Introduction To Markov Chains | Markov Chains in Python | Edureka
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A Markov chain is a stochastic process where the next state depends only on the current state, adhering to the Markov property. It utilizes a transition matrix to represent probabilities for transitioning between states and can be applied in various fields such as text generation and Google's PageRank. This document provides insights into the structure, properties, and applications of Markov chains, including practical Python implementations.
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Introduction To Markov Chains | Markov Chains in Python | Edureka
- 1. Copyright © 2017, edureka and/or its affiliates. All rights reserved.
- 2. WHAT IS A MARKOV CHAIN? UNDERSTANDING MARKOV CHAINS WITH AN EXAMPLE MARKOV CHAIN IN PYTHON MARKOV CHAIN APPLICATIONS TRANSITION MATRIX & TRANSISTION STATE DIAGRAM www.edureka.co
- 3. WHAT IS A MARKOV CHAIN? www.edureka.co
- 4. A stochastic process containing random variables, transitioning from one state to another depending on certain assumptions and definite probabilistic rules. What Is A Markov chain? Markov Property states that the calculated probability of a random process transitioning to the next possible state is only dependent on the current state and time and it is independent of the series of states that preceded it. Let the random process be, { 𝑋 𝑚 , m=0,1,2 … } This process is a Markov chain only if, 𝑃 𝑋 𝑚+1 = ȁ𝑗 𝑋 𝑚 = ⅈ, 𝑋 𝑚−1 = ⅈ 𝑚−1, … , 𝑋0 = ⅈ0 = 𝑃 𝑋 𝑚+1 = ȁ𝑗 𝑋 𝑚 = ⅈ 𝑃𝑖𝑗 = 𝑃 𝑋 𝑚+1 = ȁ𝑗 𝑋 𝑚 = ⅈ www.edureka.co
- 6. A Markov Model is a stochastic model that models random variables in such a manner that the variables follow the Markov property. • Keys denote the unique words in the sentence, i.e., 5 keys (one, two, hail, happy, edureka) • Tokens denote the total number of words, i.e. 8 tokens. one edureka two edureka hail edureka happy edureka www.edureka.co
- 7. A Markov Model is a stochastic model that models random variables in such a manner that the variables follow the Markov property. one edureka two hail happy 1 4 1 1 1 Keys Frequencies www.edureka.co
- 8. A Markov Model is a stochastic model that models random variables in such a manner that the variables follow the Markov property. one edureka two hail happy 1 4 1 1 1 Weighted distributions: 1. 'edureka' is 50% (4/8) 2. (one, two, hail, happy) is ≈ 13% (1/8) www.edureka.co
- 9. Start one edureka two edureka hail edureka happy edureka end one edureka two hail happy 1 4 1 1 1 start end 1 1 Keys Frequencies www.edureka.co
- 10. (Start, one) (one, edureka) (edureka, two) (two, edureka) (edureka, hail) (hail, edureka) (edureka, happy) (happy, edureka) (edureka, end) (end, none) (Start, one) (one, edureka) (edureka, two) (edureka, hail) (edureka, happy) (edureka, end) (two, edureka) (hail, edureka) (happy, edureka) (end, none) www.edureka.co
- 11. (Start, one) (one, edureka) (edureka, two) (edureka, hail) (edureka, happy) (edureka, end) (two, edureka) (hail, edureka) (happy, edureka) (end, none) Start [one] One [edureka] Edureka [two, hail, happy, end] Two [edureka] Hail [edureka] Happy [edureka] End [none] www.edureka.co
- 12. Start One hailtwo happy end edureka 1 1 1 1 1 1/4 1/4 1/4 1/4 Start [one] One [edureka] Edureka [two, hail, happy, end] Two [edureka] Hail [edureka] Happy [edureka] End [none] www.edureka.co
- 13. TRANSITION MATRIX & STATE DAIGRAM www.edureka.co
- 14. In a Markov Process, we use a matrix to represent the transition probabilities from one state to another. This matrix is called the Transition or probability matrix. It is usually denoted by P. What Is A Transition Matrix? 𝑝11 𝑝12 𝑝1𝑟 𝑝21 𝑝22 𝑝2𝑟 𝑝21 𝑝22 𝑝2𝑟 . . . . . . . . . . . . . . . . . P = 𝑘=1 𝑟 𝑝𝑖𝑘 = 𝑘=1 𝑟 𝑃 𝑋 𝑚+1 = ȁ𝑘 𝑋 𝑚 = ⅈ Note, 𝑝ij ≥ 0, and 'i' for all values is, www.edureka.co
- 15. Consider a Markov chain with three states 1, 2, and 3. Transition Matrix & State Diagram Example Transition matrix 1/4 0 3/4 P = 1/2 0 1/2 1/4 1/2 1/4 1 2 3 1/4 3/4 1/2 1/2 1/4 1/2 1/4 State Transition Diagram www.edureka.co
- 17. To apply Markov Property and create a Markov Model that can generate text simulations by studying Donald Trump speech data set. Problem Statement Apply Markov property Generate Text Simulations Donald Trump speeches www.edureka.co
- 19. Markov Chain Applications Google PageRank Autocomplete www.edureka.co
- 20. Markov Chain Applications Subreddit simulator Text generator www.edureka.co
- 21. Copyright © 2017, edureka and/or its affiliates. All rights reserved. www.edureka.co
- 22. www.edureka.co