دانلود کتاب A Handbook of Mathematical Models with Python

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A Handbook of Mathematical Models with Python
Contributors
About the author
About the reviewer
Preface
Who this book is for
What this book covers
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Conventions used
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Part 1:Mathematical Modeling
1
Introduction to Mathematical Modeling
Mathematical optimization
Understanding the problem
Formulation of the problem
Signal processing
Understanding the problem
Formulation of the problem
Control theory
Understanding the problem
Formulation of the problem
Summary
2
Machine Learning vis-à-vis Mathematical Modeling
ML as mathematical optimization
Example 1 – regression
Example 2 – neural network
ML – a predictive tool
E-commerce
Sales and marketing
Cybersecurity
Mathematical modeling – a prescriptive tool
Finance
Retail
Energy
Digital advertising
Summary
Part 2:Mathematical Tools
3
Principal Component Analysis
Linear algebra for PCA
Covariance matrix – eigenvalues and eigenvectors
Number of PCs – how to select for a dataset
Feature extraction methods
LDA – the difference from PCA
Applications of PCA
Noise reduction
Anomaly detection
Summary
4
Gradient Descent
Gradient descent variants
Application of gradient descent
Mini-batch gradient descent and stochastic gradient descent
Gradient descent optimizers
Momentum
Adagrad
RMSprop
Adam
Summary
5
Support Vector Machine
Support vectors in SVM
Kernels for SVM
Implementation of SVM
Summary
6
Graph Theory
Types of graphs
Undirected graphs
Directed graphs
Weighted graphs
Optimization use case
Optimization problem
Optimized solution
Graph neural networks
Summary
7
Kalman Filter
Computation of measurements
Filtration of measurements
Implementation of the Kalman filter
Summary
8
Markov Chain
Discrete-time Markov chain
Transition probability
Application of the Markov chain
Markov Chain Monte Carlo
Gibbs sampling algorithm
Metropolis-Hastings algorithm
Illustration of MCMC algorithms
Summary
Part 3:Mathematical Optimization
9
Exploring Optimization Techniques
Optimizing machine learning models
Random search
Grid search
Bayesian optimization
Optimization in operations research
Evolutionary optimization
Summary
10
Optimization Techniques for Machine Learning
General optimization algorithms
First-order algorithms
Second-order algorithms
Complex optimization algorithms
Differentiability of objective functions
Direct and stochastic algorithms
Summary
Epilogue
Index
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