A Handbook of Mathematical Models with Python

Book description

Master the art of mathematical modeling through practical examples, use cases, and machine learning techniques

Key Features

  • Gain a profound understanding of various mathematical models that can be integrated with machine learning
  • Learn how to implement optimization algorithms to tune machine learning models
  • Build optimal solutions for practical use cases
  • Purchase of the print or Kindle book includes a free PDF eBook

Book Description

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare.

Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning.

Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.

What you will learn

  • Understand core concepts of mathematical models and their relevance in solving problems
  • Explore various approaches to modeling and learning using Python
  • Work with tested mathematical tools to gather meaningful insights
  • Blend mathematical modeling with machine learning to find optimal solutions to business problems
  • Optimize ML models built with business data, apply them to understand their impact on the business, and address critical questions
  • Apply mathematical optimization for data-scarce problems where the objective and constraints are known

Who this book is for

If you are a budding data scientist seeking to augment your journey with mathematics, this book is for you. Researchers and R&D scientists will also be able to harness the concepts covered to their full potential. To make the best use of this book, a background in linear algebra, differential equations, basics of statistics, data types, data structures, and numerical algorithms will be useful.

Table of contents

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

  • Title: A Handbook of Mathematical Models with Python
  • Author(s): Dr. Ranja Sarkar
  • Release date: August 2023
  • Publisher(s): Packt Publishing
  • ISBN: 9781804616703