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Essential Math for AI
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Essential Math for AI

by Hala Nelson

Artificial Intelligence

Book Details

Book Title

Essential Math for AI

Author

Hala Nelson

Publisher

O'Reilly Media, Inc

Publication Date

2023

ISBN

9781098107635

Number of Pages

611

Language

English

Format

PDF

File Size

6MB

Subject

Artificial Intelligence

Table of Contents

  • Preface
  • 1. Why Learn the Mathematics of AI?
  • What Is AI?
  • Why Is AI So Popular Now?
  • What Is AI Able to Do?
  • What Are AI’s Limitations?
  • What Happens When AI Systems Fail?
  • Where Is AI Headed?
  • Who Are the Current Main Contributors to the AI Field?
  • What Math Is Typically Involved in AI?
  • Summary and Looking Ahead
  • 2. Data, Data, Data
  • Data for AI
  • Real Data Versus Simulated Data
  • Mathematical Models: Linear Versus Nonlinear
  • An Example of Real Data
  • An Example of Simulated Data
  • Mathematical Models: Simulations and AI
  • Where Do We Get Our Data From?
  • The Vocabulary of Data Distributions, Probability, and Statistics
  • Continuous Distributions Versus Discrete Distributions (Density Versus Mass)
  • The Power of the Joint Probability Density Function
  • Distribution of Data: The Uniform Distribution
  • Distribution of Data: The Bell-Shaped Normal (Gaussian) Distribution
  • Distribution of Data: Other Important and Commonly Used Distributions
  • The Various Uses of the Word “Distribution”
  • A/B Testing
  • Summary and Looking Ahead
  • 3. Fitting Functions to Data
  • Traditional and Very Useful Machine Learning Models
  • Numerical Solutions Versus Analytical Solutions
  • Regression: Predict a Numerical Value
  • Logistic Regression: Classify into Two Classes
  • Softmax Regression: Classify into Multiple Classes
  • Incorporating These Models into the Last Layer of a Neural Network
  • Other Popular Machine Learning Techniques and Ensembles of Techniques
  • Performance Measures for Classification Models
  • Summary and Looking Ahead
  • 4. Optimization for Neural Networks
  • The Brain Cortex and Artificial Neural Networks
  • Training Function: Fully Connected, or Dense, Feed Forward Neural Networks
  • Loss Functions
  • Optimization
  • Regularization Techniques
  • Hyperparameter Examples That Appear in Machine Learning
  • Chain Rule and Backpropagation: Calculating ∇ L ( ω → i )
  • Assessing the Significance of the Input Data Features
  • Summary and Looking Ahead
  • 5. Convolutional Neural Networks and Computer Vision
  • Convolution and Cross-Correlation
  • Convolution from a Systems Design Perspective
  • Convolution and One-Dimensional Discrete Signals
  • Convolution and Two-Dimensional Discrete Signals
  • Linear Algebra Notation
  • Pooling
  • A Convolutional Neural Network for Image Classification
  • Summary and Looking Ahead
  • 6. Singular Value Decomposition: Image Processing, Natural Language Processing, and Social Media
  • Matrix Factorization
  • Diagonal Matrices
  • Matrices as Linear Transformations Acting on Space
  • Three Ways to Multiply Matrices
  • The Big Picture
  • The Ingredients of the Singular Value Decomposition
  • Singular Value Decomposition Versus the Eigenvalue Decomposition
  • Computation of the Singular Value Decomposition
  • The Pseudoinverse
  • Applying the Singular Value Decomposition to Images
  • Principal Component Analysis and Dimension Reduction
  • Principal Component Analysis and Clustering
  • A Social Media Application
  • Latent Semantic Analysis
  • Randomized Singular Value Decomposition
  • Summary and Looking Ahead
  • 7. Natural Language and Finance AI: Vectorization and Time Series
  • Natural Language AI
  • Preparing Natural Language Data for Machine Processing
  • Statistical Models and the log Function
  • Zipf’s Law for Term Counts
  • Various Vector Representations for Natural Language Documents
  • Cosine Similarity
  • Natural Language Processing Applications
  • Transformers and Attention Models
  • Convolutional Neural Networks for Time Series Data
  • Recurrent Neural Networks for Time Series Data
  • An Example of Natural Language Data
  • Finance AI
  • Summary and Looking Ahead
  • 8. Probabilistic Generative Models
  • What Are Generative Models Useful For?
  • The Typical Mathematics of Generative Models
  • Shifting Our Brain from Deterministic Thinking to Probabilistic Thinking
  • Maximum Likelihood Estimation
  • Explicit and Implicit Density Models
  • Explicit Density-Tractable: Fully Visible Belief Networks
  • Explicit Density-Tractable: Change of Variables Nonlinear Independent Component Analysis
  • Explicit Density-Intractable: Variational Autoencoders Approximation via Variational Methods
  • Explicit Density-Intractable: Boltzman Machine Approximation via Markov Chain
  • Implicit Density-Markov Chain: Generative Stochastic Network
  • Implicit Density-Direct: Generative Adversarial Networks
  • Example: Machine Learning and Generative Networks for High Energy Physics
  • Other Generative Models
  • The Evolution of Generative Models
  • Probabilistic Language Modeling
  • Summary and Looking Ahead
  • 9. Graph Models
  • Graphs: Nodes, Edges, and Features for Each
  • Example: PageRank Algorithm
  • Inverting Matrices Using Graphs
  • Cayley Graphs of Groups: Pure Algebra and Parallel Computing
  • Message Passing Within a Graph
  • The Limitless Applications of Graphs
  • Random Walks on Graphs
  • Node Representation Learning
  • Tasks for Graph Neural Networks
  • Dynamic Graph Models
  • Bayesian Networks
  • Graph Diagrams for Probabilistic Causal Modeling
  • A Brief History of Graph Theory
  • Main Considerations in Graph Theory
  • Algorithms and Computational Aspects of Graphs
  • Summary and Looking Ahead
  • 10. Operations Research
  • No Free Lunch
  • Complexity Analysis and O() Notation
  • Optimization: The Heart of Operations Research
  • Thinking About Optimization
  • Optimization on Networks
  • The n-Queens Problem
  • Linear Optimization
  • Game Theory and Multiagents
  • Queuing
  • Inventory
  • Machine Learning for Operations Research
  • Hamilton-Jacobi-Bellman Equation
  • Operations Research for AI
  • Summary and Looking Ahead
  • 11. Probability
  • Where Did Probability Appear in This Book?
  • What More Do We Need to Know That Is Essential for AI?
  • Causal Modeling and the Do Calculus
  • Paradoxes and Diagram Interpretations
  • Large Random Matrices
  • Stochastic Processes
  • Markov Decision Processes and Reinforcement Learning
  • Theoretical and Rigorous Grounds
  • Summary and Looking Ahead
  • 12. Mathematical Logic
  • Various Logic Frameworks
  • Propositional Logic
  • First-Order Logic
  • Probabilistic Logic
  • Fuzzy Logic
  • Temporal Logic
  • Comparison with Human Natural Language
  • Machines and Complex Mathematical Reasoning
  • Summary and Looking Ahead
  • 13. Artificial Intelligence and Partial Differential Equations
  • What Is a Partial Differential Equation?
  • Modeling with Differential Equations
  • Numerical Solutions Are Very Valuable
  • Some Statistical Mechanics: The Wonderful Master Equation
  • Solutions as Expectations of Underlying Random Processes
  • Transforming the PDE
  • Solution Operators
  • AI for PDEs
  • Hamilton-Jacobi-Bellman PDE for Dynamic Programming
  • PDEs for AI?
  • Other Considerations in Partial Differential Equations
  • Summary and Looking Ahead
  • 14. Artificial Intelligence, Ethics, Mathematics, Law, and Policy
  • Good AI
  • Policy Matters
  • What Could Go Wrong?
  • How to Fix It?
  • Distinguishing Bias from Discrimination
  • The Hype
  • Final Thoughts
  • Index