Related papers: The Mat\'ern Model: A Journey through Statistics, …

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Time series forecasting is an active research topic in academia as well as industry. Although we see an increasing amount of adoptions of machine learning methods in solving some of those forecasting challenges, statistical methods remain…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

The location, timing, and abundance of gene expression (both mRNA and proteins) within a tissue define the molecular mechanisms of cell functions. Recent technology breakthroughs in spatial molecular profiling, including imaging-based…

Machine learning (ML) has transformed numerous fields, but understanding its foundational research is crucial for its continued progress. This paper presents an overview of the significant classical ML algorithms and examines the…

This paper revisits the principle of uniform convergence in statistical learning, discusses how it acts as the foundation behind machine learning, and attempts to gain a better understanding of the essential problem that current deep…

Machine translation (MT) is an area of study in Natural Language processing which deals with the automatic translation of human language, from one language to another by the computer. Having a rich research history spanning nearly three…

This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

Machine learning (ML) pervades an increasing number of academic disciplines and industries. Its impact is profound, and several fields have been fundamentally altered by it, autonomy and computer vision for example; reliability engineering…

Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…

Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…

Machine learning has been increasingly applied in climate modeling on system emulation acceleration, data-driven parameter inference, forecasting, and knowledge discovery, addressing challenges such as physical consistency, multi-scale…

Bayesian methods and software for spatial data analysis are generally now well established in the scientific community. Despite the wide application of spatial models, the analysis of multivariate spatial data using R-INLA has not been…

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a…

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has…