Markov Model

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21 Aug, 2024

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Markov Model in machine learning is a model that states that future events are only influenced or affected by current events and not by previous ones. The model's primary purpose is to determine the probability of upcoming events with the help of present events.

Russian mathematician Andrei Andreyerich Markov pioneered the original model in the 20th century. Markov developed it to experiment with the occurrence of vowels and consonants in the sentence. However, this model is only preferable in large systems with a significant probability of occurring. Moreover, these models are widely used in various fields, including physics, chemistry, economics, biology, and computer science.

What Is The Markov Model?

The Markov Model refers to a stochastic method that determines the occurrence of future events based on the current ones. Here, past events do not influence the result.
Russian Mathematician Andrei Andreyerich Markov was a pioneer in the early 1900s. It is popular in medical and data science, economics, zoology, etc.
Moreover, the system's states, transition probabilities, and the initial state together form a Markov chain, which is a type of stochastic (random) process.
They provide a valuable framework for understanding and managing risks, making investment decisions, and developing financial strategies in an uncertain and evolving environment.

Markov Model Explained

Markov Model is a stochastic process that predicts the probability of the events using current (ongoing) events. The primary characteristic of the model is that there is no memory involved. Hence, it means that future events depend on the current state but are not related to past events. Event A may depend on B, but the latter might not do the same. For example, if today's weather is sunny, it will likely be the same tomorrow. Likewise, the next day's weather will be independent of historical updates.

Moreover, the Markov model in machine learning holds the highest power to predict outcomes. Thus, the representation of the model differs from others. After its development, in the late 1960s and 1970s, American mathematician Leonard Esau Baum extended Markov's model to his colleagues. Here, it involves a Markov chain where equations are represented as a transition matrix or a graph. The transition matrix describes how an item moves from one state to another.

Furthermore, the schedule rows state the current state, and the columns state the upcoming (or next) states. Each cell within them defines the probability for it to occur. In the end, the total of each row must sum to one.

Additionally, the system's states, transition probabilities, and the initial state together form a Markov chain, which is a type of stochastic process. Thus, the Markov model analysis states that distinct conditions or situations that a system can be in. These states can be discrete or continuous.

In addition, Markov models are often employed in cost-effectiveness analyses, especially in the field of healthcare and public health, to evaluate the costs and outcomes associated with different interventions or treatment strategies over time.

Examples

Let us look at the examples of the Markov model in data compression to comprehend the concept better:

Example #1

Let's consider a Markov model example in finance, specifically in the context of modeling stock price movements. In this scenario, the states in the Markov model could represent different market conditions, such as "Bullish," "Bearish," and "Sideways." Hence, the transitions between these states are influenced by factors such as economic indicators, market sentiment, and other relevant variables.

For instance, the transition probabilities in the model might capture the likelihood of moving from a Bullish market to a Bearish market in the event of negative economic news. Conversely, positive earnings reports or favorable economic conditions could increase the probability of transitioning from a Bearish to a Bullish market.

Moreover, by simulating the model over time, financial analysts can gain insights into potential market trends, assess the impact of different economic scenarios, and develop risk management strategies. Therefore, this type of model is beneficial for understanding the dynamic nature of financial markets, where the future state depends on the current state and the evolving economic landscape. It allows for the exploration of various "what-if" scenarios and helps investors and portfolio managers make more informed decisions in an ever-changing financial environment.

Example #2

According to a study, this approach is used in the field of health. A valuable imaging technique that makes it easier to capture information from the retinal layers is optical coherence tomography (OCT). Cysts develop in the retinal layers of severe retinal disorders. Consequently, it is crucial to recognize cysts in the retinal layers. In this study, a fresh approach is put forth for the quick identification of cystic OCT B-scans. A Hidden Markov Model (HMM) is employed in the suggested strategy to model the presence of cysts numerically. In actuality, the cyst's presence in the image is a hidden condition.

HMM is a suitable technique for describing this process since the presence of a cyst in an OCT B-scan depends on the presence of a cyst in the prior B-scans. In order to estimate the HMM parameters, the features retrieved in the first phase are employed as observation vectors. The evaluation's findings demonstrate the HMM's increased accuracy performance.

Applications

Let us look at the application of the Markov model in different fields and industries for better understanding:

#1 - Animal Life Population

Zoologists use the Markov model to map animal life in the zoo and botanical areas. It helps in understanding the migration of animals and fauna to places. Plus, we can also determine the local movement behavior and resource patterns.

#2 - Search Engine Algorithms And Data Science

The constant application of the Markov model is visible in search engines. It enables them to list the sites based on the current searches conducted by the public. That is how the popular search engine "Google" ranks pages, decides their position, and updates regularly.

#3 - Music Composition

The music production industry uses the unpopular advantages of the Markov model. To compose a song, the composer sets different pieces of music like chords and calculates the probability of each chord hitting the right mood. With the proper chord matching, the composition will lead to perfect music. It also has applicability in speech recognition.

#4 - Credit Risk Management

The application of the Markov model is visible in credit risk management. With the help of a transition matrix, the financial institutions use credit ratings as states and their probability for future evolution. It determines the asset classes and the possibility of companies applying for them.

#5 - Prediction Of Market Trends

This model can be used to predict market trends and future stock prices of the companies. It is possible to predict the future probability of the financial market using bear, bull, and stagnant markets as states.

#6 - Medical Science

The advantages of the Markov model are visible in medical science also. Doctors, pharmacists, and researchers can decode a rare health condition by understanding a discrete health state and its transition. For example, if a patient is infected in the current state, the probability of recovery in the future may increase with the right medicine.

#7 - Insurance Market

Insurance companies can use this model to segregate the policies that have their health condition as states. If a policyholder is healthy, they might not redeem the health insurance in the upcoming months.

#8 - Game Theory

Moreover, this approach is employed in game theory to model strategic interactions between decision-makers, helping analyze the evolution of strategies in repeated games.

Advantages And Disadvantages Of Markov Model

The Markov model has wide popularity among data scientists, researchers, and analysts. However, there are certain disadvantages of the Markov model. Let us look at them:

Advantages	Disadvantages
It is widely applied in fields like biological science, data science, economics, and finance.	This model is only applicable to systems that exhibit the Markov property.
With the help of the Markov model, complex systems can be easily explained.	Systems that have multiple states cannot be performed on this model.
Future probability and occurrence of events are possible with this model.	The actual behavior of the events may not be predicted correctly.
It helps in predicting the long-term behavior of the events.	Moreover, these models are sensitive to the initial state, and the choice of this initial state can impact the results.

Markov Model vs Hidden Markov Model vs Decision Tree

Although Markov Model, Hidden Markov Model, and decision trees play a vital role in making decisions, all have vast differences. So, let us look at them:

Aspect	Markov Model	Hidden Markov Model	Decision Tree
Meaning	It is a stochastic process that determines future events depending on current events but not the past.	The hidden Markov Model or HMM cannot directly observe the events but does have some effect on the model's behavior.	A decision tree is a main bark that routes branches through nodes and connections.
Purpose	To determine the dependency and probability of future events on the current state.	Observe the events and find the sequence of the hidden events.	To make decisions with the help of nodes created on each bench.
Examples	If it is sunny today, there are higher chances of the same weather tomorrow.	When using a translation tool, the text converts into speech. But, the real mechanism behind it is invisible. Yet, it still affects the model.	Buying a product has various options (nodes) that include choices, suggestions, reviews, and price as parameters before making a decision.

Frequently Asked Questions (FAQs)

1. How to make a Markov model in Excel?

Following are the steps on how to use the Markov model in a spreadsheet format:
- Set up the states in the table similar to the transition matrix.
- Fill in the probability of each state.
- Calculate the transition probabilities for each state, whose total should be one.
- Observe, analyze, and make decisions based on it.

2. What is a semi-Markov model?

The Semi-Markov model is similar to the Markov renewal process. However, time is a significant factor. While the original model has a state with jump times, a time limit is considered here.

3. What Role Do Markov Models Play in Machine Learning?

In machine learning, Markov models are used for tasks such as sequence prediction, natural language processing, and image analysis. Hidden Markov Models (HMMs) are particularly relevant for tasks involving sequential data.