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I have been reviewing some papers such as this that uses Mutual Information (MI) as a criteria to obtain most informative point to approximate some large field an reduce uncertainty of the field. This large field could be Martian terrain, or ocean sampling. The concept is that we are sampling only few "most informative" locations to get the best estimate of the field.

One of the criteria is MI, were we look to sample the location where this MI is maximum based on the observations we already have taken and fitted a model such as Gaussian Process.

The question is: Why are we using MI as a search criteria or utility function, MI looks for a future observation that are most correlated with the current observations, so isnt it counter intuitive, because we want to estimate the large field so we should be looking for samples that are not correlated because the notion of correlation is that we "partially" know what those future observations shall be, so isnt it better to look for something "not correlated" in other words the future samples we have "no information" of?

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