人工智能的数学基础（影印版）
人工智能的数学基础（影印版）
Hala Nelson 著
出版时间：2024年03月
页数：568
“技术和人工智能市场就像一条河流，一部分比另一部分流动得更快。要想成功应用AI，需要具备评估流动方向的技能，还要有坚实的基础作为补充，本书以一种引人入胜、令人愉悦和包容的方式实现了这一点。Hala为人工智能未来的众多参与者带来了数学的乐趣！”
——Adri Purkayastha
法国巴黎银行AI运维风险和数字风险分析部门主管

许多部门和行业都渴望将AI和数据驱动技术整合到自己的系统和运营中。但要构建真正成功的AI系统，你需要牢掌握底层的数学知识。这本全面指南弥补了AI所展现出的无限潜力和应用与相关数学基础之间的存在的现实差距。
作者Hala Nelson并没有讨论高深的学术理论，而是以现实世界的应用和最先进的模型为重点，介绍了在人工智能领域发展所需的数学知识。你将在专门的AI背景下探索回归、神经网络、卷积、优化、概率、马尔可夫过程、微分方程等主题。工程师、数据科学家、数学家、科学家将为在AI和数学领域取得成功打下坚实的基础。
你将能够：
● 熟练运用AI、机器学习、数据科学和数学的语言
● 在数学结构下统一机器学习模型和自然语言模型
● 轻松处理图形和网络数据
● 探索真实数据，可视化空间变换，降低维度，处理图像
● 为不同的数据驱动项目选择合适的模型
● 探索AI的各种影响和局限性
  1. Preface
  2. 1. Why Learn the Mathematics of AI?
  3. What Is AI?
  4. Why Is AI So Popular Now?
  5. What Is AI Able to Do?
  6. What Are AI’s Limitations?
  7. What Happens When AI Systems Fail?
  8. Where Is AI Headed?
  9. Who Are the Current Main Contributors to the AI Field?
  10. What Math Is Typically Involved in AI?
  11. Summary and Looking Ahead
  12. 2. Data, Data, Data
  13. Data for AI
  14. Real Data Versus Simulated Data
  15. Mathematical Models: Linear Versus Nonlinear
  16. An Example of Real Data
  17. An Example of Simulated Data
  18. Mathematical Models: Simulations and AI
  19. Where Do We Get Our Data From?
  20. The Vocabulary of Data Distributions, Probability, and Statistics
  21. Continuous Distributions Versus Discrete Distributions (Density Versus Mass)
  22. The Power of the Joint Probability Density Function
  23. Distribution of Data: The Uniform Distribution
  24. Distribution of Data: The Bell-Shaped Normal (Gaussian) Distribution
  25. Distribution of Data: Other Important and Commonly Used Distributions
  26. The Various Uses of the Word “Distribution”
  27. A/B Testing
  28. Summary and Looking Ahead
  29. 3. Fitting Functions to Data
  30. Traditional and Very Useful Machine Learning Models
  31. Numerical Solutions Versus Analytical Solutions
  32. Regression: Predict a Numerical Value
  33. Logistic Regression: Classify into Two Classes
  34. Softmax Regression: Classify into Multiple Classes
  35. Incorporating These Models into the Last Layer of a Neural Network
  36. Other Popular Machine Learning Techniques and Ensembles of Techniques
  37. Performance Measures for Classification Models
  38. Summary and Looking Ahead
  39. 4. Optimization for Neural Networks
  40. The Brain Cortex and Artificial Neural Networks
  41. Training Function: Fully Connected, or Dense, Feed Forward Neural Networks
  42. Loss Functions
  43. Optimization
  44. Regularization Techniques
  45. Hyperparameter Examples That Appear in Machine Learning
  46. Assessing the Significance of the Input Data Features
  47. Summary and Looking Ahead
  48. 5. Convolutional Neural Networks and Computer Vision
  49. Convolution and Cross-Correlation
  50. Convolution from a Systems Design Perspective
  51. Convolution and One-Dimensional Discrete Signals
  52. Convolution and Two-Dimensional Discrete Signals
  53. Linear Algebra Notation
  54. Pooling
  55. A Convolutional Neural Network for Image Classification
  56. Summary and Looking Ahead
  57. 6. Singular Value Decomposition: Image Processing, Natural Language Processing, and Social Media
  58. Matrix Factorization
  59. Diagonal Matrices
  60. Matrices as Linear Transformations Acting on Space
  61. Three Ways to Multiply Matrices
  62. The Big Picture
  63. The Ingredients of the Singular Value Decomposition
  64. Singular Value Decomposition Versus the Eigenvalue Decomposition
  65. Computation of the Singular Value Decomposition
  66. The Pseudoinverse
  67. Applying the Singular Value Decomposition to Images
  68. Principal Component Analysis and Dimension Reduction
  69. Principal Component Analysis and Clustering
  70. A Social Media Application
  71. Latent Semantic Analysis
  72. Randomized Singular Value Decomposition
  73. Summary and Looking Ahead
  74. 7. Natural Language and Finance AI: Vectorization and Time Series
  75. Natural Language AI
  76. Preparing Natural Language Data for Machine Processing
  77. Statistical Models and the log Function
  78. Zipf’s Law for Term Counts
  79. Various Vector Representations for Natural Language Documents
  80. Cosine Similarity
  81. Natural Language Processing Applications
  82. Transformers and Attention Models
  83. Convolutional Neural Networks for Time Series Data
  84. Recurrent Neural Networks for Time Series Data
  85. An Example of Natural Language Data
  86. Finance AI
  87. Summary and Looking Ahead
  88. 8. Probabilistic Generative Models
  89. What Are Generative Models Useful For?
  90. The Typical Mathematics of Generative Models
  91. Shifting Our Brain from Deterministic Thinking to Probabilistic Thinking
  92. Maximum Likelihood Estimation
  93. Explicit and Implicit Density Models
  94. Explicit Density-Tractable: Fully Visible Belief Networks
  95. Explicit Density-Tractable: Change of Variables Nonlinear Independent Component Analysis
  96. Explicit Density-Intractable: Variational Autoencoders Approximation via Variational Methods
  97. Explicit Density-Intractable: Boltzman Machine Approximation via Markov Chain
  98. Implicit Density-Markov Chain: Generative Stochastic Network
  99. Implicit Density-Direct: Generative Adversarial Networks
  100. Example: Machine Learning and Generative Networks for High Energy Physics
  101. Other Generative Models
  102. The Evolution of Generative Models
  103. Probabilistic Language Modeling
  104. Summary and Looking Ahead
  105. 9. Graph Models
  106. Graphs: Nodes, Edges, and Features for Each
  107. Example: PageRank Algorithm
  108. Inverting Matrices Using Graphs
  109. Cayley Graphs of Groups: Pure Algebra and Parallel Computing
  110. Message Passing Within a Graph
  111. The Limitless Applications of Graphs
  112. Random Walks on Graphs
  113. Node Representation Learning
  114. Tasks for Graph Neural Networks
  115. Dynamic Graph Models
  116. Bayesian Networks
  117. Graph Diagrams for Probabilistic Causal Modeling
  118. A Brief History of Graph Theory
  119. Main Considerations in Graph Theory
  120. Algorithms and Computational Aspects of Graphs
  121. Summary and Looking Ahead
  122. 10. Operations Research
  123. No Free Lunch
  124. Complexity Analysis and O() Notation
  125. Optimization: The Heart of Operations Research
  126. Thinking About Optimization
  127. Optimization on Networks
  128. The n-Queens Problem
  129. Linear Optimization
  130. Game Theory and Multiagents
  131. Queuing
  132. Inventory
  133. Machine Learning for Operations Research
  134. Hamilton-Jacobi-Bellman Equation
  135. Operations Research for AI
  136. Summary and Looking Ahead
  137. 11. Probability
  138. Where Did Probability Appear in This Book?
  139. What More Do We Need to Know That Is Essential for AI?
  140. Causal Modeling and the Do Calculus
  141. Paradoxes and Diagram Interpretations
  142. Large Random Matrices
  143. Stochastic Processes
  144. Markov Decision Processes and Reinforcement Learning
  145. Theoretical and Rigorous Grounds
  146. Summary and Looking Ahead
  147. 12. Mathematical Logic
  148. Various Logic Frameworks
  149. Propositional Logic
  150. First-Order Logic
  151. Probabilistic Logic
  152. Fuzzy Logic
  153. Temporal Logic
  154. Comparison with Human Natural Language
  155. Machines and Complex Mathematical Reasoning
  156. Summary and Looking Ahead
  157. 13. Artificial Intelligence and Partial Differential Equations
  158. What Is a Partial Differential Equation?
  159. Modeling with Differential Equations
  160. Numerical Solutions Are Very Valuable
  161. Some Statistical Mechanics: The Wonderful Master Equation
  162. Solutions as Expectations of Underlying Random Processes
  163. Transforming the PDE
  164. Solution Operators
  165. AI for PDEs
  166. Hamilton-Jacobi-Bellman PDE for Dynamic Programming
  167. PDEs for AI?
  168. Other Considerations in Partial Differential Equations
  169. Summary and Looking Ahead
  170. 14. Artificial Intelligence, Ethics, Mathematics, Law, and Policy
  171. Good AI
  172. Policy Matters
  173. What Could Go Wrong?
  174. How to Fix It?
  175. Distinguishing Bias from Discrimination
  176. The Hype
  177. Final Thoughts
  178. Index
书名：人工智能的数学基础（影印版）
作者：Hala Nelson 著
国内出版社：东南大学出版社
出版时间：2024年03月
页数：568
书号：978-7-5766-1223-3
原版书书名：Essential Math for AI
原版书出版商：O'Reilly Media
Hala Nelson
 
Hala Nelson是詹姆斯·麦迪逊大学数学系副教授，专门研究数学建模，并为公共部门提供应急和基础设施服务方面的咨询。她拥有纽约大学库兰特数学科学研究所的数学博士学位。
 
 
The animal on the cover of Essential Math for AI is a harnessed bushbuck (Tragelaphus scriptus scriptus), an antelope found throughout sub-Saharan Africa. The animals live in many types of habitat, such as woodland, savanna, and rainforest. The harnessed bushbuck is named for a pattern of white stripes and spots along its back and flanks that resembles a saddle or harness. These white patches also appear on the animal’s neck, ears, and chin.

The harnessed bushbuck is the smallest of eight bushbuck subspecies, generally standing about 30 inches tall at the shoulder and weighing 70–100 pounds. Its coat is reddish-brown, though females tend to be lighter in color and have more conspicuous white markings. Male bushbucks also sport horns, which appear around the age of 10 months and eventually develop a single twist. Bushbucks graze on the leaves of trees and shrubs, as well as flowering plants—it is uncommon for them to eat grass.

The bushbuck is most active during the day and lives a solitary life within a defined territory. However, while they don’t gather in groups, neither are these animals overly aggressive. The male’s horns can be used in mating displays, to drive away competitors when a female is in heat, and for the rare territorial dispute, but adult bushbuck tend to avoid contact with each other. Female bushbucks bear one calf at a time, and hide the young one very carefully after birth, only visiting it to nurse. The mother also eats the calf ’s dung so predators are not drawn to the area. After about four months, the calf begins to accompany its mother to graze and play.
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定价：162.00元
书号：978-7-5766-1223-3
出版社：东南大学出版社
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