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.

The generalisation and robustness properties of policies learnt through Maximum-Entropy Reinforcement Learning are investigated on chaotic dynamical systems with Gaussian noise on the observable. First, the robustness under noise contamination of the agent's observation of entropy regularised policies is observed. Second, notions of statistical learning theory, such as complexity measures on the learnt model, are borrowed to explain and predict the phenomenon. Results show the existence of a relationship between entropy-regularised policy optimisation and robustness to noise, which can be described by the chosen complexity measures.

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.

Contemporary machine learning paradigm excels in statistical data analysis, solving problems that classical AI couldn't. However, it faces key limitations, such as a lack of integration with planning, incomprehensible internal structure, and inability to learn continually. We present the initial design for an AI system, Agential AI (AAI), in principle operating independently or on top of statistical methods, designed to overcome these issues. AAI's core is a learning method that models temporal dynamics with guarantees of completeness, minimality, and continual learning, using component-level variation and selection to learn the structure of the environment. It integrates this with a behavior algorithm that plans on a learned model and encapsulates high-level behavior patterns. Preliminary experiments on a simple environment show AAI's effectiveness and potential.

It is still a challenging topic to make reactive driving behaviors in complex urban environments as road users' intentions are unknown. Model-based reinforcement learning (MBRL) offers great potential to learn a reactive policy by constructing a world model that can provide informative states and imagination training. However, a critical limitation in relevant research lies in the scene-level reconstruction representation learning, which may overlook key interactive vehicles and hardly model the interactive features among vehicles and their long-term intentions. Therefore, this paper presents a novel MBRL method with a predictive individual world model (PIWM) for autonomous driving. PIWM describes the driving environment from an individual-level perspective and captures vehicles' interactive relations and their intentions via trajectory prediction task. Meanwhile, a behavior policy is learned jointly with PIWM. It is trained in PIWM's imagination and effectively navigates in the urban driving scenes leveraging intention-aware latent states. The proposed method is trained and evaluated on simulation environments built upon real-world challenging interactive scenarios. Compared with popular model-free and state-of-the-art model-based reinforcement learning methods, experimental results show that the proposed method achieves the best performance in terms of safety and efficiency.

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.

Rainfall prediction remains a persistent challenge due to the highly nonlinear and complex nature of meteorological data. Existing approaches lack systematic utilization of grid search for optimal hyperparameter tuning, relying instead on heuristic or manual selection, frequently resulting in sub-optimal results. Additionally, these methods rarely incorporate newly constructed meteorological features such as differences between temperature and humidity to capture critical weather dynamics. Furthermore, there is a lack of systematic evaluation of ensemble learning techniques and limited exploration of diverse advanced models introduced in the past one or two years. To address these limitations, we propose a robust ensemble learning grid search-tuned framework (RAINER) for rainfall prediction. RAINER incorporates a comprehensive feature engineering pipeline, including outlier removal, imputation of missing values, feature reconstruction, and dimensionality reduction via Principal Component Analysis (PCA). The framework integrates novel meteorological features to capture dynamic weather patterns and systematically evaluates non-learning mathematical-based methods and a variety of machine learning models, from weak classifiers to advanced neural networks such as Kolmogorov-Arnold Networks (KAN). By leveraging grid search for hyperparameter tuning and ensemble voting techniques, RAINER achieves promising results within real-world datasets.

Summary ------- The authors address a major drawback of constraint-based causal structure learning algorithms (PC algorithm and derivatives), namely, that for finite sample sizes the outputted graphs may be inconsistent regarding separating sets: The final graph may imply different separating sets than those identified in the algorithm. This implies in particular that outputted graphs are not guarenteed to belong to their presumed class of graphical models, for example CPDAGs or PAGs. The main reason is that PC-based methods remove too many true links in the skeleton phase. The authors' solution is based on an iterative application of a modified version of PC until the final graph is consistent with the separating sets. They prove that their solution fixes the problem and demonstrate these improvements with numerical experiments.

A clever extension to the PC algorithm for causal structure learning aimed to address inconsistency of results in terms of separating sets between the pruning step and the final graph. The new approach is somewhat incremental, but the authors provide some new formal guarantees. Experiments are reasonable, although they could be much better (please see reviews, this is also acknowledged by the authors, as currently one may wonder about the advantages wrt PC). I also suggest the authors to motivate the novelty and how it can improve/has improved results, in particular in view of a higher computational complexity.

Update: I have read the author response and am satisfied with the commitment to elaborate on \beta and \pi and to simplify the Stan PE code with a "pseudo-extended" function. This paper presents a new MCMC sampling method called pseudo-extended MCMC that uses an instrumental distribution to projects the data into a higher-dimensional space where the modes are connected, making it easier for the sampler to mix. A default instrumental distribution based on tempering is provided. The method is compared to existing baselines showing efficacy on three benchmark datasets. The paper is well-placed within the existing literature.