实例介绍
【实例简介】【2018新书】Mathematical Analysis for Machine Learning and Data Mining（机器学习与数据挖掘中的数学分析）
【实例截图】
【核心代码】
Contents Preface vii Part I. Set-Theoretical and Algebraic Preliminaries 1 1. Preliminaries 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Sets and Collections . . . . . . . . . . . . . . . . . . . . . 4 1.3 Relations and Functions . . . . . . . . . . . . . . . . . . . 8 1.4 Sequences and Collections of Sets . . . . . . . . . . . . . . 16 1.5 Partially Ordered Sets . . . . . . . . . . . . . . . . . . . . 18 1.6 Closure and Interior Systems . . . . . . . . . . . . . . . . 28 1.7 Algebras and σ-Algebras of Sets . . . . . . . . . . . . . . 34 1.8 Dissimilarity and Metrics . . . . . . . . . . . . . . . . . . 43 1.9 Elementary Combinatorics . . . . . . . . . . . . . . . . . . 47 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 54 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 64 2. Linear Spaces 65 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.2 Linear Spaces and Linear Independence . . . . . . . . . . 65 2.3 Linear Operators and Functionals . . . . . . . . . . . . . . 74 2.4 Linear Spaces with Inner Products . . . . . . . . . . . . . 85 2.5 Seminorms and Norms . . . . . . . . . . . . . . . . . . . . 88 2.6 Linear Functionals in Inner Product Spaces . . . . . . . . 107 2.7 Hyperplanes . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 113 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 116 ix May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page x x Mathematical Analysis for Machine Learning and Data Mining 3. Algebra of Convex Sets 117 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.2 Convex Sets and Affine Subspaces . . . . . . . . . . . . . 117 3.3 Operations on Convex Sets . . . . . . . . . . . . . . . . . 129 3.4 Cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.5 Extreme Points . . . . . . . . . . . . . . . . . . . . . . . . 132 3.6 Balanced and Absorbing Sets . . . May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page xi Contents xi 5.4 Continuity of Functions between Metric Spaces . . . . . . 264 5.5 Separation Properties of Metric Spaces . . . . . . . . . . . 270 5.6 Completeness of Metric Spaces . . . . . . . . . . . . . . . 275 5.7 Pointwise and Uniform Convergence . . . . . . . . . . . . 283 5.8 The Stone-Weierstrass Theorem . . . . . . . . . . . . . . . 286 5.9 Totally Bounded Metric Spaces . . . . . . . . . . . . . . . 291 5.10 Contractions and Fixed Points . . . . . . . . . . . . . . . 295 5.11 The Hausdorff Metric Hyperspace of Compact Subsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 5.12 The Topological Space (R, O) . . . . . . . . . . . . . . . . 303 5.13 Series and Schauder Bases . . . . . . . . . . . . . . . . . . 307 5.14 Equicontinuity . . . . . . . . . . . . . . . . . . . . . . . . 315 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 318 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 327 6. Topological Linear Spaces 329 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 329 6.2 Topologies of Linear Spaces . . . . . . . . . . . . . . . . . 329 6.3 Topologies on Inner Product Spaces . . . . . . . . . . . . 337 6.4 Locally Convex Linear Spaces . . . . . . . . . . . . . . . . 338 6.5 Continuous Linear Operators . . . . . . . . . . . . . . . . 340 6.6 Linear Operators on Normed Linear Spaces . . . . . . . . 341 6.7 Topological Aspects of Convex Sets . . . . . . . . . . . . . 348 6.8 The Relative Interior . . . . . . . . . . . . . . . . . . . . . 351 6.9 Separation of Convex Sets . . . . . . . . . . . . . . . . . . 356 6.10 Theorems of Alternatives . . . . . . . . . . . . . . . . . . 366 6.11 The Contingent Cone . . . . . . . . . . . . . . . . . . . . 370 6.12 Extreme Points and Krein-Milman Theorem . . . . . . . . 373 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 375 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 381 Part III. Measure and Integration 383 7. Measurable Spaces and Measures 385 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 385 7.2 Measurable Spaces . . . . . . . . . . . . . . . . . . . . . . 385 7.3 Borel Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 7.4 Measurable Functions . . . . . . . . . . . . . . . . . . . . 392 May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page xii xii Mathematical Analysis for Machine Learning and Data Mining 7.5 Measures and Measure Spaces . . . . . . . . . . . . . . . . 398 7.6 Outer Measures . . . . . . . . . . . . . . . . . . . . . . . . 417 7.7 The Lebesgue Measure on Rn . . . . . . . . . . . . . . . . 427 7.8 Measures on Topological Spaces . . . . . . . . . . . . . . . 450 7.9 Measures in Metric Spaces . . . . . . . . . . . . . . . . . . 453 7.10 Signed and Complex Measures . . . . . . . . . . . . . . . 456 7.11 Probability Spaces . . . . . . . . . . . . . . . . . . . . . . 464 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 470 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 484 8. Integration 485 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 485 8.2 The Lebesgue Integral . . . . . . . . . . . . . . . . . . . . 485 8.2.1 The Integral of Simple Measurable Functions . . . 486 8.2.2 The Integral of Non-negative Measurable Functions . . . . . . . . . . . . . . . . . . . . . . . 491 8.2.3 The Integral of Real-Valued Measurable Functions . . . . . . . . . . . . . . . . . . . . . . . 500 8.2.4 The Integral of Complex-Valued Measurable Functions . . . . . . . . . . . . . . . . . . . . . . . 505 8.3 The Dominated Convergence Theorem . . . . . . . . . . . 508 8.4 Functions of Bounded Variation . . . . . . . . . . . . . . . 512 8.5 Riemann Integral vs. Lebesgue Integral . . . . . . . . . . 517 8.6 The Radon-Nikodym Theorem . . . . . . . . . . . . . . . 525 8.7 Integration on Products of Measure Spaces . . . . . . . . 533 8.8 The Riesz-Markov-Kakutani Theorem . . . . . . . . . . . 540 8.9 Integration Relative to Signed Measures and Complex Measures . . . . . . . . . . . . . . . . . . . . . . 547 8.10 Indefinite Integral of a Function . . . . . . . . . . . . . . . 549 8.11 Convergence in Measure . . . . . . . . . . . . . . . . . . . 551 8.12 Lp and Lp Spaces . . . . . . . . . . . . . . . . . . . . . . . 556 8.13 Fourier Transforms of Measures . . . . . . . . . . . . . . . 565 8.14 Lebesgue-Stieltjes Measures and Integrals . . . . . . . . . 569 8.15 Distributions of Random Variables . . . . . . . . . . . . . 572 8.16 Random Vectors . . . . . . . . . . . . . . . . . . . . . . . 577 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 582 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 593 May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page xiii Contents xiii Part IV. Functional Analysis and Convexity 595 9. Banach Spaces 597 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 597 9.2 Banach Spaces — Examples . . . . . . . . . . . . . . . . . 597 9.3 Linear Operators on Banach Spaces . . . . . . . . . . . . 603 9.4 Compact Operators . . . . . . . . . . . . . . . . . . . . . 610 9.5 Duals of Normed Linear Spaces . . . . . . . . . . . . . . . 612 9.6 Spectra of Linear Operators on Banach Spaces . . . . . . 616 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 619 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 623 10. Differentiability of Functions Defined on Normed Spaces 625 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 625 10.2 The Fr´echet and Gˆateaux Differentiation . . . . . . . . . . 625 10.3 Taylor’s Formula . . . . . . . . . . . . . . . . . . . . . . . 649 10.4 The Inverse Function Theorem in Rn . . . . . . . . . . . . 658 10.5 Normal and Tangent Subspaces for Surfaces in Rn . . . . 663 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 666 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 675 11. Hilbert Spaces 677 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 677 11.2 Hilbert Spaces — Examples . . . . . . . . . . . . . . . . . 677 11.3 Classes of Linear Operators in Hilbert Spaces . . . . . . . 679 11.3.1 Self-Adjoint Operators . . . . . . . . . . . . . . . 681 11.3.2 Normal and Unitary Operators . . . . . . . . . . . 683 11.3.3 Projection Operators . . . . . . . . . . . . . . . . 684 11.4 Orthonormal Sets in Hilbert Spaces . . . . . . . . . . . . 686 11.5 The Dual Space of a Hilbert Space . . . . . . . . . . . . . 703 11.6 Weak Convergence . . . . . . . . . . . . . . . . . . . . . . 704 11.7 Spectra of Linear Operators on Hilbert Spaces . . . . . . 707 11.8 Functions of Positive and Negative Type . . . . . . . . . . 712 11.9 Reproducing Kernel Hilbert Spaces . . . . . . . . . . . . . 722 11.10 Positive Operators in Hilbert Spaces . . . . . . . . . . . . 733 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 736 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 745 May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page xiv xiv Mathematical Analysis for Machine Learning and Data Mining 12. Convex Functions 747 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 747 12.2 Convex Functions — Basics . . . . . . . . . . . . . . . . . 748 12.3 Constructing Convex Functions . . . . . . . . . . . . . . . 756 12.4 Extrema of Convex Functions . . . . . . . . . . . . . . . . 759 12.5 Differentiability and Convexity . . . . . . . . . . . . . . . 760 12.6 Quasi-Convex and Pseudo-Convex Functions . . . . . . . 770 12.7 Convexity and Inequalities . . . . . . . . . . . . . . . . . . 775 12.8 Subgradients . . . . . . . . . . . . . . . . . . . . . . . . . 780 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 793 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 815 Part V. Applications 817 13. Optimization 819 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 819 13.2 Local Extrema, Ascent and Descent Directions . . . . . . 819 13.3 General Optimization Problems . . . . . . . . . . . . . . . 826 13.4 Optimization without Differentiability . . . . . . . . . . . 827 13.5 Optimization with Differentiability . . . . . . . . . . . . . 831 13.6 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843 13.7 Strong Duality . . . . . . . . . . . . . . . . . . . . . . . . 849 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 854 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 863 14. Iterative Algorithms 865 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 865 14.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . 865 14.3 The Secant Method . . . . . . . . . . . . . . . . . . . . . 869 14.4 Newton’s Method in Banach Spaces . . . . . . . . . . . . 871 14.5 Conjugate Gradient Method . . . . . . . . . . . . . . . . . 874 14.6 Gradient Descent Algorithm . . . . . . . . . . . . . . . . . 879 14.7 Stochastic Gradient Descent . . . . . . . . . . . . . . . . . 882 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 884 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 892 May 2, 2018 11:28 Mathematical Analysis for Machine Learning 9in x 6in b3234-main page xv Contents xv 15. Neural Networks 893 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 893 15.2 Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893 15.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 895 15.4 Neural Networks as Universal Approximators . . . . . . . 896 15.5 Weight Adjustment by Back Propagation . . . . . . . . . 899 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 902 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 907 16. Regression 909 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 909 16.2 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . 909 16.3 A Statistical Model of Linear Regression . . . . . . . . . . 912 16.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 914 16.5 Ridge Regression . . . . . . . . . . . . . . . . . . . . . . . 916 16.6 Lasso Regression and Regularization . . . . . . . . . . . . 917 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 920 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 924 17. Support Vector Machines 925 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 925 17.2 Linearly Separable Data Sets . . . . . . . . . . . . . . . . 925 17.3 Soft Support Vector Machines . . . . . . . . . . . . . . . . 930 17.4 Non-linear Support Vector Machines . . . . . . . . . . . . 933 17.5 Perceptrons . . . . . . . . . . . . . . . . . . . . . . . . . . 939 Exercises and Supplements . . . . . . . . . . . . . . . . . . . . . 941 Bibliographical Comments . . . . . . . . . . . . . . . . . . . . . 947 Bibliography 949 Index 957
【2018新书】Mathematical Analysis for Machine Learning and Data Mining
好例子网口号：伸出你的我的手 — 分享！
小贴士
感谢您为本站写下的评论，您的评论对其它用户来说具有重要的参考价值，所以请认真填写。
- 类似“顶”、“沙发”之类没有营养的文字，对勤劳贡献的楼主来说是令人沮丧的反馈信息。
- 相信您也不想看到一排文字/表情墙，所以请不要反馈意义不大的重复字符，也请尽量不要纯表情的回复。
- 提问之前请再仔细看一遍楼主的说明，或许是您遗漏了。
- 请勿到处挖坑绊人、招贴广告。既占空间让人厌烦，又没人会搭理，于人于己都无利。
关于好例子网
本站旨在为广大IT学习爱好者提供一个非营利性互相学习交流分享平台。本站所有资源都可以被免费获取学习研究。本站资源来自网友分享，对搜索内容的合法性不具有预见性、识别性、控制性，仅供学习研究，请务必在下载后24小时内给予删除，不得用于其他任何用途，否则后果自负。基于互联网的特殊性，平台无法对用户传输的作品、信息、内容的权属或合法性、安全性、合规性、真实性、科学性、完整权、有效性等进行实质审查；无论平台是否已进行审查，用户均应自行承担因其传输的作品、信息、内容而可能或已经产生的侵权或权属纠纷等法律责任。本站所有资源不代表本站的观点或立场，基于网友分享，根据中国法律《信息网络传播权保护条例》第二十二与二十三条之规定，若资源存在侵权或相关问题请联系本站客服人员，点此联系我们。关于更多版权及免责申明参见 版权及免责申明
网友评论
我要评论