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Hands-On Mathematics for Deep Learning
Mostprogrammersanddatascientistsstrugglewithmathematics,havingeitheroverlookedorforgottencoremathematicalconcepts.ThisbookusesPythonlibrariestohelpyouunderstandthemathrequiredtobuilddeeplearning(DL)models.You'llbeginbylearningaboutcoremathematicalandmoderncomputationaltechniquesusedtodesignandimplementDLalgorithms.Thisbookwillcoveressentialtopics,suchaslinearalgebra,eigenvaluesandeigenvectors,thesingularvaluedecompositionconcept,andgradientalgorithms,tohelpyouunderstandhowtotraindeepneuralnetworks.Laterchaptersfocusonimportantneuralnetworks,suchasthelinearneuralnetworkandmultilayerperceptrons,withaprimaryfocusonhelpingyoulearnhoweachmodelworks.Asyouadvance,youwilldelveintothemathusedforregularization,multi-layeredDL,forwardpropagation,optimization,andbackpropagationtechniquestounderstandwhatittakestobuildfull-fledgedDLmodels.Finally,you’llexploreCNN,recurrentneuralnetwork(RNN),andGANmodelsandtheirapplication.Bytheendofthisbook,you'llhavebuiltastrongfoundationinneuralnetworksandDLmathematicalconcepts,whichwillhelpyoutoconfidentlyresearchandbuildcustommodelsinDL.
目錄(277章)
倒序
- 封面
- 版權信息
- About Packt
- Why subscribe?
- Contributors
- About the author
- About the reviewers
- Packt is searching for authors like you
- Preface
- Who this book is for
- What this book covers
- To get the most out of this book
- Download the color images
- Conventions used
- Get in touch
- Reviews
- Section 1: Essential Mathematics for Deep Learning
- Linear Algebra
- Comparing scalars and vectors
- Linear equations
- Solving linear equations in n-dimensions
- Solving linear equations using elimination
- Matrix operations
- Adding matrices
- Multiplying matrices
- Inverse matrices
- Matrix transpose
- Permutations
- Vector spaces and subspaces
- Spaces
- Subspaces
- Linear maps
- Image and kernel
- Metric space and normed space
- Inner product space
- Matrix decompositions
- Determinant
- Eigenvalues and eigenvectors
- Trace
- Orthogonal matrices
- Diagonalization and symmetric matrices
- Singular value decomposition
- Cholesky decomposition
- Summary
- Vector Calculus
- Single variable calculus
- Derivatives
- Sum rule
- Power rule
- Trigonometric functions
- First and second derivatives
- Product rule
- Quotient rule
- Chain rule
- Antiderivative
- Integrals
- The fundamental theorem of calculus
- Substitution rule
- Areas between curves
- Integration by parts
- Multivariable calculus
- Partial derivatives
- Chain rule
- Integrals
- Vector calculus
- Derivatives
- Vector fields
- Inverse functions
- Summary
- Probability and Statistics
- Understanding the concepts in probability
- Classical probability
- Sampling with or without replacement
- Multinomial coefficient
- Stirling's formula
- Independence
- Discrete distributions
- Conditional probability
- Random variables
- Variance
- Multiple random variables
- Continuous random variables
- Joint distributions
- More probability distributions
- Normal distribution
- Multivariate normal distribution
- Bivariate normal distribution
- Gamma distribution
- Essential concepts in statistics
- Estimation
- Mean squared error
- Sufficiency
- Likelihood
- Confidence intervals
- Bayesian estimation
- Hypothesis testing
- Simple hypotheses
- Composite hypothesis
- The multivariate normal theory
- Linear models
- Hypothesis testing
- Summary
- Optimization
- Understanding optimization and it's different types
- Constrained optimization
- Unconstrained optimization
- Convex optimization
- Convex sets
- Affine sets
- Convex functions
- Optimization problems
- Non-convex optimization
- Exploring the various optimization methods
- Least squares
- Lagrange multipliers
- Newton's method
- The secant method
- The quasi-Newton method
- Game theory
- Descent methods
- Gradient descent
- Stochastic gradient descent
- Loss functions
- Gradient descent with momentum
- The Nesterov's accelerated gradient
- Adaptive gradient descent
- Simulated annealing
- Natural evolution
- Exploring population methods
- Genetic algorithms
- Particle swarm optimization
- Summary
- Graph Theory
- Understanding the basic concepts and terminology
- Adjacency matrix
- Types of graphs
- Weighted graphs
- Directed graphs
- Directed acyclic graphs
- Multilayer and dynamic graphs
- Tree graphs
- Graph Laplacian
- Summary
- Section 2: Essential Neural Networks
- Linear Neural Networks
- Linear regression
- Polynomial regression
- Logistic regression
- Summary
- Feedforward Neural Networks
- Understanding biological neural networks
- Comparing the perceptron and the McCulloch-Pitts neuron
- The MP neuron
- Perceptron
- Pros and cons of the MP neuron and perceptron
- MLPs
- Layers
- Activation functions
- Sigmoid
- Hyperbolic tangent
- Softmax
- Rectified linear unit
- Leaky ReLU
- Parametric ReLU
- Exponential linear unit
- The loss function
- Mean absolute error
- Mean squared error
- Root mean squared error
- The Huber loss
- Cross entropy
- Kullback-Leibler divergence
- Jensen-Shannon divergence
- Backpropagation
- Training neural networks
- Parameter initialization
- All zeros
- Random initialization
- Xavier initialization
- The data
- Deep neural networks
- Summary
- Regularization
- The need for regularization
- Norm penalties
- L2 regularization
- L1 regularization
- Early stopping
- Parameter tying and sharing
- Dataset augmentation
- Dropout
- Adversarial training
- Summary
- Convolutional Neural Networks
- The inspiration behind ConvNets
- Types of data used in ConvNets
- Convolutions and pooling
- Two-dimensional convolutions
- One-dimensional convolutions
- 1 × 1 convolutions
- Three-dimensional convolutions
- Separable convolutions
- Transposed convolutions
- Pooling
- Global average pooling
- Convolution and pooling size
- Working with the ConvNet architecture
- Training and optimization
- Exploring popular ConvNet architectures
- VGG-16
- Inception-v1
- Summary
- Recurrent Neural Networks
- The need for RNNs
- The types of data used in RNNs
- Understanding RNNs
- Vanilla RNNs
- Bidirectional RNNs
- Long short-term memory
- Gated recurrent units
- Deep RNNs
- Training and optimization
- Popular architecture
- Clockwork RNNs
- Summary
- Section 3: Advanced Deep Learning Concepts Simplified
- Attention Mechanisms
- Overview of attention
- Understanding neural Turing machines
- Reading
- Writing
- Addressing mechanisms
- Content-based addressing mechanism
- Location-based address mechanism
- Exploring the types of attention
- Self-attention
- Comparing hard and soft attention
- Comparing global and local attention
- Transformers
- Summary
- Generative Models
- Why we need generative models
- Autoencoders
- The denoising autoencoder
- The variational autoencoder
- Generative adversarial networks
- Wasserstein GANs
- Flow-based networks
- Normalizing flows
- Real-valued non-volume preserving
- Summary
- Transfer and Meta Learning
- Transfer learning
- Meta learning
- Approaches to meta learning
- Model-based meta learning
- Memory-augmented neural networks
- Meta Networks
- Metric-based meta learning
- Prototypical networks
- Siamese neural networks
- Optimization-based meta learning
- Long Short-Term Memory meta learners
- Model-agnostic meta learning
- Summary
- Geometric Deep Learning
- Comparing Euclidean and non-Euclidean data
- Manifolds
- Discrete manifolds
- Spectral decomposition
- Graph neural networks
- Spectral graph CNNs
- Mixture model networks
- Facial recognition in 3D
- Summary
- Other Books You May Enjoy
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