Last updated: January 8th, 2025
Have you ever been mesmerised by how social media platforms such as LinkedIn automatically generate replies from you? Do you know how Gmail auto-completes the sentences when you write an email? You will become familiar with these after a Markov chain analysis. Markov chain is a concept that helps to compute possibilities from various state transitions of a particular event. Thus, it can predict what will happen next. As a result, the Markov chain has a vast application in data science, biology, finance, economics, and more.
So, here you will get a brief guidance about this concept.
What is the Markov Chain?
The Russian scholar Andrey Markov innovated the concept of the Markov chain. It’s an arithmetical system which assists you in understanding the probability associated with the sequence of events. Every event occurs based on the state of the prior event. The core property of the Markov chains is the ‘memorylessness’ or ‘stateless’ property. As per this property, every transition depends on the present state and never on the past states.
You can find many real-life use cases of this concept, such as social media activities, natural language processing, etc.
Markov Chain Properties
The properties of Markov chains make them feasible for numerous domains. So, let’s have a glance at them:
- Memorylessness (Markov Property)
The future state of a Markov chain is predicted only from its present state. Thus, it doesn’t depend upon the past state of the past states. As a result, the modelling process becomes more accessible.
- Stationary Distribution
Many Markov chains have the ergodic property. Under this property, the probability of a certain state remains unchanged forever. Thus, it becomes a long-term property of the Markov chains. Also, this property becomes helpful in building an equilibrium configuration for numerous problems.
- Recurrence and Transience
Recurrence indicates those states to which the systems will always return. In contrast, the transience refers to those states to which the system never returns once the system becomes out of state.
- Transition Matrix
A transition matrix includes and describes the probabilities or the states of the Markov Chains. Each element of the matrix indicates the probabilities of the transition. The sum of the probabilities for each row should be 1, meaning one transition will occur.
- Irreducibility
The irreducibility property helps you to reach one state to another with a finite number of steps. That means every state can communicate with the other states.
Types of Markov Chains
Markov chains can be differentiated by their properties, absence or presence of the states, transition periodicity, and distribution presence. So, let’s understand the types:
- Discrete-Time Markov Chains (DTMC)
For these Markov chains, the changes of the states occur with discrete time intervals. In this case, you can determine the transition possibilities through the transition matrix. They best represent the weather conditions of a specific day, such as rainy, sunny, or cloudy. Moreover, the transition matrix reveals how the weather changes daily.
- Continuous-Time Markov Chains (CTMC)
In CTMC, the transitions between the states take place at any time. In this case, the rate function measures the state transition possibilities instead of probabilities. For instance, you can consider the number of users on a site at a specific time. Here, the changes of the states represent the session start and end by the users.
- Reversible Markov Chains
In reversible Markov chains remain indistinguishable when looking forward or backward in time. That means they have the same states for the past and the future. These chains are generally used in the Monte Carlo simulations.
- Absorbing Markov Chains
It simply implies the state that has an end. For example, you can think about a game. You can observe any of these two absorbing states in a game – the win or the loss. These are the endpoints. There is no chance of anything happening beyond these two states. So, outgoing transitions are impossible in the absorbing states.
Markov Chain Example
Let’s take a simple example of a weather prediction model for Markov chain analysis. First, consider the two states for this model.
- It’s a rainy day
- It’s not a rainy day
Next, you have to add some probabilities. So, consider the probabilities might be:
- If today is a rainy day R, then there is a 60% chance that tomorrow is not a rainy day and a 40% chance of a rainy day.
- Alternatively, if today is not a rainy day N, then there is an 80% possibility that tomorrow is not a rainy day. So, there will be a 20% chance that tomorrow will be rainy.
Now, you can analyse these probabilities from the state diagram given below. The left circle represents a rainy day R and the right circle shows it’s not a rainy day N. For example, the arrow between N and R is labelled 0.2 because there is a 20% chance that tomorrow will be rainy.
Get Ready for the Next Achievement in Your Data Science Career
To stay competitive in your data science career, you should focus on skill-building in artificial intelligence, machine learning, and data science. These domains incorporate techniques, tools, and concepts such as the Markov chain, which enlarge your critical thinking ability.
So, are you looking for any professional courses? Enrol in the Executive Certification in Advanced Data Science Applications program and grab your next job opportunity! So, keep an eye on the top features of this course:
- Learn numerous methods of AI, data analysis, and deep learning
- Grab hands-on experience with computational techniques of deep learning
- Case studies through practical applications and industry projects
- Additionally, mentoring from industry experts and IIT Madras faculty
- Finally, get the certification of completion from IIT Madras
Conclusion
Markov chain analysis is a fundamental concept of data science. It refines the workflows of several applications, including decision-making, forecasting, risk measurements, constructing policies, and more. So, if you are interested in data science, you should have the right skills. The specific skills and knowledge will help you navigate towards ultimate success.
FAQs
1. What is the primary advantage of the Markov chain?
Markov chain helps to model complex systems by computing the current states and their transitions. This way, it simplifies complex systems and predicts the behaviour of these systems.
2. Where can we apply the Markov chain in bioinformatics?
In robotics, the Markov chain can analyse state-action paths in the systems to determine the proper actions based on previous incidents.
3. Is the Markov chain helpful in AI?
The Markov chain has become a powerful tool used in generative AI. For instance, it applies to NLP, images, and music generation.