机器学习导论
Introduction to Machine Learning
AI总结：
本书系统介绍机器学习算法背后的数学基础，涵盖优化、监督学习、生成式方法、无监督学习及泛化理论。
摘要：
本书介绍了推动机器学习中许多算法的开发与分析的数学基础和技术。全书以一章导论开篇，描述贯穿全书使用的记号，并回顾微积分、线性代数和概率论中的基本概念，同时介绍一些测度论术语；该章可作为阅读使用这些工具的各章节的指南。导论部分的章节还提供矩阵分析和优化方面的背景材料，其中后一章为书中使用的许多算法提供理论支持，包括随机梯度下降、近端方法等。在讨论统计预测的基本概念之后，本书介绍再生核理论和 Hilbert 空间技术，这些内容在许多地方都会用到；随后阐述用于监督统计学习的各类算法，包括线性方法、支持向量机、决策树、boosting 和神经网络。之后主题转向生成式方法，首先有一章介绍采样方法以及 Markov 链理论入门；下一章描述图模型理论，介绍面向含潜变量模型的变分方法，以及基于深度学习的生成模型。接下来的章节聚焦无监督学习方法，用于聚类、因子分析和流形学习。本书最后一章偏重理论，讨论集中不等式和泛化界。
英文摘要：
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used throughout the book and serve at a reminder of basic concepts in calculus, linear algebra and probability and also introduces some measure theoretic terminology, which can be used as a reading guide for the sections that use these tools. The introductory chapters also provide background material on matrix analysis and optimization. The latter chapter provides theoretical support to many algorithms that are used in the book, including stochastic gradient descent, proximal methods, etc. After discussing basic concepts for statistical prediction, the book includes an introduction to reproducing kernel theory and Hilbert space techniques, which are used in many places, before addressing the description of various algorithms for supervised statistical learning, including linear methods, support vector machines, decision trees, boosting, or neural networks. The subject then switches to generative methods, starting with a chapter that presents sampling methods and an introduction to the theory of Markov chains. The following chapter describe the theory of graphical models, an introduction to variational methods for models with latent variables, and to deep-learning based generative models. The next chapters focus on unsupervised learning methods, for clustering, factor analysis and manifold learning. The final chapter of the book is theory-oriented and discusses concentration inequalities and generalization bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
