Summary and Contributions: This paper provides a mix between discussing high-level conceptual ideas and perspectives and presenting a variety of experimental results, all under the umbrella of generalization in (Bayesian) deep learning. More concretely, the central argument of the paper is that Bayesian learning should be primarily viewed as aiming to marginalize over different plausible hypotheses of the data, intead of relying on a single hypothesis (which is what ordinary deep learning is doing). The ultimate goal is thus to accurately estimate the posterior _predictive_ distribution (over outputs), rather than to accurately approximate the posterior distribution (over weights). They thus recommend that Bayesian methods should ideally focus their efforts on carefully representing the posterior distribution in regions that contribute most to the predictive distribution. In this line of thought, they further argue that deep ensembles, one of the state-of-the-art approaches for obtaining well-calibrated predictive distributions, do effectively approximate the Bayesian model average (even if the individual ensemble members are not actually samples from the posterior), and thus should not be considered in competition to Bayesian methods.

Summary of main contribution (in my view): It is easy to obtain a Monte Carlo estimate of the partition function - while such an estimate is unbiased, the log of the estimate is an underestimate of log-partition function. This means that an estimate for the log-likelihood constructed using this estimate *overestimates* the log-likelihood, which causes many issues in practice because it is not good to think the model is doing better than it actually is. Prior work (notably, RAISE [a]) has developed a way of overestimating the log-partition function and therefore underestimating the log-likelihood. But to my knowledge, there does not exist a way of estimating the log-partition function and the log-likelihood in an unbiased fashion. It works by applying a simple transformation, namely the Fenchel conjugate of -log(t).

Deploying complex machine learning models on resource-constrained devices is challenging due to limited computational power, memory, and model retrainability. To address these limitations, a hybrid system can be established by augmenting the local model with a server-side model, where samples are selectively deferred by a rejector and then sent to the server for processing. The hybrid system enables efficient use of computational resources while minimizing the overhead associated with server usage. The recently proposed Learning to Help (L2H) model trains a server model given a fixed local (client) model, differing from the Learning to Defer (L2D) framework, which trains the client for a fixed (expert) server. In both L2D and L2H, the training includes learning a rejector at the client to determine when to query the server. In this work, we extend the L2H model from binary to multi-class classification problems and demonstrate its applicability in a number of different scenarios of practical interest in which access to the server may be limited by cost, availability, or policy. We derive a stage-switching surrogate loss function that is differentiable, convex, and consistent with the Bayes rule corresponding to the 0-1 loss for the L2H model. Experiments show that our proposed methods offer an efficient and practical solution for multi-class classification in resource-constrained environments.

The wind farm control problem is challenging, since conventional model-based control strategies require tractable models of complex aerodynamical interactions between the turbines and suffer from the curse of dimension when the number of turbines increases. Recently, model-free and multi-agent reinforcement learning approaches have been used to address this challenge. In this article, we introduce WFCRL (Wind Farm Control with Reinforcement Learning), the first open suite of multi-agent reinforcement learning environments for the wind farm control problem. WFCRL frames a cooperative Multi-Agent Reinforcement Learning (MARL) problem: each turbine is an agent and can learn to adjust its yaw, pitch or torque to maximize the common objective (e.g. the total power production of the farm). WFCRL also offers turbine load observations that will allow to optimize the farm performance while limiting turbine structural damages. Interfaces with two state-of-the-art farm simulators are implemented in WFCRL: a static simulator (FLORIS) and a dynamic simulator (FAST.Farm). For each simulator, $10$ wind layouts are provided, including $5$ real wind farms. Two state-of-the-art online MARL algorithms are implemented to illustrate the scaling challenges. As learning online on FAST.Farm is highly time-consuming, WFCRL offers the possibility of designing transfer learning strategies from FLORIS to FAST.Farm.

Parameter estimation and trajectory reconstruction for data-driven dynamical systems governed by ordinary differential equations (ODEs) are essential tasks in fields such as biology, engineering, and physics. These inverse problems -- estimating ODE parameters from observational data -- are particularly challenging when the data are noisy, sparse, and the dynamics are nonlinear. We propose the Eigen-Fourier Physics-Informed Gaussian Process (EFiGP), an algorithm that integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework. This approach eliminates the need for numerical integration, significantly enhancing computational efficiency and accuracy. Built on a principled Bayesian framework, EFiGP incorporates the ODE system through probabilistic conditioning, enforcing governing equations in the Fourier domain while truncating high-frequency terms to achieve denoising and computational savings. The use of eigen-decomposition further simplifies Gaussian Process covariance operations, enabling efficient recovery of trajectories and parameters even in dense-grid settings. We validate the practical effectiveness of EFiGP on three benchmark examples, demonstrating its potential for reliable and interpretable modeling of complex dynamical systems while addressing key challenges in trajectory recovery and computational cost.

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can carry greater risks than others in real-world long-tailed problems. For example, misclassifying patients (a tail class) as healthy individuals (a head class) entails far more serious consequences than the reverse scenario. To address this critical issue, we introduce Making Reliable and Flexible Decisions in Long-tailed Classification (RF-DLC), a novel framework aimed at reliable predictions in long-tailed problems. Leveraging Bayesian Decision Theory, we introduce an integrated gain to seamlessly combine long-tailed data distributions and the decision-making procedure. We further propose an efficient variational optimization strategy for the decision risk objective. Our method adapts readily to diverse utility matrices, which can be designed for specific tasks, ensuring its flexibility for different problem settings. In empirical evaluation, we design a new metric, False Head Rate, to quantify tail-sensitivity risk, along with comprehensive experiments on multiple real-world tasks, including large-scale image classification and uncertainty quantification, to demonstrate the reliability and flexibility of our method.

Supply networks require collaboration in a competitive environment. To achieve this, nodes in the network often form symbiotic relationships as they can be adversely effected by the closure of companies in the network, especially where products are niche. However, balancing support for other nodes in the network against profit is challenging. Agents are increasingly being explored to define optimal strategies in these complex networks. However, to date much of the literature focuses on homogeneous agents where a single policy controls all of the nodes. This isn't realistic for many supply chains as this level of information sharing would require an exceptionally close relationship. This paper therefore compares the behaviour of this type of agent to a heterogeneous structure, where the agents each have separate polices, to solve the product ordering and pricing problem. An approach to reward sharing is developed that doesn't require sharing profit. The homogenous and heterogeneous agents exhibit different behaviours, with the homogenous retailer retaining high inventories and witnessing high levels of backlog while the heterogeneous agents show a typical order strategy. This leads to the heterogeneous agents mitigating the bullwhip effect whereas the homogenous agents do not. In the high demand environment, the agent architecture dominates performance with the Soft Actor-Critic (SAC) agents outperforming the Proximal Policy Optimisation (PPO) agents. Here, the factory controls the supply chain. In the low demand environment the homogenous agents outperform the heterogeneous agents. Control of the supply chain shifts significantly, with the retailer outperforming the factory by a significant margin.

Renewable energy power is influenced by the atmospheric system, which exhibits nonlinear and time-varying features. To address this, a dynamic temporal correlation modeling framework is proposed for renewable energy scenario generation. A novel decoupled mapping path is employed for joint probability distribution modeling, formulating regression tasks for both marginal distributions and the correlation structure using proper scoring rules to ensure the rationality of the modeling process. The scenario generation process is divided into two stages. Firstly, the dynamic correlation network models temporal correlations based on a dynamic covariance matrix, capturing the time-varying features of renewable energy while enhancing the interpretability of the black-box model. Secondly, the implicit quantile network models the marginal quantile function in a nonparametric, continuous manner, enabling scenario generation through marginal inverse sampling. Experimental results demonstrate that the proposed dynamic correlation quantile network outperforms state-of-the-art methods in quantifying uncertainty and capturing dynamic correlation for short-term renewable energy scenario generation.

This study uses the Palestinian Oral History Archive (POHA) to investigate how Palestinian refugee groups in Lebanon sustain a cohesive collective memory of the Nakba through shared narratives. Grounded in Halbwachs' theory of group memory, we employ statistical analysis of pairwise similarity of narratives, focusing on the influence of shared gender and location. We use textual representation and semantic embeddings of narratives to represent the interviews themselves. Our analysis demonstrates that shared origin is a powerful determinant of narrative similarity across thematic keywords, landmarks, and significant figures, as well as in semantic embeddings of the narratives. Meanwhile, shared residence fosters cohesion, with its impact significantly amplified when paired with shared origin. Additionally, women's narratives exhibit heightened thematic cohesion, particularly in recounting experiences of the British occupation, underscoring the gendered dimensions of memory formation. This research deepens the understanding of collective memory in diasporic settings, emphasizing the critical role of oral histories in safeguarding Palestinian identity and resisting erasure.

This paper develops a semiparametric Bayesian instrumental variable analysis method for estimating the causal effect of an endogenous variable when dealing with unobserved confounders and measurement errors with partly interval-censored time-to-event data, where event times are observed exactly for some subjects but left-censored, right-censored, or interval-censored for others. Our method is based on a two-stage Dirichlet process mixture instrumental variable (DPMIV) model which simultaneously models the first-stage random error term for the exposure variable and the second-stage random error term for the time-to-event outcome using a bivariate Gaussian mixture of the Dirichlet process (DPM) model. The DPM model can be broadly understood as a mixture model with an unspecified number of Gaussian components, which relaxes the normal error assumptions and allows the number of mixture components to be determined by the data. We develop an MCMC algorithm for the DPMIV model tailored for partly interval-censored data and conduct extensive simulations to assess the performance of our DPMIV method in comparison with some competing methods. Our simulations revealed that our proposed method is robust under different error distributions and can have superior performance over its parametric counterpart under various scenarios. We further demonstrate the effectiveness of our approach on an UK Biobank data to investigate the causal effect of systolic blood pressure on time-to-development of cardiovascular disease from the onset of diabetes mellitus.