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所在平台: Udemy |
课程主页: https://www.udemy.com/course/matrix-calculus-machine-learning/
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课程名称：数学 0-1：数据科学与机器学习中的矩阵微积分 课程概述：欢迎来到矩阵微积分的精彩世界，这是理解和解决机器学习与数据科学问题的基本工具。在本课程中，我们将深入探讨支撑这些领域众多算法和技术的强大数学基础。课程结束时，您将具备应对矩阵相关的导数、梯度和优化等复杂问题的知识和技能。 课程目标： - 理解矩阵微积分的基础知识，包括线性形式和二次形式及其导数。 - 学会使用著名的矩阵咖啡馆（Matrix Cookbook）进行广泛的矩阵微积分操作。 - 掌握如梯度下降法和牛顿法等优化技术，涵盖一维及多维场景。 - 将所学概念应用于现实世界中的机器学习和数据科学问题，并结合实际操作和Python代码示例。 为何学习矩阵微积分？矩阵微积分是机器学习和数据科学的语言。在这些领域中，我们常常处理高维数据，因此矩阵及其导数成为解决问题的自然表现形式。理解矩阵微积分对于开发和分析算法、构建预测模型及理解大量数据至关重要。 课程结构： - 第一部分：线性和二次形式。我们将探讨线性形式的基本概念及其导数，这些内容出现在许多重要的机器学习模型中，包括线性回归、逻辑回归、支持向量机（SVM）和深度神经网络。同时，深入了解与优化问题相关的二次形式。 - 第二部分：优化技术。我们将探讨两种关键的优化方法：梯度下降法和牛顿法，学习在一维及高维空间中的优化技巧，且提供Python代码示例以帮助理解和实践。 课程结构包括理论引导、数学推导及直观解释、实践练习和Python代码示例，并提供提问与讨论的机会，以加深对内容的理解。 先决条件： - 建议具备基础的线性代数、微积分和Python编程知识。 - 强烈的学习意愿和探索矩阵微积分的兴趣。 结论：矩阵微积分是机器学习和数据科学领域不可或缺的工具，它使您能够理解、创建和优化推动当今数据驱动世界的算法与决策。本课程将为您提供必要的知识和技能，帮助您在矩阵微积分的复杂世界中游刃有余，助您成为一名优秀的数据科学家或机器学习工程师。让我们共同深入，拥抱矩阵的世界，揭开数据科学与机器学习的秘密！
Welcome to the exciting world of Matrix Calculus, a fundamental tool for understanding and solving problems in machine learning and data science. In this course, we will dive into the powerful mathematics that underpin many of the algorithms and techniques used in these fields. By the end of this course, you'll have the knowledge and skills to navigate the complex landscape of derivatives, gradients, and optimizations involving matrices.Course Objectives:Understand the basics of matrix calculus, linear and quadratic forms, and their derivatives.Learn how to utilize the famous Matrix Cookbook for a wide range of matrix calculus operations.Gain proficiency in optimization techniques like gradient descent and Newton's method in one and multiple dimensions.Apply the concepts learned to real-world problems in machine learning and data science, with hands-on exercises and Python code examples.Why Matrix Calculus? Matrix calculus is the language of machine learning and data science. In these fields, we often work with high-dimensional data, making matrices and their derivatives a natural representation for our problems. Understanding matrix calculus is crucial for developing and analyzing algorithms, building predictive models, and making sense of the vast amounts of data at our disposal.Section 1: Linear and Quadratic Forms In the first part of the course, we'll explore the basics of linear and quadratic forms, and their derivatives. The linear form appears in all of the most fundamental and popular machine learning models, including linear regression, logistic regression, support vector machine (SVM), and deep neural networks. We will also dive into quadratic forms, which are fundamental to understanding optimization problems, which appear in regression, portfolio optimization in finance, signal processing, and control theory.The Matrix Cookbook is a valuable resource that compiles a wide range of matrix derivative formulas in one place. You'll learn how to use this reference effectively, saving you time and ensuring the accuracy of your derivations.Section 2: Optimization Techniques Optimization lies at the heart of many machine learning and data science tasks. In this section, we will explore two crucial optimization methods: gradient descent and Newton's method. You'll learn how to optimize not only in one dimension but also in high-dimensional spaces, which is essential for training complex models. We'll provide Python code examples to help you grasp the practical implementation of these techniques.Course Structure:Each lecture will include a theoretical introduction to the topic.We will work through relevant mathematical derivations and provide intuitive explanations.Hands-on exercises will allow you to apply what you've learned to real-world problems.Python code examples will help you implement and experiment with the concepts.There will be opportunities for questions and discussions to deepen your understanding.Prerequisites:Basic knowledge of linear algebra, calculus, and Python programming is recommended.A strong desire to learn and explore the fascinating world of matrix calculus.Conclusion: Matrix calculus is an indispensable tool in the fields of machine learning and data science. It empowers you to understand, create, and optimize algorithms that drive innovation and decision-making in today's data-driven world. This course will equip you with the knowledge and skills to navigate the intricate world of matrix calculus, setting you on a path to become a proficient data scientist or machine learning engineer. So, let's dive in, embrace the world of matrices, and unlock the secrets of data science and machine learning together!
