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

Go to Course: https://www.coursera.org/learn/ntumlone-mathematicalfoundations

Introduction

### Course Review: Machine Learning Foundations - Mathematical Foundations on Coursera **Course Overview:** The course "機器學習基石上 (Machine Learning Foundations) - Mathematical Foundations" offered on Coursera is an essential introduction to the mathematical underpinnings of machine learning. In a world increasingly dominated by data, understanding the principles that allow machines to learn from this data is of utmost importance. This course lays down the fundamental theoretical tools that form the backbone of more advanced algorithms and applications in ML. The course is part of a two-part series, with this first segment focusing specifically on mathematical tools, while the second will delve into algorithmic techniques. It is tailored for individuals keen on building a robust foundation in the key concepts that drive machine learning applications across various domains. **Course Content and Syllabus:** The course is structured into eight comprehensive lectures, each addressing a critical aspect of the mathematical foundations of machine learning: 1. **The Learning Problem**: This introductory lecture contextualizes machine learning, explaining its core principles and how it integrates with real-world applications. 2. **Learning to Answer Yes/No**: Students will learn their first algorithm, which introduces the concept of binary classification by adaptively determining decision boundaries based on input data. 3. **Types of Learning**: Focusing on binary classification and regression, this lecture examines the various learning paradigms and their applications using supervised data. 4. **Feasibility of Learning**: The discussion centers on the conditions under which learning can be considered "probably approximately correct,” grounding the concept in statistical theory. 5. **Training versus Testing**: This session emphasizes the balance between training hypotheses and the implications on model selection, introducing the growth function as a key component of the learning paradigm. 6. **Theory of Generalization**: A crucial principle in machine learning, generalization is explored in detail, conveying how test errors can be approximated using training data under specified conditions. 7. **The VC Dimension**: Students learn about the Vapnik-Chervonenkis (VC) dimension, a core concept that determines model capacity in learning, highlighting the necessity of sufficient data and low error rates for effective learning. 8. **Noise and Error**: This concluding lecture addresses the realities of noise in data and different error metrics, reinforcing that learning is still possible even in less-than-ideal conditions. **Recommendation:** I highly recommend this course for anyone interested in gaining a deep understanding of the mathematical foundations of machine learning. It is particularly suitable for: - **Beginners**: If you're new to the field, the structured lessons provide a clear and manageable path to understanding key concepts. - **Students and Professionals**: For those already in academia or industry, this course will bolster your skill set, enriching your ability to work with machine learning algorithms with a solid mathematical background. - **Data Enthusiasts**: This course will equip you with the conceptual tools necessary to critically engage with machine learning literature, making you better prepared for advanced studies or practical applications. Coursera makes the learning experience enjoyable with its user-friendly interface, additional resources, and community forums, providing ample opportunities for discussion and clarification. In sum, "Machine Learning Foundations - Mathematical Foundations" is an invaluable resource for anyone serious about diving into the world of machine learning. It not only primes you for algorithmic studies but also enriches your analytical thinking regarding data and algorithms in practice.

Syllabus

第一講：The Learning Problem

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

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

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

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

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

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

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

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