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000019793 084__ $$2WoS$$aPhysics, Fluids & Plasmas
000019793 084__ $$2WoS$$aPhysics, Mathematical
000019793 1001_ $$0P:(DE-HGF)0$$aFoster, D.V.$$b0
000019793 245__ $$aLower bounds on mutual information
000019793 260__ $$aCollege Park, Md.$$bAPS$$c2011
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000019793 520__ $$aWe correct claims about lower bounds on mutual information (MI) between real-valued random variables made by Kraskov et al., Phys. Rev. E 69, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions. This is so in spite of the invariance of MI under reparametrizations, because linear correlations are not invariant under them. The simplest bounds are obtained for Gaussians, but the most interesting ones for practical purposes are obtained for uniform marginal distributions. The latter can be enforced in general by using the ranks of the individual variables instead of their actual values, in which case one obtains bounds on MI in terms of Spearman correlation coefficients. We show with gene expression data that these bounds are in general nontrivial, and the degree of their (non) saturation yields valuable insight.
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000019793 8567_ $$uhttp://dx.doi.org/10.1103/PhysRevE.83.010101
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