A MATLAB software package for higher order Markov chains

What is it about?

We present HOMC, the first MATLAB software package developed specifically for working with higher order Markov chains. In contrast to conventional first order Markov chains which are assumed memoryless, higher order Markov chains can take into consideration multiple past states and hence are more flexible when modeling the memory aspect of real-world systems. The HOMC package provides easy-to-use tools for performing important tasks, such as predicting the likelihood of hitting certain states, checking if a state is transient or recurrent, examining the long-term behavior of the system, and calculating the average times to reach certain states. A core part of the HOMC package is an efficient implementation of the so-called box product, a special type of tensor product that is pivotal in the analyses and computations involving higher order Markov chains.

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Photo by GuerrillaBuzz on Unsplash

Photo by GuerrillaBuzz on Unsplash

Why is it important?

Higher order Markov chains find applications in numerous practical domains like engineering, biological science, finance, and data science since they can be used for modeling processes that cannot be modeled using conventional first order Markov chains. Despite growing interest in higher order Markov chains, there were no MATLAB packages to support their analyses and computations. This gap is filled by the HOMC package, which provides a collection of user friendly MATLAB functions for higher order Markov chains. Moreover, the HOMC package makes efficient use of computer memory, thus enabling the computations on large size problems. As a result, the HOMC package is a useful toolkit for the research community in fields related to higher order Markov chains.

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