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Hands-on mathematics for deep learning : build a solid mathematical foundation for training efficient deep neural networks /
The main aim of this book is to make the advanced mathematical background accessible to someone with a programming background. This book will equip the readers with not only deep learning architectures but the mathematics behind them. With this book, you will understand the relevant mathematics that...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Birmingham :
Packt Publishing,
2020.
|
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Intro
- Title Page
- Copyright and Credits
- About Packt
- Contributors
- Table of Contents
- Preface
- 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