The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes mixed-effects models widely applied in fields such as biology, pharmacokinetics, and sociology. In this work, we propose a novel methodology for scalable Bayesian inference in hierarchical mixed-effects models. Our framework first constructs amortized approximations of the likelihood and the posterior distribution, which are then rapidly refined for each individual dataset, to ultimately approximate the parameters posterior across many individuals. The framework is easily trainable, as it uses mixtures of experts but without neural networks, leading to parsimonious yet expressive surrogate models of the likelihood and the posterior. We demonstrate the effectiveness of our methodology using challenging stochastic models, such as mixed-effects stochastic differential equations emerging in systems biology-driven problems. However, the approach is broadly applicable and can accommodate both stochastic and deterministic models. We show that our approach can seamlessly handle inference for many parameters. Additionally, we applied our method to a real-data case study of mRNA transfection. When compared to exact pseudomarginal Bayesian inference, our approach proved to be both fast and competitive in terms of statistical accuracy.

Bayesian inference provides a principled framework for quantifying uncertainty in both parameters and models by computing full posterior distributions and model evidence (Gelman et al., 2013). However, Bayesian inference is often analytically intractable, requiring the use of approximate methods like Markov chain Monte Carlo (MCMC; Brooks, 2011) or variational inference (VI; Blei et al., 2017). These methods typically necessitate repeated evaluations of the target density, and many require differentiability of the model (Neal, 2011; Kucukelbir et al., 2017). When model evaluations are computationally expensive - for instance, involving extensive numerical methods - these requirements make standard Bayesian approaches impractical. Due to these computational demands, practitioners often resort to simpler alternatives such as maximum a posteriori (MAP) estimation or maximum likelihood estimation (MLE); 1 see for example Wilson and Collins (2019); Ma et al. (2023). While these point estimates can provide useful insights, they fail to capture parameter uncertainty, potentially leading to overconfident or biased conclusions (Gelman et al., 2013). This limitation highlights the need for efficient posterior approximation methods that avoid the computational costs of standard inference techniques.1.

Inference and estimation are fundamental aspects of statistics, system identification and machine learning. For most inference problems, prior knowledge is available on the system to be modeled, and Bayesian analysis is a natural framework to impose such prior information in the form of a prior distribution. However, in many situations, coming out with a fully specified prior distribution is not easy, as prior knowledge might be too vague, so practitioners prefer to use a prior distribution that is as `ignorant' or `uninformative' as possible, in the sense of not imposing subjective beliefs, while still supporting reliable statistical analysis. Jeffreys prior is an appealing uninformative prior because it offers two important benefits: (i) it is invariant under any re-parameterization of the model, (ii) it encodes the intrinsic geometric structure of the parameter space through the Fisher information matrix, which in turn enhances the diversity of parameter samples. Despite these benefits, drawing samples from Jeffreys prior is a challenging task. In this paper, we propose a general sampling scheme using the Metropolis-Adjusted Langevin Algorithm that enables sampling of parameter values from Jeffreys prior, and provide numerical illustrations of our approach through several examples.

Bayesian optimization (BO) is a widely used algorithm for solving expensive black-box optimization problems. However, its performance decreases significantly on high-dimensional problems due to the inherent high-dimensionality of the acquisition function. In the proposed algorithm, we adaptively dropout the variables of the acquisition function along the iterations. By gradually reducing the dimension of the acquisition function, the proposed approach has less and less difficulty to optimize the acquisition function. Numerical experiments demonstrate that AdaDropout effectively tackle high-dimensional challenges and improve solution quality where standard Bayesian optimization methods often struggle. Moreover, it achieves superior results when compared with state-of-the-art high-dimensional Bayesian optimization approaches. This work provides a simple yet efficient solution for high-dimensional expensive optimization.

This study addresses the challenge of ambiguity in knowledge graph question answering (KGQA). While recent KGQA systems have made significant progress, particularly with the integration of large language models (LLMs), they typically assume user queries are unambiguous, which is an assumption that rarely holds in real-world applications. To address these limitations, we propose a novel framework that dynamically handles both entity ambiguity (e.g., distinguishing between entities with similar names) and intent ambiguity (e.g., clarifying different interpretations of user queries) through interactive clarification. Our approach employs a Bayesian inference mechanism to quantify query ambiguity and guide LLMs in determining when and how to request clarification from users within a multi-turn dialogue framework. We further develop a two-agent interaction framework where an LLM-based user simulator enables iterative refinement of logical forms through simulated user feedback. Experimental results on the WebQSP and CWQ dataset demonstrate that our method significantly improves performance by effectively resolving semantic ambiguities. Additionally, we contribute a refined dataset of disambiguated queries, derived from interaction histories, to facilitate future research in this direction.

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.

Understanding the sequence of cognitive operations that underlie decision-making is a fundamental challenge in cognitive neuroscience. Traditional approaches often rely on group-level statistics, which obscure trial-by-trial variations in cognitive strategies. In this study, we introduce a novel machine learning method that combines Hidden Multivariate Pattern analysis with a Structured State Space Sequence model to decode cognitive strategies from electroencephalography data at the trial level. We apply this method to a decision-making task, where participants were instructed to prioritize either speed or accuracy in their responses. Our results reveal an additional cognitive operation, labeled Confirmation, which seems to occur predominantly in the accuracy condition but also frequently in the speed condition. The modeled probability that this operation occurs is associated with higher probability of responding correctly as well as changes of mind, as indexed by electromyography data. By successfully modeling cognitive operations at the trial level, we provide empirical evidence for dynamic variability in decision strategies, challenging the assumption of homogeneous cognitive processes within experimental conditions. Our approach shows the potential of sequence modeling in cognitive neuroscience to capture trial-level variability that is obscured by aggregate analyses. The introduced method offers a new way to detect and understand cognitive strategies in a data-driven manner, with implications for both theoretical research and practical applications in many fields.

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.

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.

In electronic consumer Internet of Things (IoT), consumer electronic devices as edge devices require less computational overhead and the remote state estimation (RSE) of consumer electronic devices is always at risk of denial-of-service (DoS) attacks. Therefore, the adversarial strategy between consumer electronic devices and DoS attackers is critical. This paper focuses on the adversarial strategy between consumer electronic devices and DoS attackers in IoT-enabled RSE Systems. We first propose a remote joint estimation model for distributed measurements to effectively reduce consumer electronic device workload and minimize data leakage risks. The Kalman filter is deployed on the remote estimator, and the DoS attacks with open-loop as well as closed-loop are considered. We further introduce advanced reinforcement learning techniques, including centralized and distributed Minimax-DQN, to address high-dimensional decision-making challenges in both open-loop and closed-loop scenarios. Especially, the Q-network instead of the Q-table is used in the proposed approaches, which effectively solves the challenge of Q-learning. Moreover, the proposed distributed Minimax-DQN reduces the action space to expedite the search for Nash Equilibrium (NE). The experimental results validate that the proposed model can expeditiously restore the RSE error covariance to a stable state in the presence of DoS attacks, exhibiting notable attack robustness. The proposed centralized and distributed Minimax-DQN effectively resolves the NE in both open and closed-loop case, showcasing remarkable performance in terms of convergence. It reveals that substantial advantages in both efficiency and stability are achieved compared with the state-of-the-art methods.