Markov Models

Many real-world problems involve situations that change over time. Markov Models are used in Artificial Intelligence to represent systems where the future depends only on the present state, not the full history.

This idea may sound simple, but it is extremely powerful and widely used in AI systems.

What Is a Markov Model?

A Markov Model is a mathematical model that describes transitions between states using probabilities.

The key assumption is called the Markov Property.

The future state depends only on the current state.

It does not depend on how the system reached that state.

Real-World Connection

Consider weather prediction:

• If today is sunny, tomorrow might be sunny or rainy
• The prediction depends mainly on today’s weather
• Weather from a week ago is less important

This is a classic example of a Markov process.

Core Components of a Markov Model

A Markov Model consists of:

• States: Possible situations of the system
• Transitions: Movement between states
• Transition Probabilities: Likelihood of moving between states

Together, these define how the system behaves over time.

Simple Markov Chain Example

Let’s model a simple weather system with two states:

• Sunny
• Rainy

Markov Model in Python

Below is a simple Python implementation of a Markov chain.

import random

states = ["Sunny", "Rainy"]

transition_probabilities = {
    "Sunny": {"Sunny": 0.8, "Rainy": 0.2},
    "Rainy": {"Sunny": 0.4, "Rainy": 0.6}
}

def next_state(current_state):
    probabilities = transition_probabilities[current_state]
    return random.choices(
        list(probabilities.keys()),
        list(probabilities.values())
    )[0]

current = "Sunny"
for _ in range(5):
    current = next_state(current)
    print(current)
  

Code Explanation

This program simulates state transitions:

• States are defined as weather conditions
• Transition probabilities define likelihoods
• The next state is chosen based on probability

The system only uses the current state to decide the next state.

Output Explanation

The output shows a possible sequence of weather changes.

Because probabilities are involved, the sequence may differ each time the code runs.

Why Markov Models Are Important in AI

Markov Models are foundational to many AI systems.

• Speech recognition
• Natural language processing
• Recommendation systems
• Time-series prediction

They allow AI systems to reason about sequences and temporal behavior.

Limitations of Markov Models

While powerful, Markov Models have limitations:

• They assume limited memory
• They may oversimplify complex systems
• Choosing correct probabilities can be difficult

More advanced models build on Markov concepts to address these issues.

Practice Questions (Logic + Code)

Quick Quiz (Reasoning + Code)

Coming up next: Hidden Markov Models — handling hidden states and observations.