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Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure. However, processes in real-world applications often exhibit non-Gaussianity and nonstationarity. Moreover, likelihood-based inference for GPs is computationally expensive and thus prohibitive for large datasets. In this paper we propose a deep neural network (DNN) based two-stage model for spatio-temporal interpolation and forecasting. Interpolation is performed in the first step, which utilizes a dependent DNN with the embedding layer constructed with spatio-temporal basis functions. For the second stage, we use Long-Short Term Memory (LSTM) and convolutional LSTM to forecast future observations at a given location. We adopt the quantile-based loss function in the DNN to provide probabilistic forecasting. Compared to Kriging, the proposed method does not require specifying covariance functions or making stationarity assumption, and is computationally efficient. Therefore, it is suitable for large-scale prediction of complex spatio-temporal processes. We apply our method to monthly $PM_{2.5}$ data at more than $200,000$ space-time locations from January 1999 to December 2022 for fast imputation of missing values and forecasts with uncertainties.

Learning the graphical structure of Bayesian networks is key to describing data-generating mechanisms in many complex applications but poses considerable computational challenges. Observational data can only identify the equivalence class of the directed acyclic graph underlying a Bayesian network model, and a variety of methods exist to tackle the problem. Under certain assumptions, the popular PC algorithm can consistently recover the correct equivalence class by reverse-engineering the conditional independence (CI) relationships holding in the variable distribution. The dual PC algorithm is a novel scheme to carry out the CI tests within the PC algorithm by leveraging the inverse relationship between covariance and precision matrices. By exploiting block matrix inversions we can also perform tests on partial correlations of complementary (or dual) conditioning sets. The multiple CI tests of the dual PC algorithm proceed by first considering marginal and full-order CI relationships and progressively moving to central-order ones. Simulation studies show that the dual PC algorithm outperforms the classic PC algorithm both in terms of run time and in recovering the underlying network structure, even in the presence of deviations from Gaussianity. Additionally, we show that the dual PC algorithm applies for Gaussian copula models, and demonstrate its performance in that setting.

Typical machine learning regression applications aim to report the mean or the median of the predictive probability distribution, via training with a squared or an absolute error scoring function. The importance of issuing predictions of more functionals of the predictive probability distribution (quantiles and expectiles) has been recognized as a means to quantify the uncertainty of the prediction. In deep learning (DL) applications, that is possible through quantile and expectile regression neural networks (QRNN and ERNN respectively). Here we introduce deep Huber quantile regression networks (DHQRN) that nest QRNNs and ERNNs as edge cases. DHQRN can predict Huber quantiles, which are more general functionals in the sense that they nest quantiles and expectiles as limiting cases. The main idea is to train a deep learning algorithm with the Huber quantile regression function, which is consistent for the Huber quantile functional. As a proof of concept, DHQRN are applied to predict house prices in Australia. In this context, predictive performances of three DL architectures are discussed along with evidential interpretation of results from an economic case study.

Existing traffic signal control systems rely on oversimplified rule-based methods, and even RL-based methods are often suboptimal and unstable. To address this, we propose a cooperative multi-objective architecture called Multi-Objective Multi-Agent Deep Deterministic Policy Gradient (MOMA-DDPG), which estimates multiple reward terms for traffic signal control optimization using age-decaying weights. Our approach involves two types of agents: one focuses on optimizing local traffic at each intersection, while the other aims to optimize global traffic throughput. We evaluate our method using real-world traffic data collected from an Asian country's traffic cameras. Despite the inclusion of a global agent, our solution remains decentralized as this agent is no longer necessary during the inference stage. Our results demonstrate the effectiveness of MOMA-DDPG, outperforming state-of-the-art methods across all performance metrics. Additionally, our proposed system minimizes both waiting time and carbon emissions. Notably, this paper is the first to link carbon emissions and global agents in traffic signal control.

In the field of cryptography, the selection of relevant features plays a crucial role in enhancing the security and efficiency of cryptographic algorithms. This paper presents a novel approach of applying fuzzy feature selection to key-based cryptographic transformations. The proposed fuzzy feature selection leverages the power of fuzzy logic to identify and select optimal subsets of features that contribute most effectively to the cryptographic transformation process. By incorporating fuzzy feature selection into key-based cryptographic transformations, this research aims to improve the resistance against attacks and enhance the overall performance of cryptographic systems. Experimental evaluations may demonstrate the effectiveness of the proposed approach in selecting secure key features with minimal computational overhead. This paper highlights the potential of fuzzy feature selection as a valuable tool in the design and optimization of key-based cryptographic algorithms, contributing to the advancement of secure information exchange and communication in various domains.

Automated variable selection is widely applied in statistical model development. Algorithms like forward, backward or stepwise selection are available in statistical software packages like R and SAS. Many researchers have criticized the use of these algorithms because the models resulting from automated selection algorithms are not based on theory and tend to be unstable. Furthermore, simulation studies have shown that they often select incorrect variables due to random effects which makes these model building strategies unreliable. In this article, a comprehensive stepwise selection algorithm tailored to logistic regression is proposed. It uses multiple criteria in variable selection instead of relying on one single measure only, like a $p$-value or Akaike's information criterion, which ensures robustness and soundness of the final outcome. The result of the selection process might not be unambiguous. It might select multiple models that could be considered as statistically equivalent. A simulation study demonstrates the superiority of the proposed variable selection method over available alternatives.

We introduce a Loss Discounting Framework for model and forecast combination which generalises and combines Bayesian model synthesis and generalized Bayes methodologies. We use a loss function to score the performance of different models and introduce a multilevel discounting scheme which allows a flexible specification of the dynamics of the model weights. This novel and simple model combination approach can be easily applied to large scale model averaging/selection, can handle unusual features such as sudden regime changes, and can be tailored to different forecasting problems. We compare our method to both established methodologies and state of the art methods for a number of macroeconomic forecasting examples. We find that the proposed method offers an attractive, computationally efficient alternative to the benchmark methodologies and often outperforms more complex techniques.

Graph neural networks (GNNs) have emerged as a series of competent graph learning methods for diverse real-world scenarios, ranging from daily applications like recommendation systems and question answering to cutting-edge technologies such as drug discovery in life sciences and n-body simulation in astrophysics. However, task performance is not the only requirement for GNNs. Performance-oriented GNNs have exhibited potential adverse effects like vulnerability to adversarial attacks, unexplainable discrimination against disadvantaged groups, or excessive resource consumption in edge computing environments. To avoid these unintentional harms, it is necessary to build competent GNNs characterised by trustworthiness. To this end, we propose a comprehensive roadmap to build trustworthy GNNs from the view of the various computing technologies involved. In this survey, we introduce basic concepts and comprehensively summarise existing efforts for trustworthy GNNs from six aspects, including robustness, explainability, privacy, fairness, accountability, and environmental well-being. Additionally, we highlight the intricate cross-aspect relations between the above six aspects of trustworthy GNNs. Finally, we present a thorough overview of trending directions for facilitating the research and industrialisation of trustworthy GNNs.

Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.