Preface

This special issue includes papers presented at the Eighth International Workshop on Perspectives on High-Dimensional Data Analysis (HDDA-VIII) held at CIMAT <www.cimat.mx>, Guanajuato, Mexico, from June 15-19, 2017. Technical development is allowing scientists to collect data of increasingly unprecedented size and complexity. Many times, this data consists of hundreds and thousands of observations across subjects (or units) generating massive high-dimensional data sets. Examples include epigenomic data, genomic data, proteomic data, high-resolution image data, high frequency financial data, functional and longitudinal data, and network data. This wealth of information has created new concerns (such as collinearity and high-dimensionality analysis) faced by new statistical development to solve problems such as variable selection, parameter estimation, clustering, and prediction. This workshop aims to foster the interaction of researchers in high-dimensional data analysis and stimulate research. The HDDA series has become a well-established tradition and one of the most visible annual events on innovative methodology for high-dimensional data. From environmental sciences to cybersecurity to fMRI imaging, there is a broad range of studies in which this data can be applied. I am very proud of having initiated this important and broadly appreciated workshop series. This workshop went very smooth and was a great success. In addition to domestic partners, it has attracted many international participants from various countries. This workshop has successfully fulfilled the agenda of promoting research activities in high-dimensional data analysis. It has created a rather focused venue for participants to actively discuss and exchange research ideas via presentations and informal postpresentation discussions. The list of speakers at the workshop was impressive, and most of the talks were based on unpublished and on-going work. I am grateful to Professor Fabrizio Ruggeri, editor-in-chief of Applied Stochastic Models in Business and Industry, for arranging this special issue. After completing the refereeing process, six papers have been selected to be featured in this issue. Their respective contributions are highlighted in the following. Weak signal detection has stimulated much interest in recent high-dimensional literature. However, the concept of weak but correlated (WBC) signals, ie, variables with marginally weak effects, which are also partially correlated with marginally strong signals, has been largely overlooked. The paper by Li, Hong, Ahmed, and Li introduces this new concept and laid out a general framework for utilizing WBC signals to reduce biases in parameter estimates and improve prediction in high-dimensional settings. By decomposing the set of the true signals into three sets containing, respectively, strong signals, WBC, and weak signals that are uncorrelated with strong signals, they provided a comprehensive toolbox for detection of weak signals and postshrinkage estimates of true signals and prediction models. Large sample properties provided by the authors further informed the utility of the methods. The authors illustrated their methods by predicting the GDP growth based on several indices among developing countries in the early 1960s. However, it is envisioned that their methods may find applications in broad areas, such as in genome-wide association studies (GWASs) for detection of novel SNPs that may further explain heritability of traits or in finance for the construction of potentially lucrative portfolios of stocks. The change point problem in time series data has been of interest to statisticians for many decades. Traditionally, researchers examined methods for detecting change points in the mean structure of, firstly, univariate and, eventually, multivariate time series. However, in many applications, to capture the dynamic structure, it is of interest to quantify the evolving interdependencies between (possible) high-dimensional multivariate time series. Cribben discusses two robust methods for finding change points in the network structure between (possible) high-dimensional multivariate time series. After finding the change points, authors estimated a graph, or series of relationships between time series, for data in the temporal partition that falls between pairs of change points. In the first technique, they apply glasso, whereas, in the second, they apply tlasso, which is a tool for robust model selection that builds upon the glasso. The usual setup for finding change points in time series analysis is to assume that the data follows a parametric model, but their techniques do not make any assumptions on the model, thereby making it more flexible. The methods are applied to simulated multivariate t-distributed (heavy tailed) time series data as well as two financial returns data sets of stock and indices. The information arising from the proposed methods could potentially be used as a tool for portfolio optimization. The manual segmentation of hematoma and edema from computed tomography (CT) scans is common practice but a time-consuming and labor-intensive task. The automated segmentation is challenging due to the poorly defined boundary between edema and the surrounding healthy brain tissue. Tu, Kong, Karunamuni, Butcher, Zheng, and McCourt propose a fully automated pipeline for brain hematoma and edema segmentation. Since the pipeline is unsupervised, no training and parameter tuning is needed. This is appealing in this application because of the large intra and interrater variation presented in the data. The proposed framework mainly has two stages. During the initialization stage, nonlocal spatial fuzzy C-means clustering is used to get an initial contour. For the refinement stage, an active contour without edge is used to further improve the boundaries. The proposed pipeline achieved a comparable result with the manual segmentation. Feng, Li, and Ying proposed a new family of penalty functions that are adaptive to the likelihood format. By using this specific penalty family, we can show that the associated penalized maximum likelihood estimate has asymptotic stability, parameter estimation consistency, and model selection consistency properties. The solution path generated by using this penalty is smoother than using state-of-the-art nonconvex penalty functions. As a special type of big data, high-dimensional data, which has a moderate sample size but a large number of covariates, is now a routine in business and industrial problems. The work by Li, Li, Qin, Wu, and Ma explores two specific yet important problems in high-dimensional data analysis. The first is interaction, which is almost trivial with low-dimensional data but gets obnoxiously challenging with high-dimensional data. The second is integrative analysis, which can effectively pool data and thus improve the quality of estimation and variable selection. The methodological innovation of this article is worth highlighting, where a thresholding approach is developed to accommodate the high dimensionality, hierarchy in interaction, and heterogeneity in integrative analysis. It is reasonable to foresee that the proposed technique can have broad applications in a variety of high-dimensional problems. Mode hunting is of significance because modes represent a set of maximum accumulation points, which is closely related to the idea of finding maxima, which itself has a long history of importance in statistics. Mode identification has proven to be challenging in high dimensions because specifying complex fully parametric distributions is difficult, and fully nonparametric approaches can suffer from issues like the curse of dimensionality. In this work, Diaz-Pachon, Saenz, Rao, and Dazard develop an approach for mode hunting, which is grounded in information theory based upon the idea of measuring how much information is added as a computer search is performed. The authors take this active information (AI) and formulate it in terms of mode hunting. The AI mode hunting (AIMH) is a hybrid between being fully parametric and nonparametric. The authors show how AIMH cannot only detect the existence of modes but also where exactly they are located. Most interestingly, AIMH can reduce dimensionality in high-dimensional problems without resorting to traditional approaches like principal components, which can suffer from eliminating dimensions that may be associated with a response of interest. The authors prove that AIMH has asymptotically optimal properties in that it is consistent for finding modes. To drive this point home, they present some theoretical examples that illustrate its reach. Finally, the authors apply AIMH to a very interesting application from Kickstarter, a reward-based crowdfunding platform that allows people to seek funding for creative projects. Using this data, they hunt for modes comparing goals and pledges. My special thanks go to Dr. L. Leticia Ramirez, the local organizers, superb staff, and the management at CIMAT for their time, effort, and support in organizing this workshop. Finally, I would like to thank all the reviewers for their time and due diligence reviews of the papers to ensure that all authors have equal opportunity for publication of their work.