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What Is a Markov Random Field?

Kenneth W. Michael Wills
Kenneth W. Michael Wills

Central to understanding a Markov Random Field is having a firm foundation of stochastic process in probability theory. Stochastic process depicts a sequence of random possibilities that can occur in a process over a continuum of time, such as predicting currency fluctuations in the currency exchanges market. With a Markov Random Field, however, time is replaced with space that occupies two or more dimensions and offers potentially wider applications for predicting random possibilities in physics, sociology, computer vision tasks, machine learning and economics. The Ising Model is the prototype model used in physics. In computers, it is most often used to predict image restoration processes.

Predicting random possibilities and their probabilities is increasingly important in a number of fields, including science, economics and information technology. Firmly understanding and accounting for random possibilities allows scientists and researchers to make quicker advances in research and model more accurate probabilities, such as predicting and modeling economic losses from hurricanes of various intensities. Using stochastic process, researchers can predict multiple possibilities and determine which ones are most probable in a given task.

Woman doing a handstand with a computer
Woman doing a handstand with a computer

When the future stochastic process does not depend on the past, based on its present state, it is said to have a Markov property, which is defined as a property without memory.The property can react randomly from its present state since it lacks memory. Markov assumption is a term assigned to the stochastic process when a property is assumed to hold such a state; the process is then termed Markovian or a Markov property. Markov Random Field, however, does not specify time, but rather represents a characteristic that derives its value based on immediate neighboring locations, rather than time. Most researchers use an undirected graph model to represent a Markov Random Field.

To illustrate, when a hurricane makes landfall, how the hurricane acts and how much destruction it causes is directly related to what it encounters when making landfall. Hurricanes hold no memory of past destruction, but react according to immediate environmental factors. Scientists could use Markov Random Field theory to graph potential random possibilities of economic destruction based on how hurricanes have responded in similar geographic situations.

Making use of Markov Random Field is potentially helpful in a variety of other situations. Polarization phenomena in sociology are one such application as well as using the Ising model in understanding physics. Machine learning is also another application and may prove particularly useful in finding hidden patterns. Pricing and the design of products may benefit from using the theory as well.

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      Woman doing a handstand with a computer