Title :
The information topology
Author :
Harremoës, Peter
Author_Institution :
Dept. of Math., Copenhagen Univ., Denmark
Abstract :
If (Qn)n∈N is a sequence of probability distributions, we say that (Qn)n∈N converges to Q in information, if D(Qn||Q)→0 for n→∞, where D(P||Q)=∫ log(dP/dQ)dP is the information divergence from P to Q. Convergence in information has been proved in many cases of statistical importance. On the set of probability distributions M+1 (Ω,B) there exists several relevant topologies. For instance the strong topology is defined by the total variation norm ||P-Q||=sup|f|≤1{∫ΩfdP-∫ΩfdQ}. Since it has long been known that the divergence balls B(Q, r)={P∈M+1 (Ω,B) | D(P || Q)\n\n\t\t
Keywords :
convergence; entropy; information theory; probability; topology; convergence; divergence balls; entropy function; information divergence; information theory; information topology; neighborhood filter; probability distributions; strong topology; total variation norm; Convergence; Entropy; Filtering theory; Information filtering; Information filters; Information theory; Probability distribution; Topology;
Conference_Titel :
Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on
Print_ISBN :
0-7803-7501-7
DOI :
10.1109/ISIT.2002.1023703
