Mutual Information - Applications of Mutual Information

Applications of Mutual Information

In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:

• In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.
• Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.
• RNA secondary structure prediction from a multiple sequence alignment.
• Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.
• Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.
• Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.
• Mutual information is often used as a significance function for the computation of collocations in corpus linguistics.
• Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.
• Detection of phase synchronization in time series analysis
• In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm
• Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.
• Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.
• In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information. Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).

• The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit : learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.