Greedy Algorithms for Optimal Distribution Approximation
Institute for Communications Engineering, Technical University of Munich, Munich 80290, Germany
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 14 June 2016 / Revised: 1 July 2016 / Accepted: 11 July 2016 / Published: 18 July 2016
The approximation of a discrete probability distribution
by an M
is considered. The approximation error is measured by the informational divergence
, which is an appropriate measure, e.g., in the context of data compression. Properties of the optimal approximation are derived and bounds on the approximation error are presented, which are asymptotically tight. A greedy algorithm is proposed that solves this M
-type approximation problem optimally. Finally, it is shown that different instantiations of this algorithm minimize the informational divergence
or the variational distance
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Geiger, B.C.; Böcherer, G. Greedy Algorithms for Optimal Distribution Approximation. Entropy 2016, 18, 262.
Geiger BC, Böcherer G. Greedy Algorithms for Optimal Distribution Approximation. Entropy. 2016; 18(7):262.
Geiger, Bernhard C.; Böcherer, Georg. 2016. "Greedy Algorithms for Optimal Distribution Approximation." Entropy 18, no. 7: 262.
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