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Markov random fields replace time with space to predict random possibilities in physics, sociology, computer vision, machine learning, and economics. The Ising model is used in physics and image recovery. Understanding random chance allows for more accurate predictions in science, business, and information technology. Markov property is memoryless and reacts based on present state. Markov random fields derive value from nearby locations. Applications include hurricanes, polarization phenomena, machine learning, pricing, and product design.
Fundamental to understanding a Markov random field is to have a solid foundation of the stochastic process in probability theory. Stochastic process describes a sequence of random possibilities that can occur in a process over a time continuum, such as predicting currency fluctuations in the foreign exchange market. With a Markov random field, however, time is replaced with space that spans two or more dimensions and offers potentially broader 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 often used to predict image recovery processes.
The prediction of random possibilities and their probabilities is increasingly important in a number of fields, including science, business, and information technology. Firmly understanding and accounting for random chance allows scientists and researchers to make faster research progress and to model more accurate probabilities, such as predicting and modeling economic losses from hurricanes of varying strengths. Using the stochastic process, researchers can predict multiple possibilities and determine which ones are more likely in a given task.
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 memoryless property. The property can randomly react from its present state as it lacks memory. The Markov assumption is a term assigned to the stochastic process when a property is assumed to maintain that state; the process is then called Markovian or Markov property. Markov Random Field, however, does not specify time, but rather represents a feature that derives its value based on immediately nearby locations, rather than time. Most researchers use an undirected graph model to represent a random Markov 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 it makes landfall. Hurricanes retain no memory of past destruction, but react based on immediate environmental factors. Scientists could use Markov random field theory to graph potential random chances of economic destruction based on how hurricanes responded in similar geographic situations.
Making use of Markov Random Field is potentially useful in a variety of other situations. Polarization phenomena in sociology are one such application, as is the use of the Ising model in understanding physics. Machine learning is also another application and can prove particularly useful in finding hidden patterns. Pricing and product design can also benefit from using the theory.
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