Understanding how individual agents make strategic decisions within collectives is important for advancing fields as diverse as economics, neuroscience, and multi-agent systems. Two complementary approaches can be integrated to this end. The Active Inference framework (AIF) describes how agents employ a generative model to adapt their beliefs about and behaviour within their environment. Game theory formalises strategic interactions between agents with potentially competing objectives. To bridge the gap between the two, we propose a factorisation of the generative model whereby each agent maintains explicit, individual-level beliefs about the internal states of other agents, and uses them for strategic planning in a joint context. We apply our model to iterated general-sum games with 2 and 3 players, and study the ensemble effects of game transitions, where the agents' preferences (game payoffs) change over time. This non-stationarity, beyond that caused by reciprocal adaptation, reflects a more naturalistic environment in which agents need to adapt to changing social contexts. Finally, we present a dynamical analysis of key AIF quantities: the variational free energy (VFE) and the expected free energy (EFE) from numerical simulation data. The ensemble-level EFE allows us to characterise the basins of attraction of games with multiple Nash Equilibria under different conditions, and we find that it is not necessarily minimised at the aggregate level. By integrating AIF and game theory, we can gain deeper insights into how intelligent collectives emerge, learn, and optimise their actions in dynamic environments, both cooperative and non-cooperative.

Conditional simulation is a fundamental task in statistical modeling: Generate samples from the conditionals given finitely many data points from a joint distribution. One promising approach is to construct conditional Brenier maps, where the components of the map pushforward a reference distribution to conditionals of the target. While many estimators exist, few, if any, come with statistical or algorithmic guarantees. To this end, we propose a non-parametric estimator for conditional Brenier maps based on the computational scalability of \emph{entropic} optimal transport. Our estimator leverages a result of Carlier et al. (2010), which shows that optimal transport maps under a rescaled quadratic cost asymptotically converge to conditional Brenier maps; our estimator is precisely the entropic analogues of these converging maps. We provide heuristic justifications for choosing the scaling parameter in the cost as a function of the number of samples by fully characterizing the Gaussian setting. We conclude by comparing the performance of the estimator to other machine learning and non-parametric approaches on benchmark datasets and Bayesian inference problems.

Humans excel at adapting perceptions and actions to diverse environments, enabling efficient interaction with the external world. This adaptive capability relies on the biological nervous system (BNS), which activates different brain regions for distinct tasks. Meta-learning similarly trains machines to handle multiple tasks but relies on a fixed network structure, not as flexible as BNS. To investigate the role of flexible network structure (FNS) in meta-learning, we conduct extensive empirical and theoretical analyses, finding that model performance is tied to structure, with no universally optimal pattern across tasks. This reveals the crucial role of FNS in meta-learning, ensuring meta-learning to generate the optimal structure for each task, thereby maximizing the performance and learning efficiency of meta-learning. Motivated by this insight, we propose to define, measure, and model FNS in meta-learning. First, we define that an effective FNS should possess frugality, plasticity, and sensitivity. Then, to quantify FNS in practice, we present three measurements for these properties, collectively forming the \emph{structure constraint} with theoretical supports. Building on this, we finally propose Neuromodulated Meta-Learning (NeuronML) to model FNS in meta-learning. It utilizes bi-level optimization to update both weights and structure with the structure constraint. Extensive theoretical and empirical evaluations demonstrate the effectiveness of NeuronML on various tasks. Code is publicly available at \href{https://github.com/WangJingyao07/NeuronML}{https://github.com/WangJingyao07/NeuronML}.

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.

Country instability is a global issue, with unpredictably high levels of instability thwarting socio-economic growth and possibly causing a slew of negative consequences. As a result, uncertainty prediction models for a country are becoming increasingly important in the real world, and they are expanding to provide more input from 'big data' collections, as well as the interconnectedness of global economies and social networks. This has culminated in massive volumes of qualitative data from outlets like television, print, digital, and social media, necessitating the use of artificial intelligence (AI) tools like machine learning to make sense of it all and promote predictive precision [1]. The Global Database of Activities, Voice, and Tone (GDELT Project) records broadcast, print, and web news in over 100 languages every second of every day, identifying the people, locations, organisations, counts, themes, outlets, and events that propel our global community and offering a free open platform for computation on the entire world. The main goal of our research is to investigate how, when our data grows more voluminous and fine-grained, we can conduct a more complex methodological analysis of political conflict. The GDELT dataset, which was released in 2012, is the first and potentially the most technologically sophisticated publicly accessible dataset on political conflict.

We address the challenge of causal discovery in structural equation models with additive noise without imposing additional assumptions on the underlying data-generating process. We introduce local search in additive noise model (LoSAM), which generalizes an existing nonlinear method that leverages local causal substructures to the general additive noise setting, allowing for both linear and nonlinear causal mechanisms. We show that LoSAM achieves polynomial runtime, and improves runtime and efficiency by exploiting new substructures to minimize the conditioning set at each step. Further, we introduce a variant of LoSAM, LoSAM-UC, that is robust to unmeasured confounding among roots, a property that is often not satisfied by functional-causal-model-based methods. We numerically demonstrate the utility of LoSAM, showing that it outperforms existing benchmarks.

The goal of this paper is to demonstrate and address challenges related to all aspects of performing a complete uncertainty quantification (UQ) analysis of a complicated physics-based simulation like a 2D slab burner direct numerical simulation (DNS). The UQ framework includes the development of data-driven surrogate models, propagation of parametric uncertainties to the fuel regression rate--the primary quantity of interest--and Bayesian calibration of critical parameters influencing the regression rate using experimental data. Specifically, the parameters calibrated include the latent heat of sublimation and a chemical reaction temperature exponent. Two surrogate models, a Gaussian Process (GP) and a Hierarchical Multiscale Surrogate (HMS) were constructed using an ensemble of 64 simulations generated via Latin Hypercube sampling. Both models exhibited comparable performance during cross-validation. However, the HMS was more stable due to its ability to handle multiscale effects, in contrast with the GP which was very sensitive to kernel choice. Analysis revealed that the surrogates do not accurately predict all spatial locations of the slab burner as-is. Subsequent Bayesian calibration of the physical parameters against experimental observations resulted in regression rate predictions that closer align with experimental observation in specific regions. This study highlights the importance of surrogate model selection and parameter calibration in quantifying uncertainty in predictions of fuel regression rates in complex combustion systems.

Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kriging. Estimation of Kriging weights relies on the inversion of the process' covariance matrix, creating a computational bottleneck for large spatial datasets. In this paper, we propose an Amortized Bayesian Local Interpolation NetworK (A-BLINK) for fast covariance parameter estimation, which uses two pre-trained deep neural networks to learn a mapping from spatial location coordinates and covariance function parameters to Kriging weights and the spatial variance, respectively. The fast prediction time of these networks allows us to bypass the matrix inversion step, creating large computational speedups over competing methods in both frequentist and Bayesian settings, and also provides full posterior inference and predictions using Markov chain Monte Carlo sampling methods. We show significant increases in computational efficiency over comparable scalable GP methodology in an extensive simulation study with lower parameter estimation error. The efficacy of our approach is also demonstrated using a temperature dataset of US climate normals for 1991--2020 based on over 7,000 weather stations.

Portfolio construction is the science of balancing reward and risk; it is at the core of modern finance. In this paper, we tackle the question of optimal decision-making within a Bayesian paradigm, starting from a decision-theoretic formulation. Despite the inherent intractability of the optimal decision in any interesting scenarios, we manage to rewrite it as a saddle-point problem. Leveraging the literature on variational Bayes (VB), we propose a relaxation of the original problem. This novel methodology results in an efficient algorithm that not only performs well but is also provably convergent. Furthermore, we provide theoretical results on the statistical consistency of the resulting decision with the optimal Bayesian decision. Using real data, our proposal significantly enhances the speed and scalability of portfolio selection problems. We benchmark our results against state-of-the-art algorithms, as well as a Monte Carlo algorithm targeting the optimal decision.

This paper presents a monitoring framework that infers the level of autonomous vehicle (AV) collision risk based on its object detector's performance using only monocular camera images. Essentially, the framework takes two sets of predictions produced by different algorithms and associates their inconsistencies with the collision risk via fuzzy inference. The first set of predictions is obtained through retrieving safety-critical 2.5D objects from a depth map, and the second set comes from the AV's 3D object detector. We experimentally validate that, based on Intersection-over-Union (IoU) and a depth discrepancy measure, the inconsistencies between the two sets of predictions strongly correlate to the safety-related error of the 3D object detector against ground truths. This correlation allows us to construct a fuzzy inference system and map the inconsistency measures to an existing collision risk indicator. In particular, we apply various knowledge- and data-driven techniques and find using particle swarm optimization that learns general fuzzy rules gives the best mapping result. Lastly, we validate our monitor's capability to produce relevant risk estimates with the large-scale nuScenes dataset and show it can safeguard an AV in closed-loop simulations.