A mathematical system called a Markov chain transitions between states based on a set of probabilistic rules. The distinguishing feature of a Markov chain is that, regardless of how the system got to its current state, the potential future states are fixed. In other words, only the current state and the amount of time have any influence on the likelihood of transitioning to any specific state.

There are numerous uses for Markov chains, including in natural language processing. A Markov chain can be used to simulate the likelihood of a word sequence in a text in natural language processing. Each word is treated as a state in the chain, and transitions between states are determined by the likelihoods that particular words will appear after other words. As a result, the Markov chain can forecast the likelihood that specific words will appear given the input’s context.

Take the phrase “The cat sat on the mat,” for instance. We can create the following transition diagram if we think of each word as a state in a Markov chain:

The arrows in this diagram show the transitions between states, and the weights on the arrows stand in for the probabilities of those transitions. Because the word “cat” always comes after the word “The” in the sentence, the probability of changing from the state “The” to the state “cat” in this instance is 1. Because the word “sat” always comes after the word “cat” in the sentence, the probability of changing from the state “cat” to the state “sat” is also 1.

This model allows us to determine the probability that any string of words will appear in the sentence. For instance, since the transition from “The” to “cat” has a probability of 1, the probability of the sequence “The cat” occurring is 1. The sequence “The cat sat on” also has a probability of 1 because it is equally likely for “The” to become “cat” and for “cat” to become “sat.”

Markov chains can be extended to model longer sequences of words, and they can also be trained on large bodies of text data to improve their accuracy. This makes them a powerful tool for natural language processing tasks, such as language modeling and text generation.