(ML 14.1) Markov models - motivating examples

Step-by-Step Tutorial: Understanding Markov Models

1. Introduction to Markov Models:

   • Markov models are named after Andre Markov, a Russian mathematician known for his work in stochastic processes in the late 1800s.
   • The fundamental idea behind a Markov model is that the future is independent of the past given the present state.

2. Understanding the Concept:

   • In the context of Markov models, knowing the current state of the system is sufficient to predict the future, regardless of the past states.
   • This concept holds true on a large scale and is widely used to model various types of temporal data such as weather patterns, economic trends, language, and music.

3. Applications of Markov Models:

   • Markov models are utilized in various applications like speech recognition software, where they convert spoken words into text using probabilistic models.
   • They are also used in music composition, generating compositions based on patterns learned from existing music data.

4. Real-World Examples:

   • Consider scenarios like tracking the position of a robot using GPS data or analyzing seasonal changes in CO2 levels as practical examples where Markov models can be applied.

5. Language Modeling:

   • Markov models are commonly used in natural language processing to predict the next word in a sentence or fill in missing words based on the context.

6. Modeling Temporal Data:

   • When dealing with sequential data like GPS positions or climate data, Markov models offer a probabilistic approach to capturing dependencies between data points.

7. Dependency in Data:

   • Understanding the dependencies between data points is crucial in selecting the appropriate model. Markov models consider recent data points more informative than distant ones.

8. Generative Model Design:

   • Designing a generative model involves choosing dependencies between data points. For instance, selecting the current state based on the most recent data points up to a certain historical point.

9. Implementing Markov Models:

   • Start by defining the states of the system and determining the dependencies between consecutive states based on the context of the problem.
   • Experiment with different values of 'M' (representing the number of previous states considered) to optimize the model for accurate predictions.

10. Further Exploration:

    • Dive deeper into Markov models and Markov chains to explore advanced concepts and applications in probabilistic modeling.

By following these steps, you can gain a better understanding of Markov models and how they can be applied to analyze and predict patterns in various types of data.