LLM-generated causal structures, specifically Bayesian networks (BNs), were benchmarked against traditional statistical methods (e.g., Bayesian Information Criterion) using healthcare datasets. Validation techniques included structural equation modeling (SEM) to verifying relationships, and measures such as entropy, predictive accuracy, and robustness to compare network structures. Results and Discussion: LLM-generated BNs demonstrated lower entropy than expert-elicited and statistically generated BNs, suggesting higher confidence and precision in predictions. However, limitations such as contextual constraints, hallucinated dependencies, and potential biases inherited from training data require further investigation. Conclusion: LLMs represent a novel frontier in expert elicitation for probabilistic causal modeling, promising to improve transparency and reduce uncertainty in the decision-making using such models.

Controllers trained with Reinforcement Learning tend to be very specialized and thus generalize poorly when their testing environment differs from their training one. We propose a Model-Based approach to increase generalization where both world model and policy are trained in a dimensionless state-action space. To do so, we introduce the Dimensionless Markov Decision Process ($Π$-MDP): an extension of Contextual-MDPs in which state and action spaces are non-dimensionalized with the Buckingham-$Π$ theorem. This procedure induces policies that are equivariant with respect to changes in the context of the underlying dynamics. We provide a generic framework for this approach and apply it to a model-based policy search algorithm using Gaussian Process models. We demonstrate the applicability of our method on simulated actuated pendulum and cartpole systems, where policies trained on a single environment are robust to shifts in the distribution of the context.

We propose the Metropolis-Hastings Captioning Game (MHCG), a method to fuse knowledge of multiple vision-language models (VLMs) by learning from each other. Although existing methods that combine multiple models suffer from inference costs and architectural constraints, MHCG avoids these problems by performing decentralized Bayesian inference through a process resembling a language game. The knowledge fusion process establishes communication between two VLM agents alternately captioning images and learning from each other. We conduct two image-captioning experiments with two VLMs, each pre-trained on a different dataset. The first experiment demonstrates that MHCG achieves consistent improvement in reference-free evaluation metrics. The second experiment investigates how MHCG contributes to sharing VLMs' category-level vocabulary by observing the occurrence of the vocabulary in the generated captions.

Hattrick is a free web-based probabilistic football manager game with over 200,000 users competing for titles at national and international levels. Launched in Sweden in 1997 as part of an MSc project, the game's slow-paced design has fostered a loyal community, with many users remaining active for decades. Hattrick's game-engine mechanics are partially hidden, and users have attempted to decode them with incremental success over the years. Rule-based, statistical and machine learning models have been developed to aid this effort and are widely used by the community. However, these models or tools have not been formally described or evaluated in the scientific literature. This study is the first to explore Hattrick using structure learning techniques and Bayesian networks, integrating both data and domain knowledge to develop models capable of explaining and simulating the game engine. We present a comprehensive analysis assessing the effectiveness of structure learning algorithms in relation to knowledge-based structures, and show that while structure learning may achieve a higher overall network fit, it does not result in more accurate predictions for selected variables of interest, when compared to knowledge-based networks that produce a lower overall network fit. Additionally, we introduce and publicly share a fully specified Bayesian network model that matches the performance of top models used by the Hattrick community. We further demonstrate how analysis extends beyond prediction by providing a visual representation of conditional dependencies, and using the best performing Bayesian network model for in-game decision-making. To support future research, we make all data, graphical structures, and models publicly available online.

Humans are sensitive to suspicious coincidences when generalizing inductively over data, as they make assumptions as to how the data was sampled. This results in smaller, more specific hypotheses being favored over more general ones. For instance, when provided the set {Austin, Dallas, Houston}, one is more likely to think that this is sampled from "Texas Cities" over "US Cities" even though both are compatible. Suspicious coincidence is strongly connected to pragmatic reasoning, and can serve as a testbed to analyze systems on their sensitivity towards the communicative goals of the task (i.e., figuring out the true category underlying the data). In this paper, we analyze whether suspicious coincidence effects are reflected in language models' (LMs) behavior. We do so in the context of two domains: 1) the number game, where humans made judgments of whether a number (e.g., 4) fits a list of given numbers (e.g., 16, 32, 2); and 2) by extending the number game setup to prominent cities. For both domains, the data is compatible with multiple hypotheses and we study which hypothesis is most consistent with the models' behavior. On analyzing five models, we do not find strong evidence for suspicious coincidences in LMs' zero-shot behavior. However, when provided access to the hypotheses space via chain-of-thought or explicit prompting, LMs start to show an effect resembling suspicious coincidences, sometimes even showing effects consistent with humans. Our study suggests that inductive reasoning behavior in LMs can be enhanced with explicit access to the hypothesis landscape.

DV ANCEMENTS in AI-driven technologies have significantly enhanced modern education through personalized tutoring and adaptive learning strategies on online platforms [1], [2]. Intelligent T utoring Systems (ITSs) exemplify this progress by leveraging advanced machine learning and natural language processing models to create interactive learning environments that improve outcomes across domains like literacy [3], mathematics [4], language learning [5], biology [6] and other STEM fields [7]. As human learners interact with ITSs, often through question-and-answer scenarios with immediate responses, their performance data becomes crucial for learner modeling, enabling systems to track progress, predict future performance, and adapt instruction accordingly [8]. Learner models like Bayesian Knowledge Tracing (BKT) and other knowledge tracing variants utilize the learner performance data to uncover learning characteristics, estimate knowledge states and acquisition [9]. However, in real-world scenarios, missing learner performance data is prevalent due to factors, such as learner dropout or disengagement [10], technical issues or incomplete data logging [11], biased sampling within experimental groups [12], and more. These challenges often lead to sparse data, where items (i.e., questions or problems) remain unattempted (e.g., learners may bypass the question, leave it unanswered due to a lack of response initiation, or make no attempt to engage with it), alongside limited learner interactions [13], [14]. As shown in Figure 1, missing performance records can occur along both the attempt and question dimensions during learner-ITS interactions. In the right portion of the figure's two matrices, entries marked with "?

Existing distribution compression methods, like Kernel Herding (KH), were originally developed for unlabelled data. However, no existing approach directly compresses the conditional distribution of labelled data. To address this gap, we first introduce the Average Maximum Conditional Mean Discrepancy (AMCMD), a natural metric for comparing conditional distributions. We then derive a consistent estimator for the AMCMD and establish its rate of convergence. Next, we make a key observation: in the context of distribution compression, the cost of constructing a compressed set targeting the AMCMD can be reduced from $\mathcal{O}(n^3)$ to $\mathcal{O}(n)$. Building on this, we extend the idea of KH to develop Average Conditional Kernel Herding (ACKH), a linear-time greedy algorithm that constructs a compressed set targeting the AMCMD. To better understand the advantages of directly compressing the conditional distribution rather than doing so via the joint distribution, we introduce Joint Kernel Herding (JKH), a straightforward adaptation of KH designed to compress the joint distribution of labelled data. While herding methods provide a simple and interpretable selection process, they rely on a greedy heuristic. To explore alternative optimisation strategies, we propose Joint Kernel Inducing Points (JKIP) and Average Conditional Kernel Inducing Points (ACKIP), which jointly optimise the compressed set while maintaining linear complexity. Experiments show that directly preserving conditional distributions with ACKIP outperforms both joint distribution compression (via JKH and JKIP) and the greedy selection used in ACKH. Moreover, we see that JKIP consistently outperforms JKH.

Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized linear models (GLMs), where responses follow exponential family distributions, aggregation offers an attractive alternative to classical parametric modeling. This paper investigates the problem of sparse aggregation in GLMs, aiming to approximate the true parameter vector by a sparse linear combination of predictors. We prove that an exponential weighted aggregation scheme yields a sharp oracle inequality for the Kullback-Leibler risk with leading constant equal to one, while also attaining the minimax-optimal rate of aggregation. These results are further enhanced by establishing high-probability bounds on the excess risk.

--Deep reinforcement learning can seamlessly transfer agile locomotion and navigation skills from the simulator to real world. However, bridging the sim-to-real gap with domain randomization or adversarial methods often demands expert physics knowledge to ensure policy robustness. Even so, cutting-edge simulators may fall short of capturing every real-world detail, and the reconstructed environment may introduce errors due to various perception uncertainties. T o address these challenges, we propose Neural Fidelity Calibration (NFC), a novel framework that employs conditional score-based diffusion models to calibrate simulator physical coefficients and residual fidelity domains online during robot execution. Specifically, the residual fidelity reflects the simulation model shift relative to the real-world dynamics and captures the uncertainty of the perceived environment, enabling us to sample realistic environments under the inferred distribution for policy fine-tuning. Our framework is informative and adaptive in three key ways: (a) we fine-tune the pretrained policy only under anomalous scenarios, (b) we build sequential NFC online with the pretrained NFC's proposal prior, reducing the diffusion model's training burden, and (c) when NFC uncertainty is high and may degrade policy improvement, we leverage optimistic exploration to enable "hallucinated" policy optimization. Our framework achieves superior simulator calibration precision compared to state-of-the-art methods across diverse robots with high-dimensional parametric spaces. We study the critical contribution of residual fidelity to policy improvement in simulation and real-world experiments. Notably, our approach demonstrates robust robot navigation under challenging real-world conditions, such as a broken wheel axle on snowy surfaces. Zero-shot sim-to-real reinforcement learning (RL) has empowered agile policy to various robots across soft [74], wheeled [83], aerial [18], and quadruped [45] embodiments. In the context of policy resilience against the real-world diversities, the proximal works in domain randomization (DR) [75] and adversarial training [19] emerge as powerful strategies by artificially introducing noise or attacks into the agent's states. Safety RL, which incorporates safety constraints into the optimization [10], remains tied to DR via exploration of diverse unsafe scenarios. Despite these advancements, expert real-world knowledge is often required to determine domain ranges [48], reconstruct environments [15], or design adversarial scenarios [66]. In theory, one could uniformly sample every domain parameter and environment variation, but this is usually impractical. Y u and L. Liu are with the Luddy School of Informatics, Computing, and Engineering at Indiana University, Bloomington, IN 47408, USA.

We develop a correspondence between the structure of Turing machines and the structure of singularities of real analytic functions, based on connecting the Ehrhard-Regnier derivative from linear logic with the role of geometry in Watanabe's singular learning theory. The correspondence works by embedding ordinary (discrete) Turing machine codes into a family of noisy codes which form a smooth parameter space. On this parameter space we consider a potential function which has Turing machines as critical points. By relating the Taylor series expansion of this potential at such a critical point to combinatorics of error syndromes, we relate the local geometry to internal structure of the Turing machine. The potential in question is the negative log-likelihood for a statistical model, so that the structure of the Turing machine and its associated singularity is further related to Bayesian inference. Two algorithms that produce the same predictive function can nonetheless correspond to singularities with different geometries, which implies that the Bayesian posterior can discriminate between distinct algorithmic implementations, contrary to a purely functional view of inference. In the context of singular learning theory our results point to a more nuanced understanding of Occam's razor and the meaning of simplicity in inductive inference.