فهرست مطالب

• 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