Data Science

Ivo D. Dinov; Milen Velchev Velev

Published by De Gruyter 2022

Data Science

Time Complexity, Inferential Uncertainty, and Spacekime Analytics

Ivo D. Dinov and Milen Velchev Velev

In the series De Gruyter STEM

https://doi.org/10.1515/9783110697827

Overview
Contents

About this book

The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces.

By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated.

Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces).

The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive.

The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework.

The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.

includes open mathematical problems and technological challenges that need to be solved
extensive online supplementary materials: datasets, interactive web demonstrations, analytical case‐studies, R software code, and a community support network

Author information

Ivo D. Dinov, University of Michigan, USA; Milen V. Velev, Burgas "Prof. Dr. Asen Zlatarov" University, Bulgaria.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Foreword Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XV
Use and Disclaimer Publicly Available Download PDF	XIX
Glossary, Common Notations, and Abbreviations Publicly Available Download PDF	XXI
Chapter 1 Motivation Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2 Mathematics and Physics Foundations Requires Authentication Unlicensed Licensed Download PDF	35
Chapter 3 Time Complexity Requires Authentication Unlicensed Licensed Download PDF	55
Chapter 4 Kime-series Modeling and Spacekime Analytics Requires Authentication Unlicensed Licensed Download PDF	190
Chapter 5 Inferential Uncertainty Requires Authentication Unlicensed Licensed Download PDF	274
Chapter 6 Applications Requires Authentication Unlicensed Licensed Download PDF	382
7 Summary Requires Authentication Unlicensed Licensed Download PDF	440
References Requires Authentication Unlicensed Licensed Download PDF	445
Index Requires Authentication Unlicensed Licensed Download PDF	459

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Professional data scientists, graduate and postgraduate students.
Pages
- Front matter: 26
- Main content: 463
Illustrations
- Coloured Illustrations: 50
- Tables: 30
Keywords: Data Science; Time Complexity; Inferential Uncertainty; Predictive Analysis

eBook

Published: December 6, 2021
ISBN: 9783110697827

Hardcover

Published: December 20, 2021
ISBN: 9783110697803