机器学习基础 – 数学基础

课程概况

机器学习旨在让电脑能由资料中累积的经验来自我进步。本课程将介绍各领域中的机器学习使用者都应该知道的基础算法、理论及实用工具。

欢迎大家！这门课将采用英文投影片配合中文的教学讲解，我们希望能借这次中文教学的机会，将机器学习介绍给更多华人世界的初学者。课程中使用的英文投影片不会使用到艰深的英文，如果你能了解以下两段的课程简介，你应该也可以了解课程所使用的英文投影片。

Machine learning is an exciting field with lots of applications in engineering, science, finance, and commerce. It is also a very dynamic field, where many new techniques are being designed every day, and the hot techniques and theories at times can rise and disappear rapidly. Thus, users of machine learning from other fields often face the problem of choosing or using the techniques properly. In this course, we emphasize the necessary fundamentals that give any student of machine learning a solid foundation, and enable him or her to exploit current techniques properly, explore further techniques and theories, or perhaps to contribute their own in the future.

课程大纲

周1
完成时间为 2 小时
第一講：The Learning Problem
what machine learning is and its connection to applications and other fields
5 个视频 （总计 70 分钟）, 5 个阅读材料

周2
完成时间为 1 小时
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
4 个视频 （总计 61 分钟）

周3
完成时间为 1 小时
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
4 个视频 （总计 61 分钟）

周4
完成时间为 2 小时
第四講：Feasibility of Learning
learning can be "probably approximately correct" when given enough statistical data and finite number of hypotheses
4 个视频 （总计 60 分钟）, 1 个测验

周5
完成时间为 1 小时
第五講：Training versus Testing
what we pay in choosing hypotheses during training: the growth function for representing effective number of choices
4 个视频 （总计 53 分钟）

周6
完成时间为 1 小时
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
4 个视频 （总计 52 分钟）

周7
完成时间为 1 小时
第七講: The VC Dimension
learning happens if there is finite model complexity (called VC dimension), enough data, and low training error
4 个视频 （总计 50 分钟）

周8
完成时间为 2 小时
第八講: Noise and Error
learning can still happen within a noisy environment and different error measures

预备知识

我们希望修课的同学对于基本的微分、向量与矩阵运算、及机率的工具有所了解。有些作业会需要写作或执行一些程式，所以我们建议修课的同学能在你所熟悉的平台上有一些编程背景。

参考资料

虽然这门课的录影课程及投影片应该足以帮大家了解所有的内容，我们推荐有兴趣的同学们阅读 Learning from Data一书，该书包含了本课程中所介绍的大部份的内容。