Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the super-exponential scaling of topologies. This scaling challenge limits the efficiency of Euclidean-based approximate inference methods. Motivated by the geometric connections between trees and hyperbolic space, we develop novel hyperbolic extensions of two sequential search algorithms: Combinatorial and Nested Combinatorial Sequential Monte Carlo (\textsc{Csmc} and \textsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods (\textsc{H-Vcsmc} and \textsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.

Safe reinforcement learning has traditionally relied on predefined constraint functions to ensure safety in complex real-world tasks, such as autonomous driving. However, defining these functions accurately for varied tasks is a persistent challenge. Recent research highlights the potential of leveraging pre-acquired task-agnostic knowledge to enhance both safety and sample efficiency in related tasks. Building on this insight, we propose a novel method to learn shared constraint distributions across multiple tasks. Our approach identifies the shared constraints through imitation learning and then adapts to new tasks by adjusting risk levels within these learned distributions. This adaptability addresses variations in risk sensitivity stemming from expert-specific biases, ensuring consistent adherence to general safety principles even with imperfect demonstrations. Our method can be applied to control and navigation domains, including multi-task and meta-task scenarios, accommodating constraints such as maintaining safe distances or adhering to speed limits. Experimental results validate the efficacy of our approach, demonstrating superior safety performance and success rates compared to baselines, all without requiring task-specific constraint definitions. These findings underscore the versatility and practicality of our method across a wide range of real-world tasks.

We provide new connections between two distinct federated learning approaches based on (i) ADMM and (ii) Variational Bayes (VB), and propose new variants by combining their complementary strengths. Specifically, we show that the dual variables in ADMM naturally emerge through the "site" parameters used in VB with isotropic Gaussian covariances. Using this, we derive two versions of ADMM from VB that use flexible covariances and functional regularisation, respectively. Through numerical experiments, we validate the improvements obtained in performance. The work shows connection between two fields that are believed to be fundamentally different and combines them to improve federated learning. The goal of federated learning is to train a global model in the central server by using the data distributed over many local clients (McMahan et al., 2016). Such distributed learning improves privacy, security, and robustness, but is challenging due to frequent communication needed to synchronise training among nodes. This is especially true when the data quality differs drastically from client to client and needs to be appropriately weighted. Designing new methods to deal with such challenges is an active area of research in federated learning. We focus on two distinct federated-learning approaches based on the Alternating Direction Method of Multipliers (ADMM) and Variational Bayes (VB), respectively. The ADMM approach synchronises the global and local models by using constrained optimisation and updates both primal and dual variables simultaneously.

Transformers have emerged as the dominant architecture in the field of deep learning, with a broad range of applications and remarkable in-context learning (ICL) capabilities. While not yet fully understood, ICL has already proved to be an intriguing phenomenon, allowing transformers to learn in context -- without requiring further training. In this paper, we further advance the understanding of ICL by demonstrating that transformers can perform full Bayesian inference for commonly used statistical models in context. More specifically, we introduce a general framework that builds on ideas from prior fitted networks and continuous normalizing flows which enables us to infer complex posterior distributions for methods such as generalized linear models and latent factor models. Extensive experiments on real-world datasets demonstrate that our ICL approach yields posterior samples that are similar in quality to state-of-the-art MCMC or variational inference methods not operating in context.

Learning curves are a concept from social sciences that has been adopted in the context of machine learning to assess the performance of a learning algorithm with respect to a certain resource, e.g., the number of training examples or the number of training iterations. Learning curves have important applications in several machine learning contexts, most notably in data acquisition, early stopping of model training, and model selection. For instance, learning curves can be used to model the performance of the combination of an algorithm and its hyperparameter configuration, providing insights into their potential suitability at an early stage and often expediting the algorithm selection process. Various learning curve models have been proposed to use learning curves for decision making. Some of these models answer the binary decision question of whether a given algorithm at a certain budget will outperform a certain reference performance, whereas more complex models predict the entire learning curve of an algorithm. We contribute a framework that categorises learning curve approaches using three criteria: the decision-making situation they address, the intrinsic learning curve question they answer and the type of resources they use. We survey papers from the literature and classify them into this framework.

Weaknesses: - Can we interpret the results as follows: If the TAR assumption is satisfied with positive limits, and we use MLE, then temporal interference does not cause bias. If this interpretation is correct, then it would be illuminating if the authors provide the intuitive connection between the TAR assumption and temporal interference. It is not clear if the estimations that the authors have required are feasible if the state space is large. The next natural question is how robust the results are if we use other methods for estimation. This could have been shown by providing some simulations, which is a part missing from the manuscript.

The paper studied the online experimental design problem where there are temporal dependencies between the two control policies/treatments. The novelty of the problem setup and the theoretical analysis in the paper are appreciated by all the reviewers. Although the analysis is the main contribution, the paper would be much stronger if there are meaningful experiments on toy problems to showcase the performance the online MLE-based approach vs the standard experimental design approaches.

This paper contributes a new technique for the estimation of structure in continuous time Bayesian networks, and completes the picture with an accompanying inference method and an illustration on a real-world problem. There is agreement among reviewers that this is a high quality contribution, if one takes the confidence-weighted scores from reviewers into account. As a point for improvement for the paper, we could reiterate a comment that was raised in the reviewer discussion: "[the paper] is missing reasonable and helpful experimental comparisons that are not hard to do, given that the code exists already in CTBN-RLE" and the authors are encouraged to consider broadening their experimental comparisons for a final published version.

Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder---a commonly used but unproven conjecture---which we refer to as self-consistency.

Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional Machine Learning (ML) models excel at predicting outcomes, such as identifying high risk patients, they are limited in addressing what-if questions about interventions. This study introduces the Probabilistic Causal Fusion (PCF) framework, which integrates Causal Bayesian Networks (CBNs) and Probability Trees (PTrees) to extend beyond predictions. PCF leverages causal relationships from CBNs to structure PTrees, enabling both the quantification of factor impacts and simulation of hypothetical interventions. PCF was validated on three real-world healthcare datasets i.e. MIMIC-IV, Framingham Heart Study, and Diabetes, chosen for their clinically diverse variables. It demonstrated predictive performance comparable to traditional ML models while providing additional causal reasoning capabilities. To enhance interpretability, PCF incorporates sensitivity analysis and SHapley Additive exPlanations (SHAP). Sensitivity analysis quantifies the influence of causal parameters on outcomes such as Length of Stay (LOS), Coronary Heart Disease (CHD), and Diabetes, while SHAP highlights the importance of individual features in predictive modeling. By combining causal reasoning with predictive modeling, PCF bridges the gap between clinical intuition and data-driven insights. Its ability to uncover relationships between modifiable factors and simulate hypothetical scenarios provides clinicians with a clearer understanding of causal pathways. This approach supports more informed, evidence-based decision-making, offering a robust framework for addressing complex questions in diverse healthcare settings.