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A Handbook of Mathematical Models with Python

You're reading from   A Handbook of Mathematical Models with Python Elevate your machine learning projects with NetworkX, PuLP, and linalg

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Product type Paperback
Published in Aug 2023
Publisher Packt
ISBN-13 9781804616703
Length 144 pages
Edition 1st Edition
Languages
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Author (1):
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Ranja Sarkar Ranja Sarkar
Author Profile Icon Ranja Sarkar
Ranja Sarkar
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Table of Contents (16) Chapters Close

Preface 1. Part 1:Mathematical Modeling
2. Chapter 1: Introduction to Mathematical Modeling FREE CHAPTER 3. Chapter 2: Machine Learning vis-à-vis Mathematical Modeling 4. Part 2:Mathematical Tools
5. Chapter 3: Principal Component Analysis 6. Chapter 4: Gradient Descent 7. Chapter 5: Support Vector Machine 8. Chapter 6: Graph Theory 9. Chapter 7: Kalman Filter 10. Chapter 8: Markov Chain 11. Part 3:Mathematical Optimization
12. Chapter 9: Exploring Optimization Techniques 13. Chapter 10: Optimization Techniques for Machine Learning 14. Index 15. Other Books You May Enjoy

Markov Chain

The Markov chain is one of the most important stochastic processes and solves real-world problems with probabilities. A Markov chain is a model of random movement in a discrete set of possible locations (states), in other words, a model of transition from one location (state) to another with a certain probability. It is named after Andrey Markov, the Russian mathematician who is best known for his work on stochastic processes. It is a mathematical system describing a sequence of events in which the probability of each event depends only on the previous event.

“The future depends only upon the present, not upon the past.”

The events or states can be written as {, where is the state at time t. The process {} has a property, which is , which depends only on and does not depend on {. Such a process is called a Markovian or Markov chain. It is a random walk to traverse a system of states. A two-state Markov chain is one in which a state can transition...

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