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機器學習基石上 (Machine Learning Foundations)---Mathematical Foundations

Machine learning is the study that allows computers to adaptively improve their performance with experience accumulated from the data observed. Our two sister courses teach the most fundamental algorithmic, theoretical and practical tools that any user of machine learning needs to know. This first course of the two would focus more on mathematical tools, and the other course would focus more on algorithmic tools. [機器學習旨在讓電腦能由資料中累積的經驗來自我進步。我們的兩項姊妹課程將介紹各領域中的機器學習使用者都應該知道的基礎演算法、理論及實務工具。本課程將較為著重數學類的工具，而另一課程將較為著重方法類的工具。]

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What's inside

Syllabus

第一講：The Learning Problem

what machine learning is and its connection to applications and other fields

第二講：Learning to Answer Yes/No

your first learning algorithm (and the world's first!) that "draws the line" between yes and no by adaptively searching for a good line based on data

第三講：Types of Learning

learning comes with many possibilities in different applications, with our focus being binary classification or regression from a batch of supervised data with concrete features

第四講：Feasibility of Learning

learning can be "probably approximately correct" when given enough statistical data and finite number of hypotheses

第五講：Training versus Testing

what we pay in choosing hypotheses during training: the growth function for representing effective number of choices

第六講: Theory of Generalization

test error can approximate training error if there is enough data and growth function does not grow too fast

第七講: The VC Dimension

learning happens if there is finite model complexity (called VC dimension), enough data, and low training error

第八講: Noise and Error

learning can still happen within a noisy environment and different error measures

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Taught by 林軒田, whose research influences many of the key topics and tools taught in this course

Suitable for those who want a strong foundation in the fundamentals of machine learning

Covers the basics of machine learning algorithms and theory, making it accessible to beginners

Provides a solid foundation for further exploration in machine learning, by giving an enough background information

Introduces other basic topics in machine learning, like the types of learning and feasibility of learning

Requires some prior background in statistics and probability

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Reviews summary

A math-heavy foundation in ml

This course on the mathematical foundations of ML presents theoretical concepts in great detail. Students appreciate the depth of knowledge offered but note that the difficulty can be high, especially for those without a strong background in math. The material is presented in a logical and structured way, making it easier to grasp complex topics.

Concepts are explained in an organized way.

"講解十分有條理，邏輯好理解。"

Covers ML theory with mathematical proofs.

"數理推导及其丰富，谢谢老师"

"老师讲课讲得非常好！---上的数学理论要求比较高"

Assignments can be challenging.

"This course is not as fantastic as it is widely advertised. The material taught is not enough to cope with the difficulty of homework."

Requires a strong math background.

"Really great theoretical ML course! And it is really hard lol~"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 機器學習基石上 (Machine Learning Foundations)---Mathematical Foundations with these activities:

阅读《机器学习实战》

Show steps

通过阅读经典著作，深入了解机器学习的基础概念和算法。

View Machine Learning with Python dialysis combat... on Amazon

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阅读绪论和第 1-3 章
完成第 1-3 章的练习题

学习 TensorFlow 的基础教程

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通过实践教程，掌握机器学习框架 TensorFlow 的使用，为实践机器学习算法奠定基础。

Browse courses on TensorFlow

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完成 TensorFlow 官网上的入门教程
尝试构建一个简单的线性回归模型

撰写机器学习博客文章

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通过分享知识，巩固对机器学习概念的理解，并提高沟通能力。

Show steps

选择一个感兴趣的机器学习主题
研究主题并整理相关材料
撰写博客文章，深入浅出地阐述主题

One other activity

Expand to see all activities and additional details

Show all four activities

阅读《Pattern Recognition and Machine Learning》

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通过阅读高级著作，拓展对机器学习理论和方法的理解。

View Pattern Recognition and Machine Learning... on Amazon

Show steps

阅读绪论和第 1-4 章
完成第 1-4 章的习题

Career center

Learners who complete 機器學習基石上 (Machine Learning Foundations)---Mathematical Foundations will develop knowledge and skills that may be useful to these careers:

Machine Learning Engineer

Machine Learning Engineers are responsible for developing and maintaining machine learning models. To do so, it is essential to have a strong foundation in the mathematics of machine learning, which Machine Learning Foundations will provide you. In particular, The Learning Problem can help you understand the fundamental concepts of machine learning, and Theory of Generalization can help you understand how to generalize test error from training error.

See salaries and explore the career path for Machine Learning Engineer

Artificial Intelligence Engineer

Artificial Intelligence Engineers are responsible for developing and maintaining artificial intelligence systems. To do so, it is essential to have a strong foundation in machine learning, and Machine Learning Foundations can provide you with that foundation. In particular, The Learning Problem will introduce you to the fundamental concepts of machine learning and its connection to other fields.

See salaries and explore the career path for Artificial Intelligence Engineer

Data Scientist

As a Data Scientist, you would collect, clean, analyze, and interpret data to draw informed conclusions and generate predictions. Machine Learning Foundations can equip you with the mathematical background for building machine learning models that process this data. In particular, The Learning Problem introduces the fundamental concepts of machine learning and shows you how it is used across different fields. The VC Dimension can help you learn about handling noisy environments and its impact on learning.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve complex problems in business and industry, primarily through the use of machine learning algorithms. Machine Learning Foundations can help you will provide you with the mathematical background for building and analyzing these models. In particular, The Learning Problem introduces the fundamental concepts of machine learning, and Feasibility of Learning can help you understand how to assess the feasibility of learning given different parameters.

See salaries and explore the career path for Operations Research Analyst

Data Engineer

Data Engineers are responsible for building, deploying, and managing big data systems. To do so, it is indispensable to understand data well, and the mathematical tools of Machine Learning Foundations can help you build that foundation. The Learning Problem and Types of Learning will introduce you to fundamental concepts of machine learning and the different types of learning algorithms. Feasibility of Learning will show you how to evaluate the feasibility of learning based on statistical data and number of hypotheses.

See salaries and explore the career path for Data Engineer

Statistician

Statisticians are responsible for collecting, analyzing, and interpreting data. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Statistician

Data Analyst

Data Analysts are responsible for collecting, cleaning, and analyzing data to draw informed conclusions. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Data Analyst

Actuary

Actuaries are responsible for assessing and managing risk. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Actuary

Risk Analyst

Risk Analysts are responsible for assessing and managing risk. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Risk Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Quantitative Analyst

Business Analyst

Business Analysts are responsible for analyzing business data to make recommendations for improvement. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Business Analyst

Consultant

Consultants are responsible for providing advice to businesses on a variety of topics. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Consultant

Software Engineer

Software Engineers are responsible for developing and maintaining software systems. To do so, it is helpful to have a strong foundation in the mathematics of machine learning, which Machine Learning Foundations will provide you. In particular, The Learning Problem will introduce you to the fundamental concepts of machine learning, and Theory of Generalization can help you understand how to generalize test error from training error.

See salaries and explore the career path for Software Engineer

Teacher

Teachers are responsible for educating students in a variety of subjects. To teach data science or machine learning, it is helpful to have a strong foundation in the mathematics of machine learning, which Machine Learning Foundations will provide you. In particular, The Learning Problem will introduce you to the fundamental concepts of machine learning, and Theory of Generalization can help you understand how to generalize test error from training error.

See salaries and explore the career path for Teacher

Financial Analyst

Financial Analysts use data to make investment recommendations. To do so, it is helpful to have a strong foundation in statistics and machine learning, which Machine Learning Foundations can provide you. In particular, The Learning Problem and Types of Learning will introduce you to the fundamental concepts of machine learning and the different types of learning algorithms.

See salaries and explore the career path for Financial Analyst

Reading list

We've selected 18 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in 機器學習基石上 (Machine Learning Foundations)---Mathematical Foundations.

机器学习理论导引

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本书是清华大学周志华教授编写的机器学习教材，全面系统地介绍了机器学习的基本原理、算法和应用。内容涵盖了监督学习、无监督学习、强化学习和深度学习，并提供了丰富的习题和编程练习。

機器學習基石上 (Machine Learning Foundations)---Mathematical Foundations

What's inside

Syllabus

Good to know

Save this course

Reviews summary

A math-heavy foundation in ml

Activities

Career center

Reading list

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