Data Science and Machine Learning

Mathematical and Statistical Methods

Dirk P. Kroese, Zdravko Botev, Thomas Taimre, Radislav Vaisman

• Publisher: Chapman and Hall/CRC
• Year: 2019
• Print ISBN: 9781138492530
• eBook ISBN: 9781000731071
• Topic: Economics
• Subtopic: Computer Science General
• Index: Economics

"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

CHAPTER 1

IMPORTING, SUMMARIZING, AND VISUALIZING DATA

This chapter describes where to find useful data sets, how to load them into Python, and how to (re)structure the data. We also discuss various ways in which the data can be summarized via tables and figures. Which type of plots and numerical summaries are appropriate depends on the type of the variable(s) in play. Readers unfamiliar with Python are advised to read Appendix D first.

1.1 Introduction

Data comes in many shapes and forms, but can generally be thought of as being the result of some random experiment — an experiment whose outcome cannot be determined in advance, but whose workings are still subject to analysis. Data from a random experiment are often stored in a table or spreadsheet. A statistical convention is to denote variables — often called features — as columns and the individual items (or units) as rows. It is useful to think of three types of columns in such a spreadsheet:

FEATURES

1. The first column is usually an identifier or index column, where each unit/row is given a unique name or ID.

2. Certain columns (features) can correspond to the design of the experiment, specifying, for example, to which experimental group the unit belongs. Often the entries in these columns are deterministic; that is, they stay the same if the experiment were to be repeated.

3. Other columns represent the observed measurements of the experiment. Usually, these measurements exhibit variability; that is, they would change if the experiment were to be repeated.

There are many data sets available from the Internet and in software packages. A well-known repository of data sets is the Machine Learning Repository maintained by the University of California at Irvine (UCI), found at https://archive.ics.uci.edu/.

These data sets are typically stored in a CSV (comma separated values) format, which can be easily read into Python. For example, to access the abalone data set from this website with Python, download the file to your working directory, import the pandas package via

import pandas as pd

and read in the data as follows:

abalone = pd.read_csv('abalone.data'.header = None)

It is important to add header = None, as this lets Python know that the first line of the CSV does not contain the names of the features, as it assumes so by default. The data set was originally used to predict the age of abalone from physical measurements, such as shell weight and diameter.

Another useful repository of over 1000 data sets from various packages in the R programming language, collected by Vincent Arel-Bundock, can be found at:

https://vincentarelbundock.github.io/Rdatasets/datasets.html.

For example, to read Fisher’s famous iris data set from R’s datasets package into Python, type:

urlprefix = 'https://vincentarelbundock.github.io/Rdataset...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Notation
• 1 Importing, Summarizing, and Visualizing Data
• 2 Statistical Learning
• 3 Monte Carlo Methods
• 4 Unsupervised Learning
• 5 Regression
• 6 Regularization and Kernel Methods
• 7 Classification
• 8 Decision Trees and Ensemble Methods
• 9 Deep Learning
• A Linear Algebra and Functional Analysis
• B Multivariate Differentiation and Optimization
• C Probability and Statistics
• D Python Primer
• Bibliography
• Index