Math and Architectures of Deep Learning
Artificial Intelligence
Book Details
Book Title
Math and Architectures of Deep Learning
Author
Krishnendu Chaudhury
Publisher
Manning
Publication Date
2024
ISBN
9781617296482
Number of Pages
553
Language
English
Format
File Size
12.6MB
Subject
Computers > Cybernetics: Artificial Intelligence
Table of Contents
- Cover
- Brief Contents
- Contents
- Foreword
- Preface
- Chapter 1. An overview of machine learning and deep learning
- A first look at machine/deep learning: A paradigm shift in computation
- A function approximation view of machine learning: Models and their training
- A simple machine learning model: The cat brain
- Geometrical view of machine learning
- Regression vs. classification in machine learning
- Linear vs. nonlinear models
- Higher expressive power through multiple nonlinear layers: Deep neural networks
- Summary
- Chapter 2. Vectors, matrices and tensors in machine learning
- Vectors and their role in machine learning
- PyTorch code for vector manipulations
- Matrices and their role in machine learning
- Python code: Introducing matrices, tensors and images via PyTorch
- Basic vector and matrix operations in machine learning
- Python code: Basic vector and matrix operations via PyTorch
- Linear combinations, vector spans, basis vectors and collinearity preservation
- Linear transforms: Geometric and algebraic interpretations
- Multidimensional arrays, multilinear transforms and tensors
- Linear systems and matrix inverse
- Eigenvalues and eigenvectors: Swiss Army knives of machine learning
- Orthogonal (rotation) matrices and their eigenvalues and eigenvectors
- Matrix diagonalization
- Spectral decomposition of a symmetric matrix
- An application relevant to machine learning: Finding the axes of a hyperellipse
- Summary
- Chapter 3. Classifiers and vector calculus
- Geometrical view of image classification
- Error, aka loss function
- Minimizing loss functions: Gradient vectors
- Local approximation for the loss function
- PyTorch code for gradient descent, error minimization and model training
- Convex and nonconvex functions and global and local minima
- Convex sets and functions
- Summary
- Chapter 4. Linear algebraic tools in machine learning
- Distribution of feature data points and true dimensionality
- Quadratic forms and their minimization
- Spectral and Frobenius norms of a matrix
- Principal component analysis
- Singular value decomposition
- Machine learning application: Document retrieval
- Summary
- Chapter 5. Probability distributions in machine learning
- Probability: The classical frequentist view
- Probability distributions
- Basic concepts of probability theory
- Joint probabilities and their distributions
- Geometrical view: Sample point distributions for dependent and independent variables
- Continuous random variables and probability density
- Properties of distributions: Expected value, variance and covariance
- Sampling from a distribution
- Some famous probability distributions
- Summary
- Chapter 6. Bayesian tools for machine learning
- Conditional probability and Bayes’ theorem
- Entropy
- Cross-entropy
- KL divergence
- Conditional entropy
- Model parameter estimation
- Latent variables and evidence maximization
- Maximum likelihood parameter estimation for Gaussians
- Gaussian mixture models
- Summary
- Chapter 7. Function approximation: How neural networks model the world
- Neural networks: A 10,000-foot view
- Expressing real-world problems: Target functions
- The basic building block or neuron: The perceptron
- Toward more expressive power: Multilayer perceptrons (MLPs)
- Layered networks of perceptrons: MLPs or neural networks
- Summary
- Chapter 8. Training neural networks: Forward propagation and backpropagation
- Differentiable step-like functions
- Why layering?
- Linear layers
- Training and backpropagation
- Training a neural network in PyTorch
- Summary
- Chapter 9. Loss, optimization and regularization
- Loss functions
- Optimization
- Regularization
- Summary
- Chapter 10. Convolutions in neural networks
- One-dimensional convolution: Graphical and algebraical view
- Convolution output size
- Two-dimensional convolution: Graphical and algebraic view
- Three-dimensional convolution
- Transposed convolution or fractionally strided convolution
- Adding convolution layers to a neural network
- Pooling
- Summary
- Chapter 11. Neural networks for image classification and object detection
- CNNs for image classification: LeNet
- Toward deeper neural networks
- Object detection: A brief history
- Faster R-CNN: A deep dive
- Summary
- Chapter 12. Manifolds, homeomorphism and neural networks
- Manifolds
- Homeomorphism
- Neural networks and homeomorphism between manifolds
- Summary
- Chapter 13. Fully Bayes model parameter estimation
- Fully Bayes estimation: An informal introduction
- MLE for Gaussian parameter values (recap)
- Fully Bayes parameter estimation: Gaussian, unknown mean, known precision
- Small and large volumes of training data and strong and weak priors
- Conjugate priors
- Fully Bayes parameter estimation: Gaussian, unknown precision, known mean
- Fully Bayes parameter estimation: Gaussian, unknown mean, unknown precision
- Example: Fully Bayesian inferencing
- Fully Bayes parameter estimation: Multivariate Gaussian, unknown mean, known precision
- Fully Bayes parameter estimation: Multivariate, unknown precision, known mean
- Summary
- Chapter 14. Latent space and generative modeling, autoencoders and variational autoencoders
- Geometric view of latent spaces
- Generative classifiers
- Benefits and applications of latent-space modeling
- Linear latent space manifolds and PCA
- Autoencoders
- Smoothness, continuity and regularization of latent spaces
- Variational autoencoders
- Summary
- Appendix
- Notations
- Index