3 reference

The canonical choice is the Renyi entropy:

$H_\alpha=\frac{1}{1-\alpha}\log P_\alpha$, with $P_{\alpha}(p_1,...,p_n)=\sum_{i=1}^{n}p_i^{\alpha}$

your entropy (the Shannon entropy) is the limit $\alpha\rightarrow 1$ of $H_\alpha$

this choice of approximation is useful because it has many meaningful applications, in a variety of contexts.

http://en.wikipedia.org/wiki/Renyi_entropy

For quantitative bounds on the rate of convergence of Renyi entropy towards Shannon entropy see

N. Harvey, J. Nelson, K. Onak, Streaming algorithms for estimating entropy, IEEE ITW '08 proceedings, online at

http://www.math.uwaterloo.ca/~harvey/Publications/StreamingEntropy/ITW.pdf

The canonical choice is the Renyi entropy:

$H_\alpha=\frac{1}{1-\alpha}\log P_\alpha$, with $P_{\alpha}(p_1,...,p_n)=\sum_{i=1}^{n}p_i^{\alpha}$

your entropy (the Shannon entropy) is the limit $\alpha\rightarrow 1$ of $H_\alpha$

this choice of approximation is useful because it has many meaningful applications, in a variety of contexts.

http://en.wikipedia.org/wiki/Renyi_entropy

For quantitative bounds on the rate of convergence of Renyi entropy towards Shannon entropy see

http://www.math.uwaterloo.ca/~harvey/Publications/StreamingEntropy/ITW.pdf

1

The canonical choice is the Renyi entropy:

$H_\alpha=\frac{1}{1-\alpha}\log P_\alpha$, with $P_{\alpha}(p_1,...,p_n)=\sum_{i=1}^{n}p_i^{\alpha}$

your entropy (the Shannon entropy) is the limit $\alpha\rightarrow 1$ of $H_\alpha$

this choice of approximation is useful because it has many meaningful applications, in a variety of contexts.

http://en.wikipedia.org/wiki/Renyi_entropy