Numerical foundations for scalable statistical and machine learning methods

Across modern data-intensive disciplines, the union of numerical computation, statistics, and machine learning has become central to scientific progress. The exponential increase in data volume, model complexity, and available computational power has led to paradigm shifts in how statistical inference and learning algorithms are designed and implemented. From large-scale Bayesian modeling and nonparametric inference to deep neural networks and stochastic modeling, numerical algorithms form the hidden infrastructure that determines what is computationally and scientifically feasible. Despite remarkable advances, persistent challenges remain—ensuring numerical stability in large-scale systems, maintaining reproducibility, and understanding theoretical trade-offs between approximation accuracy and statistical efficiency. The fragmentation between numerical analysts, statisticians, and machine learning researchers continues to limit coordinated advancement in this critical area. This Research Topic aims to promote interdisciplinary collaboration at the intersection of numerical analysis, statistical methodology, and machine learning. Its goal is to stimulate the development and theoretical understanding of numerical algorithms that underpin efficient, stable, and scalable data processing and inference. Contributors are invited to propose and analyze new algorithms, develop unified theoretical frameworks, explore the integration of numerical computation into statistical workflows, and present innovative applications to real-world data problems. This effort seeks not only to improve computational performance but also to strengthen the reliability and interpretability of modern data science tools. By gathering contributions from multiple research communities, the Research Topic will help shape a unified vision for the numerical foundations of 21st-century statistics and machine learning. The scope of this Research Topic encompasses theory, methodology, and applications that illuminate the essential numerical aspects of data analysis and learning systems. It welcomes contributions from fields such as applied mathematics, computer science, and statistical science, emphasizing both theoretical innovation and practical relevance. To gather further insights into this evolving field, we welcome articles addressing, but not limited to, the following themes: - Numerical optimization for statistical estimation and learning: Development of efficient optimization strategies in high-dimensional and non-convex settings using second-order, proximal, or heuristic algorithms to improve convergence and scalability. - Numerical linear algebra in high-dimensional inference: Exploration of advanced matrix factorization, randomized algorithms, and GPU-accelerated methods to handle large-scale linear algebra challenges in statistical estimation. - Numerical approaches to Bayesian computation: Design of scalable and robust methods for sampling and variational inference, including adaptive Monte Carlo and hybrid simulation-optimization frameworks. - Numerical schemes for stochastic differential equations and probabilistic modeling: Investigation of accurate integration and discretization methods for SDEs and their role in diffusion models, time-series inference, and probabilistic learning. - EM-type algorithms and accelerated iterative methods: Enhancement of classical iterative estimation approaches through acceleration techniques, variance reduction, and parallel implementations for large or streaming data. - Numerical methods for nonparametric and semiparametric models: Development of efficient algorithms for kernel-based, spline-based, and shape-constrained inference, with emphasis on scalability and numerical accuracy. - Computational techniques for spatial statistics and spatio-temporal modeling: Advancement of approximate and hierarchical methods for large-scale spatial and spatio-temporal data, addressing non-stationary and anisotropic behavior. - Numerical strategies for deep learning, kernel methods, and graph-based learning: Examination of the numerical stability of differentiable programming, kernel approximations, and graph-based numerical solvers in machine learning. - High-performance computing and scalable numerical algorithms for big data: Study of memory-efficient, parallel, and distributed frameworks enabling large-scale inference and learning on modern hardware architectures. - Applications in engineering, environmental science, bioinformatics, and physical sciences: Translation of numerical innovations into applied domains, including uncertainty quantification, genomic analysis, and scientific machine learning. We encourage the submission of original research, reviews, perspectives, and benchmarking studies that integrate mathematical rigor with practical impact. By highlighting the pivotal role of numerical methods in the evolution of statistical and machine learning paradigms, this Research Topic will serve as a cornerstone for future interdisciplinary collaboration and innovation. Topic editors: Francisco Novoa-Muñoz, Bernardo Lagos Source: https://www.frontiersin.org/research-topics/82434/numerical-foundations-for-scalable-statistical-and-machine-learning-methods