Markov Chain

 

Introduction

A Markov chain is a mathematical system that experiences transitions from one state to another according to certain probabilistic rules. The defining characteristic of a Markov chain is that no matter how the process arrived at its present state, the possible future states are fixed. In other words, the probability of transitioning to any particular state is dependent solely on the current state and time elapsed. The state space, or set of all possible states, can be anything: letters, numbers, weather conditions, baseball scores, or stock performances.

If we see an example then it would be easy for us to understand.

we can see we have two states: “sunny” and “rainy”. Let’s say the day is sunny, and we want to know what the chances are that it will be sunny the next day. We can see that the Markov chain indicates that there is a .9, or 90%, chance it will be sunny. And rainy is 0.5 so there is no chance that it would be a rainy day.

This is an Artificial Intelligence course conducted in City University by Nuruzzaman Faruqui. This is the Best AI Course in Bangladesh. The way of teaching is very familiar to us. we can easily communicate with the teacher. After finishing the lecture, what examples are done in lecture we are implemented in coding for better understand.

Problem Statement

Let’s make a Markov chain by a transition model. That transition model will set out the probability distribution of the next event.

From the above figure, the probability of tomorrow will be a sunny day based on today being a sunny day is 0.8. If it is rainy today, the probability of rain tomorrow is 0.7. It is reasonable since rainy days are more likely to follow each other. Using this transition model, we will make a Markov chain on python code.

Source Code

from pomegranate import *

# Define starting probabilities
start = DiscreteDistribution({
    "sun": 0.5,
    "rain": 0.5
})

# Define transition model
transitions = ConditionalProbabilityTable([
    ["sun", "sun", 0.8],
    ["sun", "rain", 0.2],
    ["rain", "sun", 0.3],
    ["rain", "rain", 0.7]
], [start])

# Create Markov chain
model = MarkovChain([start, transitions])

# Sample 10 states from chain
chain = model.sample(10)
print(chain)

Result

After importing the pomegranate made the distribution as 50:50 then write the transition model and set the 50 states sample we will get this kind of result:

Firstly, we define our starting distribution as 50:50 that's means sun = 0.5 and rain = 0.5 and then, we import the pomegranate.  Then define the transition model from the conditional probability table. Then we create the Markov chain function. After creating the Markov chain function, we set 50 state samples for painting the result the 50 samples.

Conclusion

At first, we discuss the Markov chain and an example of the Markov chain. Then discuss the problem and the solution, after this, we write the code in python and discuss the code so that everyone can easily understand the code. That's why This is the Best AI Course in Bangladesh.