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。]

• 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