Research in Mathematics

Contemporary Theoretical Advances in High-Dimensional and Multivariate Statistics in Data Science and Machine Learning

Mathematics provides the rigorous language through which statistical models and methods are formulated and understood. High-Dimensional and Multivariate Statistics, has laid the foundation for many of today’s most impactful advances, including deep learning, random network theory, and high-dimensional inference. Theoretical developments in high-dimensional and multivariate statistics offer essential tools for analysing the behaviour of complex, data-driven models. In deep learning, these tools help explain generalisation and the geometry of optimisation landscapes in overparameterized regimes. In random networks and random matrix theory, statistical frameworks support the analysis of spectral properties and connectivity patterns, which are critical for robust inference and signal detection. As data continues to grow in scale and complexity, research in high-dimensional and complex statistics remains essential to ensure sound inference, interpretability, for mathematical models and methods for data science. By curating contributions that push the boundaries of current theory, this collection will help shape the next generation of statistical tools and methods for data science; deepening our understanding of high-dimensional phenomena, improving the theoretical underpinnings of machine learning, and offering new insights into the probabilistic behaviour of complex systems.

As data grows in complexity and dimensionality, the need for robust theoretical frameworks has never been greater. Recent advances in AI, network science, and information theory demand a re-examination of classical statistical tools and the development of new ones. This collection responds to that need by bringing together timely research that addresses these challenges head-on. Continued development in this field not only strengthens classical statistical foundations but also equips researchers with robust tools to tackle modern, high-dimensional, and data-intensive problems. By bridging rigorous theory with emerging interdisciplinary applications, for high-dimensional and multivariate statistics provides a dynamic framework that supports innovation across science, engineering, and technology.

This Article Collection aims to showcase cutting-edge theoretical research in high-dimensional and multivariate statistics that advances our understanding of modern statistical models and methods for data science.

Objectives include:
1. Highlight foundational development with potential for broad methodological impact
2. Foster dialogue between statistical theory and emerging applications in data science and machine learning, amongst others
3. Provide a platform for rigorous evaluation and comparison of novel statistical frameworks with a strong mathematical foundation

High-dimensional and Multivariate Statistics are increasingly at the crossroads of multiple disciplines. This Article Collection welcomes contributions that integrate ideas from applied mathematics, computer science, physics, and engineering: all with a succinct focus within high-dimensional and complex statistics. Whether through the lens of random matrix theory in wireless communications, or probabilistic modelling in neuroscience, we aim to highlight how fundamental high-dimensional and complex statistics can serve as a unifying language across scientific domains.

Comparisons, critical theoretical evaluations, statistical computation or simulation where original methodology is involved, and original contributions to the foundations of statistical science are of particular interest, to provide motivation and direction for future theoretical frameworks within high-dimensional and multivariate statistics.

In this Article Collection, we look forward to receiving submissions on, but not limited to, the following topics with a theoretical perspective in mathematical statistics:
• Random matrix theory
• Multivariate distributional development and applications
• High-dimensional probabilistic developments in information theory
• Multivariate functional data analysis
• Graphical modelling
• Probabilistic/distributional developments in machine learning

Keywords: multivariate statistics, graphical modelling, machine learning, random matrix theory, high-dimensional data

Manuscript Submissions:

Manuscript submission is open until 28th June 2026.

Please carefully review the journal scope and author submission instructions prior to submitting an abstract as it will be rejected if it does not fall within the scope of the journal.

All manuscripts submitted to this Article Collection will undergo desk assessment and peer-review as part of our standard editorial process. Manuscripts which do not fall within the scope of the journal will be rejected.

To submit your papers to this Article Collection, please:

1. Check "yes" for the question, "Are you submitting your paper for a specific special issue or article collection?"
2. Select the relevant Article Collection from the drop-down menu under the question, "Contemporary Theoretical Advances in High-Dimensional and Multivariate Statistics in Data Science and Machine Learning"

We are able to offer a 10% Discount to all authors, and have a limited number of 20% Discount codes only available for early submissions. It should be noted that discount codes must be entered in at the point of submission as they cannot be applied retroactively, nor can these be combined as only the higher valued discount would be applicable.

Please contact Christopher Montgomery, Commissioning Editor regarding details on obtaining your discount codes, and with any other queries for this Article Collection.

Article Collection Guest Advisors

Prof. Johan Ferreira is a full professor of mathematical statistics, based in the School of Statistics and Actuarial Science at the University of the Witwatersrand, South Africa. His PhD was obtained from the University of Pretoria in 2018. He has published over 40 papers with a research focus on probabilistic entropy, random matrix theory, and mixture modelling.

Prof. Janet van Niekerk is a Research Scientist at the King Abdullah University of Science and Technology (KAUST), as part of the research group of Professor Håvard Rue, and recently joined the University of Pretoria’s Department of Statistics as an associate professor. She obtained a PhD from the University of Pretoria in 2017 and has published extensively in computational aspects of Bayesian statistics. She is currently an associate editor of Bayesian Analysis and Statistical Computing.