AbstractThe discrete empirical interpolation method (DEIM) is well established as a means of performing model order reduction in approximating solutions to differential equations, but it has also more recently demonstrated potential in performing data class detection through subset selection. Leveraging the singular value decomposition (SVD) for dimension reduction, DEIM uses interpolatory projection to identify the representative rows and/or columns of a data matrix. This approach has been adapted to develop additional algorithms, including a CUR matrix factorization for performing dimension reduction while preserving the interpretability of the data. DEIM‐oversampling techniques have also been developed expressly for the purpose of index selection in identifying more DEIM representatives than would typically be allowed by the matrix rank. Even with these developments, there is still a relatively large gap in the literature regarding the use of DEIM in performing unsupervised learning tasks to analyze large datasets. Known examples of DEIM's demonstrated applicability include contexts such as physics‐based modeling/monitoring, electrocardiogram data summarization and classification, and document term subset selection. This overview presents a description of DEIM and some DEIM‐related algorithms, discusses existing results from the literature with an emphasis on more statistical‐learning‐based tasks, and identifies areas for further exploration moving forward.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

AbstractThis article provides a systematic review of the theoretical and empirical academic literature on the development and extension of the log‐periodic power law singularity (LPPLS) model, which is also known as the Johansen–Ledoit–Sornette (JLS) model or log‐periodic power law (LPPL) model. Developed at the interface of financial economics, behavioral finance and statistical physics, the LPPLS model provides a flexible and quantitative framework for detecting financial bubbles and crashes by capturing two salient empirical characteristics of price trajectories in speculative bubble regimes: the faster‐than‐exponential growth of price leading to unsustainable growth ending with a finite crash‐time and the accelerating log‐periodic oscillations. We also demonstrate the LPPLS model by detecting the recent bubble status of the S&P 500 index between April 2020 and December 2022, during which the S&P 500 index reaches its all‐time peak at the end of 2021. We find that the strong corrections of the S&P 500 index starting from January 2022 stem from the increasingly systemic instability of the stock market itself, while the well‐known external shocks, such as the decades‐high inflation, aggressive monetary policy tightening by the Federal Reserve, and the impact of the Russia/Ukraine war, may serve as sparks.This article is categorized under: Applications of Computational Statistics > Computational Finance Algorithms and Computational Methods > Computational Complexity Statistical Models > Nonlinear Models

AbstractThe Central Limit Theorem justifies using a normal distribution when looking at sums of many terms. In a parallel way, extreme value distributions arise in the study of maxima of many terms. The goal of this paper is to briefly review the univariate theory of extremes based on the Fisher‐Tippet‐Gnedenko Theorem. We then state the basics of the multivariate theory, which is significantly more complicated because it requires a measure to define the distribution. Some properties of these laws are explored, including a description of the support, an expression for the density when it exists, and some examples that illustrate possible joint dependence structures.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Applications of Computational Statistics > Computational Finance

AbstractThe realm of Natural Language Processing and Text Mining has seen a surge in interest from researchers in hate speech detection, leading to an increase in related studies. This analysis aims to create a valuable resource by summarizing the methods and strategies used to combat hate speech in social media. We perform a detailed review to achieve a deep knowledge of the hate speech detection landscape from 2018 to 2023, revealing global incidents of hate speech in 2022–2023. Sixty‐six relevant articles were selected for this review. Existing studies were analyzed and categorized into five method categories: Machine Learning, Deep Learning, Ensemble models, Graph Neural Networks, and Graph Convolutional Networks. These advancements can aid social networking services in identifying hate messages before being posted, reducing the risk of harassment. The review also covers available hate speech datasets and highlights research challenges, but it is clear that a definitive solution to this problem is yet to be found. Future research directions are recommended to address the ongoing challenges in Hate Speech Detection.This article is categorized under: Applications of Computational Statistics > Computational Linguistics Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery Statistical Learning and Exploratory Methods of the Data Sciences > Classification and Regression Trees (CART) Statistical Learning and Exploratory Methods of the Data Sciences > Text Mining

AbstractOur goal is to provide a review of deep learning methods which provide insight into structured high‐dimensional data. Merging the two cultures of algorithmic and statistical learning sheds light on model construction and improved prediction and inference, leveraging the duality and trade‐off between the two. Prediction, interpolation, and uncertainty quantification can be achieved using probabilistic methods at the output layer of the model. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of semi‐affine input transformations to provide a predictive rule. Applying these layers of transformations leads to a set of attributes (or, features) to which probabilistic statistical methods can be applied. Thus, the best of both worlds can be achieved: scalable prediction rules fortified with uncertainty quantification where sparse regularization finds the features. We review the duality between shallow and wide models such as principal components regression, and partial least squares and deep but skinny architectures such as autoencoders, multilayer perceptrons, convolutional neural net, and recurrent neural net. The connection with data transformations is of practical importance for finding good network architectures. By incorporating probabilistic components at the output level, the predictive uncertainty is allowed. We illustrate this idea by comparing plain Gaussian processes (GP) with partial least squares + Gaussian process (PLS + GP) and deep learning + Gaussian process (DL + GP).This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning

AbstractThe mechanisms of network generation have undergone extensive analysis and found broad applications in various real‐world scenarios. Among the fruitful literature on network models, numerous studies seek to explore and interpret fundamental graph structure properties, including the clustering effect, exchangeability, and scale‐free properties. In this paper, we present a comprehensive review of the statistical modeling methods for the mechanisms of network generation. We specifically focus on three representative classes of models, namely the stochastic block models, the exchangeable network models, and the preferential attachment models. For each model type, our approach begins by reviewing existing methods and model setups, followed by an exploration of the core modeling principles behind them. We also summarize relevant statistical inference techniques and provide a unified understanding of theoretical analyses. Furthermore, we emphasize several challenges and open problems that could shed light on future research. We conclude this review with the identification of some possible directions for future study.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Algorithms and Computational Methods > Networks and Security

AbstractThe sparse prior has been widely adopted to establish data models for numerous applications. In this context, most of them are based on one of three foundational paradigms: the conventional sparse representation, the convolutional sparse representation, and the multi‐layer convolutional sparse representation. When the data morphology has been adequately addressed, a sparse representation can be obtained by solving the sparse coding problem specified by the data model. This article presents a comprehensive overview of these three models and their corresponding sparse coding problems and demonstrates that they can be solved using convex and non‐convex optimization approaches. When the data morphology is not known or cannot be analyzed, it must be learned from training data, thereby formulating dictionary learning problems. This article addresses two different dictionary learning paradigms. In an unsupervised scenario, dictionary learning involves the alternating or joint resolution of sparse coding and dictionary updating. Another option is to create a recurrent neural network by unrolling algorithms designed to solve sparse coding problems. These networks can then be used in a supervised learning setting to facilitate the training of dictionaries via forward‐backward optimization. This article lists numerous applications in various domains and outlines several directions for future research related to the sparse prior.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical Models > Nonlinear Models

AbstractModel calibration is crucial for optimizing the performance of complex computer models across various disciplines. In the era of Industry 4.0, symbolizing rapid technological advancement through the integration of advanced digital technologies into industrial processes, model calibration plays a key role in advancing digital twin technology, ensuring alignment between digital representations and real‐world systems. This comprehensive review focuses on the Kennedy and O'Hagan (KOH) framework (Kennedy and O'Hagan, Journal of the Royal Statistical Society: Series B 2001; 63(3):425–464). In particular, we explore recent advancements addressing the challenges of the unidentifiability issue while accommodating model inadequacy within the KOH framework. In addition, we explore recent advancements in adapting the KOH framework to complex scenarios, including those involving multivariate outputs and functional calibration parameters. We also delve into experimental design strategies tailored to the unique demands of model calibration. By offering a comprehensive analysis of the KOH approach and its diverse applications, this review serves as a valuable resource for researchers and practitioners aiming to enhance the accuracy and reliability of their computer models.This article is categorized under: Statistical Models > Semiparametric Models Statistical Models > Simulation Models Statistical Models > Bayesian Models

AbstractWith the development of technology and its integration with scientific realities, computer systems continue to evolve as infrastructure. One of the most important obstacles in front of quantum computers with high‐speed processing is that its existing systems cause security vulnerabilities. Therefore, in order to take advantage of quantum systems, existing systems that are already secure must also be secure in the post‐quantum scenario. One of these systems is edge computing. There are challenges in terms of computational power for the implementation of pre‐ and post‐quantum methods in structures with resource‐constrained devices. This article reviews the post‐quantum security threats of edge devices and systems and the secure methods developed for them. Although there is relatively little research in this field, it remains relevant. In the studies reviewed, lattice‐based approaches are often highlighted for making edge systems quantum‐resistant. Additionally, these studies indicate that there has been an increasing trend in this field in recent years.This article is categorized under: Applications of Computational Statistics > Defense and National Security Algorithms and Computational Methods > Networks and Security