Mathematical Methods In Data Science

"This textbook is a well-rounded, rigorous, and informative work presenting the mathematics behind modern machine learning techniques. It hits all the right notes: the choice of topics is up-to-date and perfect for a course on data science for mathematics students at the advanced undergraduate or early graduate level. This book fills a sorely-needed gap in the existing literature by not sacrificing depth for breadth, presenting proofs of major theorems and subsequent derivations, as well as providing a copious amount of Python code. I only wish a book like this had been around when I first began my journey!" -Nicholas Hoell, University of Toronto "This is a well-written book that provides a deeper dive into data-scientific methods than many introductory texts. The writing is clear, and the text logically builds up regularization, classification, and decision trees. Compared to its probable competitors, it carves out a unique niche. -Adam Loy, Carleton College The purpose of Data Science and Machine Learning: Mathematical and Statistical Methods is to provide an accessible, yet comprehensive textbook intended for students interested in gaining a better understanding of the mathematics and statistics that underpin the rich variety of ideas and machine learning algorithms in data science. Key Features: Focuses on mathematical understanding. Presentation is self-contained, accessible, and comprehensive. Extensive list of exercises and worked-out examples. Many concrete algorithms with Python code. Full color throughout. Further Resources can be found on the authors website: https://github.com/DSML-book/Lectures

This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful.

Mathematical Methods in Data Science covers a broad range of mathematical tools used in data science, including calculus, linear algebra, optimization, network analysis, probability and differential equations. Based on the authors’ recently published and previously unpublished results, this book introduces a new approach based on network analysis to integrate big data into the framework of ordinary and partial differential equations for dataanalysis and prediction. With data science being used in virtually every aspect of our society, the book includes examples and problems arising in data science and the clear explanation of advanced mathematical concepts, especially data-driven differential equations, making it accessible to researchers and graduate students in mathematics and data science. Combines a broad spectrum of mathematics, including linear algebra, optimization, network analysis and ordinary and partial differential equations for data science Written by two researchers who are actively applying mathematical and statistical methods as well as ODE and PDE for data analysis and prediction Highly interdisciplinary, with content spanning mathematics, data science, social media analysis, network science, financial markets, and more Presents a wide spectrum of topics in a logical order, including probability, linear algebra, calculus and optimization, networks, ordinary differential and partial differential equations

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

In order best exploit the incredible quantities of data being generated in most diverse disciplines data sciences increasingly gain worldwide importance. The book gives the mathematical foundations to handle data properly. It introduces basics and functionalities of the R programming language which has become the indispensable tool for data sciences. Thus it delivers the reader the skills needed to build own tool kits of a modern data scientist.

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In this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary context. Exercises serve to improve understanding of the underlying theory. Complete solutions for exercises can be consulted by the interested reader at the end of the textbook; for some which have to be solved numerically, we provide descriptions of algorithms in Python code as supplementary material.This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.

Discover how data science can help you gain in-depth insight into your business - the easy way! Jobs in data science abound, but few people have the data science skills needed to fill these increasingly important roles. Data Science For Dummies is the perfect starting point for IT professionals and students who want a quick primer on all areas of the expansive data science space. With a focus on business cases, the book explores topics in big data, data science, and data engineering, and how these three areas are combined to produce tremendous value. If you want to pick-up the skills you need to begin a new career or initiate a new project, reading this book will help you understand what technologies, programming languages, and mathematical methods on which to focus. While this book serves as a wildly fantastic guide through the broad, sometimes intimidating field of big data and data science, it is not an instruction manual for hands-on implementation. Here’s what to expect: Provides a background in big data and data engineering before moving on to data science and how it's applied to generate value Includes coverage of big data frameworks like Hadoop, MapReduce, Spark, MPP platforms, and NoSQL Explains machine learning and many of its algorithms as well as artificial intelligence and the evolution of the Internet of Things Details data visualization techniques that can be used to showcase, summarize, and communicate the data insights you generate It's a big, big data world out there—let Data Science For Dummies help you harness its power and gain a competitive edge for your organization.