TY  - JOUR
AU  - Foster, D.V.
AU  - Grassberger, P.
TI  - Lower bounds on mutual information
JO  - Physical review / E
VL  - 83
IS  - 1
SN  - 1539-3755
CY  - College Park, Md.
PB  - APS
M1  - PreJuSER-19793
SP  - 010101
PY  - 2011
N1  - Record converted from VDB: 12.11.2012
AB  - 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.
KW  - J (WoSType)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000286758900001
DO  - DOI:10.1103/PhysRevE.83.010101
UR  - https://juser.fz-juelich.de/record/19793
ER  -