Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are optimised via gradient descent on variational free energy. However, implementations of PC rely on maximum \textit{a posteriori} (MAP) estimates of hidden states and maximum likelihood (ML) estimates of parameters, limiting their ability to quantify epistemic uncertainty. In this work, we investigate a Bayesian extension to PC that estimates a posterior distribution over network parameters. This approach, termed Bayesian Predictive coding (BPC), preserves the locality of PC and results in closed-form Hebbian weight updates. Compared to PC, our BPC algorithm converges in fewer epochs in the full-batch setting and remains competitive in the mini-batch setting. Additionally, we demonstrate that BPC offers uncertainty quantification comparable to existing methods in Bayesian deep learning, while also improving convergence properties. Together, these results suggest that BPC provides a biologically plausible method for Bayesian learning in the brain, as well as an attractive approach to uncertainty quantification in deep learning.

Traffic congestion in modern cities is exacerbated by the limitations of traditional fixed-time traffic signal systems, which fail to adapt to dynamic traffic patterns. Adaptive Traffic Signal Control (ATSC) algorithms have emerged as a solution by dynamically adjusting signal timing based on real-time traffic conditions. However, the main limitation of such methods is that they are not transferable to environments under real-world constraints, such as balancing efficiency, minimizing collisions, and ensuring fairness across intersections. In this paper, we view the ATSC problem as a constrained multi-agent reinforcement learning (MARL) problem and propose a novel algorithm named Multi-Agent Proximal Policy Optimization with Lagrange Cost Estimator (MAPPO-LCE) to produce effective traffic signal control policies. Our approach integrates the Lagrange multipliers method to balance rewards and constraints, with a cost estimator for stable adjustment. We also introduce three constraints on the traffic network: GreenTime, GreenSkip, and PhaseSkip, which penalize traffic policies that do not conform to real-world scenarios. Our experimental results on three real-world datasets demonstrate that MAPPO-LCE outperforms three baseline MARL algorithms by across all environments and traffic constraints (improving on MAPPO by 12.60%, IPPO by 10.29%, and QTRAN by 13.10%). Our results show that constrained MARL is a valuable tool for traffic planners to deploy scalable and efficient ATSC methods in real-world traffic networks. We provide code at https://github.com/Asatheesh6561/MAPPO-LCE.

Real-world event sequences are often generated by different temporal point processes (TPPs) and thus have clustering structures. Nonetheless, in the modeling and prediction of event sequences, most existing TPPs ignore the inherent clustering structures of the event sequences, leading to the models with unsatisfactory interpretability. In this study, we learn structure-enhanced TPPs with the help of Gromov-Wasserstein (GW) regularization, which imposes clustering structures on the sequence-level embeddings of the TPPs in the maximum likelihood estimation framework.In the training phase, the proposed method leverages a nonparametric TPP kernel to regularize the similarity matrix derived based on the sequence embeddings. In large-scale applications, we sample the kernel matrix and implement the regularization as a Gromov-Wasserstein (GW) discrepancy term, which achieves a trade-off between regularity and computational efficiency.The TPPs learned through this method result in clustered sequence embeddings and demonstrate competitive predictive and clustering performance, significantly improving the model interpretability without compromising prediction accuracy.

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of `asymptotic dependence' and `asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.

In this work, we propose a factor graph optimization (FGO) framework to simultaneously solve the calibration problem for Ultra-WideBand (UWB) anchors and the robot localization problem. Calibrating UWB anchors manually can be time-consuming and even impossible in emergencies or those situations without special calibration tools. Therefore, automatic estimation of the anchor positions becomes a necessity. The proposed method enables the creation of a soft sensor providing the position information of the anchors in a UWB network. This soft sensor requires only UWB and LiDAR measurements measured from a moving robot. The proposed FGO framework is suitable for the calibration of an extendable large UWB network. Moreover, the anchor calibration problem and robot localization problem can be solved simultaneously, which saves time for UWB network deployment. The proposed framework also helps to avoid artificial errors in the UWB-anchor position estimation and improves the accuracy and robustness of the robot-pose. The experimental results of the robot localization using LiDAR and a UWB network in a 3D environment are discussed, demonstrating the performance of the proposed method. More specifically, the anchor calibration problem with four anchors and the robot localization problem can be solved simultaneously and automatically within 30 seconds by the proposed framework. The supplementary video and codes can be accessed via https://github.com/LiuxhRobotAI/Simultaneous_calibration_localization.

In this work, we present a novel cooperative multi-agent reinforcement learning method called \textbf{Loc}ality based \textbf{Fac}torized \textbf{M}ulti-Agent \textbf{A}ctor-\textbf{C}ritic (Loc-FACMAC). Existing state-of-the-art algorithms, such as FACMAC, rely on global reward information, which may not accurately reflect the quality of individual robots' actions in decentralized systems. We integrate the concept of locality into critic learning, where strongly related robots form partitions during training. Robots within the same partition have a greater impact on each other, leading to more precise policy evaluation. Additionally, we construct a dependency graph to capture the relationships between robots, facilitating the partitioning process. This approach mitigates the curse of dimensionality and prevents robots from using irrelevant information. Our method improves existing algorithms by focusing on local rewards and leveraging partition-based learning to enhance training efficiency and performance. We evaluate the performance of Loc-FACMAC in three environments: Hallway, Multi-cartpole, and Bounded-Cooperative-Navigation. We explore the impact of partition sizes on the performance and compare the result with baseline MARL algorithms such as LOMAQ, FACMAC, and QMIX. The experiments reveal that, if the locality structure is defined properly, Loc-FACMAC outperforms these baseline algorithms up to 108\%, indicating that exploiting the locality structure in the actor-critic framework improves the MARL performance.

In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. Here, we investigate quantum Doeblin coefficients as a generalization of the classical concept. In particular, we define various new quantum Doeblin coefficients, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. We also develop various interpretations of two of the quantum Doeblin coefficients, including representations as minimal singlet fractions, exclusion values, reverse max-mutual and oveloH informations, reverse robustnesses, and hypothesis testing reverse mutual and oveloH informations. Our interpretations of quantum Doeblin coefficients as either entanglement-assisted or unassisted exclusion values are particularly appealing, indicating that they are proportional to the best possible error probabilities one could achieve in state-exclusion tasks by making use of the channel. We also outline various applications of quantum Doeblin coefficients, ranging from limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus), on error mitigation protocols, on the sample complexity of noisy quantum hypothesis testing, on the fairness of noisy quantum models, and on mixing times of time-varying channels. All of these applications make use of the fact that quantum Doeblin coefficients appear in upper bounds on various trace-distance contraction coefficients of a channel. Furthermore, in all of these applications, our analysis using Doeblin coefficients provides improvements of various kinds over contributions from prior literature, both in terms of generality and being efficiently computable.

We study a long-run mean-variance team stochastic game (MV-TSG), where each agent shares a common mean-variance objective for the system and takes actions independently to maximize it. MV-TSG has two main challenges. First, the variance metric is neither additive nor Markovian in a dynamic setting. Second, simultaneous policy updates of all agents lead to a non-stationary environment for each individual agent. Both challenges make dynamic programming inapplicable. In this paper, we study MV-TSGs from the perspective of sensitivity-based optimization. The performance difference and performance derivative formulas for joint policies are derived, which provide optimization information for MV-TSGs. We prove the existence of a deterministic Nash policy for this problem. Subsequently, we propose a Mean-Variance Multi-Agent Policy Iteration (MV-MAPI) algorithm with a sequential update scheme, where individual agent policies are updated one by one in a given order. We prove that the MV-MAPI algorithm converges to a first-order stationary point of the objective function. By analyzing the local geometry of stationary points, we derive specific conditions for stationary points to be (local) Nash equilibria, and further, strict local optima. To solve large-scale MV-TSGs in scenarios with unknown environmental parameters, we extend the idea of trust region methods to MV-MAPI and develop a multi-agent reinforcement learning algorithm named Mean-Variance Multi-Agent Trust Region Policy Optimization (MV-MATRPO). We derive a performance lower bound for each update of joint policies. Finally, numerical experiments on energy management in multiple microgrid systems are conducted.

Land cover classification involves the production of land cover maps, which determine the type of land through remote sensing imagery. Over recent years, such classification is being performed by machine learning classification models, which can give highly accurate predictions on land cover per pixel using large quantities of input training data. However, such models do not currently take account of input measurement uncertainty, which is vital for traceability in metrology. In this work we propose a Bayesian classification framework using generative modelling to take account of input measurement uncertainty. We take the specific case of Bayesian quadratic discriminant analysis, and apply it to land cover datasets from Copernicus Sentinel-2 in 2020 and 2021. We benchmark the performance of the model against more popular classification models used in land cover maps such as random forests and neural networks. We find that such Bayesian models are more trustworthy, in the sense that they are more interpretable, explicitly model the input measurement uncertainty, and maintain predictive performance of class probability outputs across datasets of different years and sizes, whilst also being computationally efficient.

Context: Astronomy and astrophysics demand rigorous handling of uncertainties to ensure the credibility of outcomes. The growing integration of artificial intelligence offers a novel avenue to address this necessity. This convergence presents an opportunity to create advanced models capable of quantifying diverse sources of uncertainty and automating complex data relationship exploration. What: We introduce a hierarchical Bayesian architecture whose probabilistic relationships are modeled by neural networks, designed to forecast stellar attributes such as mass, radius, and age (our main target). This architecture handles both observational uncertainties stemming from measurements and epistemic uncertainties inherent in the predictive model itself. As a result, our system generates distributions that encapsulate the potential range of values for our predictions, providing a comprehensive understanding of their variability and robustness. Methods: Our focus is on dating main sequence stars using a technique known as Chemical Clocks, which serves as both our primary astronomical challenge and a model prototype. In this work, we use hierarchical architectures to account for correlations between stellar parameters and optimize information extraction from our dataset. We also employ Bayesian neural networks for their versatility and flexibility in capturing complex data relationships. Results: By integrating our machine learning algorithm into a Bayesian framework, we have successfully propagated errors consistently and managed uncertainty treatment effectively, resulting in predictions characterized by broader uncertainty margins. This approach facilitates more conservative estimates in stellar dating. Our architecture achieves age predictions with a mean absolute error of less than 1 Ga for the stars in the test dataset.