Python下的统计学方法：机器学习基石

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《统计方法与机器学习》是由Jason Brownlee编著的一本指南，该书旨在帮助读者理解并掌握如何利用Python将数据转化为知识在机器学习领域中的实际应用。作为一本教育性资源，它明确指出内容仅供学习使用，作者不对因本书信息的准确性或完整性导致的任何损失或责任负责。在使用时，读者需自行承担风险。书中深入浅出地探讨了统计学在机器学习中的核心地位，强调了它是理解并构建机器学习模型的基础。读者将通过阅读本书了解到一系列关键的主题，包括： 1. **统计基础**：章节中会详细讲解统计学的基本概念，如概率论、分布、中心极限定理等，这些都是机器学习算法背后的数学支撑。 2. **机器学习中的统计方法**：涵盖回归分析（如线性回归、逻辑回归）、分类技术（如决策树、支持向量机）、以及聚类分析（如K-means）中所运用的统计原理。 3. **汇总统计**：介绍如何通过计算均值、中位数、标准差等指标来描述和理解数据集的特征。 4. **假设检验**：了解如何设计和执行假设检验，以验证数据是否符合特定假设，这对于特征选择和模型评估至关重要。 5. **非参数统计**：与参数方法相对，非参数统计方法不依赖于特定数据分布，适用于数据分布未知或复杂的场景。 6. **重新采样方法**：包括随机梯度下降、自助法（Bootstrap）和交叉验证等，这些技术用于处理数据不平衡问题、估计模型性能和调整模型参数。 7. **Python实践**：书中使用Python作为主要工具，介绍如何运用NumPy、Pandas和SciPy等库进行数据预处理、统计分析和建模。 8. **案例研究**：通过具体的实例演示，使理论知识更具可操作性和实用性，帮助读者掌握实际应用中的统计方法。每一部分都配以清晰的解释和逐步教学，使得即使是初学者也能逐步提升对统计方法在机器学习中的理解和技能。这是一本不仅适合机器学习专业人士，也适合对数据分析感兴趣的学习者参考的实用教材。

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How to evaluate and interpret the relationship between variables and the independence of

variables.



How to calculate and interpret parametric statistical hypothesis tests for comparing two

or more data samples.



How to calculate and interpret interval statistics for distributions, population parameters,

and observations.



How to use statistical resampling to make good economic use of available data in order to

evaluate predictive models.



How to calculate and interpret nonparametric statistical hypothesis tests for comparing

two or more data samples that do not conform to the expectations of parametric tests.

This new basic understanding of statistical methods will impact your practice of machine

learning in the following ways:



Use descriptive statistics and data visualizations to quickly and more deeply understand

the shape and relationships in data.



Use inferential statistical tests to quickly and eﬀectively quantify the relationships between

samples, such as the results of experiments with diﬀerent predictive algorithms or diﬀering

conﬁgurations.



Use estimation statistics to quickly and eﬀectively quantify the conﬁdence in estimated

model skill and model predictions.

This book is not a substitute for an undergraduate course in statistics or a textbook for such

a course, although it could complement such materials. For a good list of top courses, textbooks,

and other resources on statistics, see the Further Reading section at the end of each tutorial.

How to Read This Book

This book was written to be read linearly, from start to ﬁnish. That being said, if you know the

basics and need help with a speciﬁc notation or operation, then you can ﬂip straight to that

section and get started. This book was designed for you to read on your workstation, on the

screen, not on a tablet or eReader. My hope is that you have the book open right next to your

editor and run the examples as you read about them.

This book is not intended to be read passively or be placed in a folder as a reference text. It

is a playbook, a workbook, and a guidebook intended for you to learn by doing and then apply

your new understanding with working Python examples. To get the most out of the book, I

would recommend playing with the examples in each tutorial. Extend them, break them, then

ﬁx them. Try some of the extensions presented at the end of each lesson and let me know how

you do.

xvi

About the Book Structure

This book was designed around major statistical techniques that are directly relevant to applied

machine learning. There are a lot of things you could learn about statistics, from theory to

abstract concepts to APIs. My goal is to take you straight to developing an intuition for the

elements you must understand with laser-focused tutorials. I designed the tutorials to focus on

how to get things done with statistics. They give you the tools to both rapidly understand and

apply each technique or operation.

Each of the tutorials are designed to take you about one hour to read through and complete,

excluding the extensions and further reading. You can choose to work through the lessons one

per day, one per week, or at your own pace. I think momentum is critically important, and this

book is intended to be read and used, not to sit idle. I would recommend picking a schedule

and sticking to it. The tutorials are divided into 6 parts, they are:

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Part 1: Statistics

. Provides a gentle introduction to the ﬁeld of statistics, the relationship

to machine learning, and the importance that statistical methods have when working

through a predictive modeling problem.

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Part 2: Foundation

. Introduction to descriptive statistics, data visualization, random

numbers, and important ﬁndings in statistics such as the law of large numbers and the

central limit theorem.



Part 3: Hypothesis Testing

. Covers statistical hypothesis tests for comparing popula-

tions of samples and the interpretation of tests with p-values and critical values.



Part 4: Resampling

. Covers methods from statistics used to economically use small

samples of data to evaluate predictive models such as

-fold cross-validation and the

bootstrap.



Part 5: Estimation Statistics

. Covers an alternative to hypothesis testing called

estimation statistics, including tolerance intervals, conﬁdence intervals, and prediction

intervals.



Part 6: Nonparametric Methods

. Covers nonparametric statistical hypothesis testing

methods for use when data does not meet the expectations of parametric tests.

Each part targets a speciﬁc learning outcome, and so does each tutorial within each part.

This acts as a ﬁlter to ensure you are only focused on the things you need to know to get to a

speciﬁc result and do not get bogged down in the math or near-inﬁnite number of digressions.

The tutorials were not designed to teach you everything there is to know about each of the

theories or techniques of statistics. They were designed to give you an understanding of how

they work, how to use them, and how to interpret the results the fastest way I know how: to

learn by doing.

About Python Code Examples

The code examples were carefully designed to demonstrate the purpose of a given lesson. Code

examples are complete and standalone. The code for each lesson will run as-is with no code

xvii

from prior lessons or third-parties required beyond the installation of the required packages. A

complete working example is presented with each tutorial for you to inspect and copy-and-paste.

All source code is also provided with the book and I would recommend running the provided

ﬁles whenever possible to avoid any copy-paste issues.

The provided code was developed in a text editor and intended to be run on the command

line. No special IDE or notebooks are required. If you are using a more advanced development

environment and are having trouble, try running the example from the command line instead.

All code examples were tested on a POSIX-compatible machine with Python 3.

About Further Reading

Each lesson includes a list of further reading resources. This may include:



Books and book chapters.



API documentation.



Articles and Webpages.

Wherever possible, I try to list and link to the relevant API documentation for key functions

used in each lesson so you can learn more about them. I have tried to link to books on Amazon

so that you can learn more about them. I don’t know everything, and if you discover a good

resource related to a given lesson, please let me know so I can update the book.

About Getting Help

You might need help along the way. Don’t worry; you are not alone.



Help with a Technique?

If you need help with the technical aspects of a speciﬁc

operation or technique, see the Further Reading section at the end of each lesson.



Help with Python APIs?

If you need help with using the NumPy or SciPy libraries,

see the list of resources in the Further Reading section at the end of each lesson, and also

see Appendix A.



Help with your workstation?

If you need help setting up your environment, I would

recommend using Anaconda and following my tutorial in Appendix B.



Help with the math?

I provided a list of locations where you can search for answers

and ask questions about statistics math in Appendix A. You can also see Appendix C for

a crash course on math notation.



Help in general? You can shoot me an email. My details are in Appendix A.

Summary

Are you ready? Let’s dive in! Next up you will discover a gentle introduction to the ﬁeld of

statistics.

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