Difference Between Markov Chains and Hidden Markov Models

When exploring machine learning, and artificial intelligence especially in probabilistic models and time-series analysis, you'll likely come across two crucial concepts: Discrete & Continuous Markov Chains as well as Hidden Markov Models. Of them, the first one is the approach based purely on probability theory while the second one has certain differences in the structure, application and in fact, in the complexity level. To effectively use these differences it is crucial to comprehend them by employing into practical application such as speech to text conversion, finance, and natural language processing.

This article will provide an overview of Markov Chains and Hidden Markov Models, compare and contrast the two and discuss some practical uses of each model.

What is a Markov Chain?

A Markov Chain is a Markov model that provides the probability of a series of events and differs is that the likelihood of any event is contingent on the preceding event's occurrence. Otherwise known as the Markov model, this model is based on the Markov property, which argues that the state in the future is independent of the state in the past save for the current state.

Key Elements of Markov Chains

• States: The states that the system can either be in.
• Transitions: The chances of change from one state to another.
• Transition Matrix: A chart that exhibits the chance of passing from one state to another for the total system.

A Markov Chain model is depicted using a graph in which nodes are states and directed arcs represent the transitions between states, their probabilities. This model is widely used in such areas where "memoryless" property can be practiced; for instance, weather prediction, queuing systems and game theory.

Example of a Markov Chains

Consider a simple weather model with two states: Sunny and Rainy. If the probability of a sunny day following a rainy day is 0.3, and a rainy day following a sunny day is 0.4, we can create a transition matrix like this:

[P(Sunny|Sunny), P(Rainy|Sunny)] = [0.6, 0.4]
[P(Sunny|Rainy), P(Rainy|Rainy)] = [0.3, 0.7]

Using this transition matrix, one can simulate the subsequent day's weather condition from the currently prevailing one.

Real-World Applications of Markov Chains

The following are some real-world applications of Markov Chains -

1. Weather Forecasting: Forecast weather based on a model of the transition probability from one state to another (for instance, from sunny to rainy).
2. Customer Behavior Prediction: Determines and forecasts other customer states, including browsing and buying.
3. Inventory Management: It nicely adapts the order of stock replenishments as a result of preceding states of inventories.

What is a Hidden Markov Model (HMM)?

A Hidden Markov Model (HMM) extends the notion of a standard Markov Chain where orthonormal states are substituted by a layer of hidden states. In HMMs the states that the system goes through are hidden states; they do not occur at the visible level. However, the observable output of the Hidden States, also referred to as emission, is produced by each Hidden State.

Key Elements of Hidden Markov Models

• Hidden States: The latent conditions of the system which are not directly measurable or observable.
• Observations: The visible world related to each of them esoteric modes of working Outputs = V.
• Transition Probabilities: The probability at any point of time that a patient will transition from one hidden state to another.
• Emission Probabilities: The likelihoods of seeing a particular worthy output depending on the hidden state.
• Initial State Probabilities: The probability of the system beginning in every mystery state.

The Hidden Markov Model is even more useful with time series data and sequential activities where variable states are not directly observable but derived from data. This model has been famously applied in speech-based application like voice-activated assistant, genomics and biopharmaceutical, financial services, and natural language processing.

Example of a Hidden Markov Models

Suppose we want to model daily emotional states (e.g., Happy or Sad) based on observed behaviors like smiling or frowning. In this example:

• Hidden States: Happy, Sad
• Observations: Smiling, Frowning
• Transition Probabilities: The chance of moving from Happy state to Sad state or from Sad state to Happy state.
• Emission Probabilities: Joint probability of Smiling or Frowning as the result when the model has the hidden state.

With HMMs it is feasible to predict the possible sequence of underlying emotional states that caused some behavior observing that the true emotional states are unobservable.

Real-World Applications of Hidden Markov Models

The following are some real-world applications of Hidden Markov Modes -

1. Speech Recognition: Produces alphabets, by estimating phonic conditions.
2. Financial Market Analysis: Covers models some forms of economical cycles for example the bull and bear market.
3. Natural Language Processing (NLP): Completes related activities such as the part-of-speech tagger which predicts syntactic categories of a word given sequences of words.

Differences Between Markov Chains and Hidden Markov Models

The following table highlights major differences between Markov Chains and Hidden Markov Model -

Choosing Between Markov Chains and Hidden Markov Models

A Markov Chain is a more suitable for the system, when the states are observable, otherwise, the Hidden Markov Model is a better option. But if all the states are observable there is no need for hidden layers in the process and the data can be managed by constructing a normal Markov Chain. But if you are working with systems in which states are not directly observed, and their value can only be estimated on the basis of other data, then an HMM is better.

Summary

Markov Chains and Hidden Markov Models are two exciting and important concepts in the frameworks of probabilistic modeling and machine learning. They are useful when modelling sequential tasks with distinguishable states while the Hidden Markov Models come in handy when there are underlying states that require inference from the observation. Regardless of whether you are focused on time series analysis or developing speech recognition or predictive models, knowing distinctions between these models will allow choosing the right approach.

Understanding the difference between Markov Chains and Hidden Markov Models can be critical when you choose the right probabilistic model for improving your predictive analysis, data modeling, machine learning and other applications.