دانلود کتاب Math for Deep Learning: What You Need to Know to Understand Neural Networks

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Brief Contents Contents in Detail Foreword Acknowledgments Introduction Who Is This Book For? About This Book Chapter 1: Setting the Stage Installing the Toolkits Linux macOS Windows NumPy Defining Arrays Data Types 2D Arrays Zeros and Ones Advanced Indexing Reading and Writing to Disk SciPy Matplotlib Scikit-Learn Summary Chapter 2: Probability Basic Concepts Sample Space and Events Random Variables Humans Are Bad at Probability The Rules of Probability Probability of an Event Sum Rule Product Rule Sum Rule Revisited The Birthday Paradox Conditional Probability Total Probability Joint and Marginal Probability Joint Probability Tables Chain Rule for Probability Summary Chapter 3: More Probability Probability Distributions Histograms and Probabilities Discrete Probability Distributions Continuous Probability Distributions Central Limit Theorem The Law of Large Numbers Bayes' Theorem Cancer or Not Redux Updating the Prior Bayes' Theorem in Machine Learning Summary Chapter 4: Statistics Types of Data Nominal Data Ordinal Data Interval Data Ratio Data Using Nominal Data in Deep Learning Summary Statistics Means and Median Measures of Variation Quantiles and Box Plots Missing Data Correlation Pearson Correlation Spearman Correlation Hypothesis Testing Hypotheses The t-test The Mann-Whitney U Test Summary Chapter 5: Linear Algebra Scalars, Vectors, Matrices, and Tensors Scalars Vectors Matrices Tensors Arithmetic with Tensors Array Operations Vector Operations Matrix Multiplication Kronecker Product Summary Chapter 6: More Linear Algebra Square Matrices Why Square Matrices? Transpose, Trace, and Powers Special Square Matrices The Identity Matrix Determinants Inverses Symmetric, Orthogonal, and Unitary Matrices Definiteness of a Symmetric Matrix Eigenvectors and Eigenvalues Finding Eigenvalues and Eigenvectors Vector Norms and Distance Metrics L-Norms and Distance Metrics Covariance Matrices Mahalanobis Distance Kullback-Leibler Divergence Principal Component Analysis Singular Value Decomposition and Pseudoinverse SVD in Action Two Applications Summary Chapter 7: Differential Calculus Slope Derivatives A Formal Definition Basic Rules Rules for Trigonometric Functions Rules for Exponentials and Logarithms Minima and Maxima of Functions Partial Derivatives Mixed Partial Derivatives The Chain Rule for Partial Derivatives Gradients Calculating the Gradient Visualizing the Gradient Summary Chapter 8: Matrix Calculus The Formulas A Vector Function by a Scalar Argument A Scalar Function by a Vector Argument A Vector Function by a Vector A Matrix Function by a Scalar A Scalar Function by a Matrix The Identities A Scalar Function by a Vector A Vector Function by a Scalar A Vector Function by a Vector A Scalar Function by a Matrix Jacobians and Hessians Concerning Jacobians Concerning Hessians Some Examples of Matrix Calculus Derivatives Derivative of Element-Wise Operations Derivative of the Activation Function Summary Chapter 9: Data Flow in Neural Networks Representing Data Traditional Neural Networks Deep Convolutional Networks Data Flow in Traditional Neural Networks Data Flow in Convolutional Neural Networks Convolution Convolutional Layers Pooling Layers Fully Connected Layers Data Flow Through a Convolutional Neural Network Summary Chapter 10: Backpropagation What Is Backpropagation? Backpropagation by Hand Calculating the Partial Derivatives Translating into Python Training and Testing the Model Backpropagation for Fully Connected Networks Backpropagating the Error Calculating Partial Derivatives of the Weights and Biases A Python Implementation Using the Implementation Computational Graphs Summary Chapter 11: Gradient Descent The Basic Idea Gradient Descent in One Dimension Gradient Descent in Two Dimensions Stochastic Gradient Descent Momentum What Is Momentum? Momentum in 1D Momentum in 2D Training Models with Momentum Nesterov Momentum Adaptive Gradient Descent RMSprop Adagrad and Adadelta Adam Some Thoughts About Optimizers Summary Epilogue Appendix: Going Further Probability and Statistics Linear Algebra Calculus Deep Learning Index