Related papers: The Foundation of Big Data: Experiments, Formulati…
This article presents the theoretical foundation of a new frontier of research-`LP Mixed Data Science'-that simultaneously extends and integrates the practice of traditional and novel statistical methods for nonparametric exploratory data…
We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering,…
Recent advances in big/foundation models reveal a promising path for deep learning, where the roadmap steadily moves from big data to big models to (the newly-introduced) big learning. Specifically, the big learning exhaustively exploits…
Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
Big data has now become a strong focus of global interest that is increasingly attracting the attention of academia, industry, government and other organizations. Big data can be situated in the disciplinary area of traditional geospatial…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
This paper presents mathematics as a general science of computation in a way different from the tradition. It is based on the radical philosophical standpoint according to which the content, meaning and justification of experience lies in…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be…
The term big data has become ubiquitous. Owing to a shared origin between academia, industry and the media there is no single unified definition, and various stakeholders provide diverse and often contradictory definitions. The lack of a…
In this communication, the approach of phenomenological universalities of growth are considered to describe the behaviour of a system showing oscillatory growth. Two phenomenological classes are proposed to consider the behaviour of a…
Data visualization in the form of charts plays a pivotal role in data analysis, offering critical insights and aiding in informed decision-making. Automatic chart understanding has witnessed significant advancements with the rise of large…
Synthetic data is often positioned as a solution to replace sensitive fixed-size datasets with a source of unlimited matching data, freed from privacy concerns. There has been much progress in synthetic data generation over the last decade,…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…