This math book, which has been written by senior ml researchers for 7 years, is available in free electronic version

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This few days , a copy Free math tutorial Be crazy in machine learning circle .

This book is called 《 Probability values 》（Probabilistic Numerics）, The author is from Mapu Institute 、 Oxford University and INRIA Three machine learning bulls , One of them has a Google academic citation of 17000+.

Philipp Hennig、Michael A. Osborne and Hans P. Kersting When the three authors wrote this book , A total of 7 year , Long 400 Multi page .

After the release of the new book , One of the authors Philipp Hennig Sigh on twitter ： It finally came out .

In addition to physical publishing , The authors also shared the free electronic version of the book online .（ps: At the end of the article, you can check ~）

say concretely , This book hopes that from a mathematical point of view , Teach everyone how Optimize machine learning model .

Usually , Machine learning involves a lot of linear algebra 、 integral 、 Or finding the minimum value of nonlinear function , And these problems often Occupy a lot of computing resources .

therefore , The author hopes to explain the principle of numerical calculation of probability behind , Let's understand the model “ Reasons for energy consumption ”, So as to better optimize the model .

For this book , Lecturer in machine learning at the University of Edinburgh Antonio Vergari I like it ：

Numerical integration is not just machine learning 、 The core of AI , Also Engineering 、 The core of physics and other fields .

In addition to the angle of numerical analysis , From the field of model reasoning and propagation uncertainty , It's also very valuable .

What's the use of this book ？

In the computer , There are many problems related to the solution of complex systems .

For example, using computers to predict the weather 、 Cancer cell gene mutation and other problems , Are related to complex systems , Because this system is easy to introduce uncertainty , It will also lead to a waste of computing resources .

In machine learning , The prediction results given by the model are not necessarily reliable , Various factors will also lead to the uncertainty of output results .

at present , With the improvement of data accuracy , The amount of calculation caused by uncertainty is also further increasing .

Mathematically speaking , How to quantify this uncertainty 、 Reduce the waste of computing resources , It involves probability values （ probability statistics 、 Numerical analysis, etc ） The theory and method of .

If you can master its theoretical skills , Computers can process data more efficiently , This uncertainty can also be used to make the optimal decision of calculation , Including the use of Bayesian inference and other theories , To build more flexible 、 More efficient 、 More personalized Algorithm .

In the book , The author not only fully explained the principle of probability numerical calculation , It also further teaches you how to optimize a machine learning model by hand through exercises , And all important exercises are equipped with solutions .

This has been praised by netizens .

As the author said in the introduction ：

We wrote this book for everyone who needs to use numerical calculations , Whether astrophysicists or deep learning hackers .

For those who are or are planning to become developers in the field of numerical computing , And people who are learning machine learning , We hope this book will be interesting .

What does the book say ？

With the rapid development of machine learning , This book aims to give an overview of the emerging field of probability numerical .

The content of the book mainly starts from the following aspects ：

1、 Mathematical basis

Probabilistic numerical computation is the bridge between machine learning and Applied Mathematics , To learn machine learning , Mathematics is an inextricable topic .

This chapter is about the probability reasoning that will be used later 、 Gauss function 、 Return to 、 Key concepts such as linear algebra are introduced .

Readers with a background in statistics or machine learning will read easily ～

2、 integral

This chapter uses the basic concept of integral , The core of probability numerical calculation is introduced —— Bayes integral formula 、 Classical quadrature formula and other theories , And reconstruct the existing numerical quadrature rules , Develop new functions on existing methods .

3、 linear algebra

Linear algebra operations , It can be said to be the most basic numerical calculation . And matrix operation 、 Vector operations are the same , They are the cornerstone of almost all heavyweight operations in the contemporary computer field . therefore , The research in this field is very in-depth .

First , You need to know some basic knowledge of linear algebra —— Vectorization matrix 、 Kronecker's product 、 Positive definite matrix 、 Frobenius matrix norm and so on .

secondly , The book is devoted to cultivating an intuitive understanding of linear algebra , This helps us better understand the essence of Mathematics 、 Understand the simplest routine behind complex formulas .

4、 Local optimization

In the process of numerical calculation , Improper modeling will lead to many problems , This is particularly evident in areas such as deep learning .

This chapter focuses on nonlinear optimization problems , Take the step selection as an example to explain .

5、 Global optimization

This chapter introduces a very effective global optimization algorithm —— Bayesian optimization , This method can solve the problem of high computing cost without limitation 、 The problem of unknown derivative , And the global minimum can be found in as few steps as possible .

6、 Solution of ordinary differential equations

In the process of studying ordinary differential equations , We need to treat dialectically the relationship between ordinary differential equations and partial differential equations , And it needs to be transformed in time . such , We can flexibly solve ordinary differential equations .

This chapter mainly starts from the classic ODE solver 、ODE Explain the filter and smoother .

7、 prospects

The future of probability values is vast , Many basic mathematics in this field 、 Engineering and philosophical problems remain to be solved . In this chapter , We will focus on some open issues that may at least affect the development of academia in the next decade .

8、 practice & answer

In addition to the above written materials , This book also provides many exercises with solutions .

Who are the three authors ？

One of the authors Michael A. Osborne Shared on twitter yesterday “ We from 2015 In, he began to write this book about the new computing foundation of machine learning , Now it grows up like my child ”.

Michael A. Osborne, Professor of machine learning at Oxford University , It's also Mind Foundry Co founder of the company .

Osborne Focus on active learning in the field of machine learning 、 Bayesian Optimization and Bayesian integration , And he is keen on the emerging field of probability value .

Philipp Hennig, Professor of machine learning methods at the University of tibingen , It's also MPII（ Marx · Planck Institute for Intelligent Systems ） Part time researcher ,ELLIS( European learning and Intelligent Systems Laboratory ) Learn machine theory 、 Co director of the algorithms and computing research project .

In his career , Probabilistic numerical method is one of the main research directions .Hennig The research of Amy · Norte (Emmy Noether)、 Marx · The Planck (Max Planck) and ERC Scholarship support .

Hans P. Kersting,INRIA（ National Institute of information and automation, France ） and ENS（ Ecole Normale Superieure ） Postdoctoral researcher of , Engaged in machine learning , The main research direction is Bayesian inference 、 Dynamic system optimization .

Finally, the author's 《 Probability values 》 Free electronic version , Interested friends, take a quick look ！

《 Probability values 》：https://www.probabilistic-numerics.org/assets/ProbabilisticNumerics.pdf