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@ARTICLE{Foster:19793,
      author       = {Foster, D.V. and Grassberger, P.},
      title        = {{L}ower bounds on mutual information},
      journal      = {Physical review / E},
      volume       = {83},
      number       = {1},
      issn         = {1539-3755},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-19793},
      pages        = {010101},
      year         = {2011},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {We 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.},
      keywords     = {J (WoSType)},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing (FUEK411) / 411 - Computational
                      Science and Mathematical Methods (POF2-411)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-HGF)POF2-411},
      shelfmark    = {Physics, Fluids $\&$ Plasmas / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000286758900001},
      doi          = {10.1103/PhysRevE.83.010101},
      url          = {https://juser.fz-juelich.de/record/19793},
}