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
Author(s): Dr. Ranja Sarker
Edition: 1
Publisher: Packt Publishing Pvt Ltd
Year: 2023
Language: English
Pages: 140
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
Get in touch
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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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