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Team:TU Darmstadt/Modelling/Statistics
From 2013.igem.org
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| - | In information theory the Kullback-Leibler-Divergence (DKL <sup><span style="color:blue">[1]</span></sup>) describes and quantifies the distance between | + | In information theory the Kullback-Leibler-Divergence (DKL<sup><span style="color:blue">[1]</span></sup>) describes and quantifies the distance between |
two distributions P and Q. Where P denotes an experimental distribution, it is compared with Q, a reference distribution. DKL is also known as ‘relative entropy’ as well as ‘mutual information’. | two distributions P and Q. Where P denotes an experimental distribution, it is compared with Q, a reference distribution. DKL is also known as ‘relative entropy’ as well as ‘mutual information’. | ||
Although DKL is often used as a metric or distance measurement, it is not a true measurement because it is not symmetric. | Although DKL is often used as a metric or distance measurement, it is not a true measurement because it is not symmetric. | ||
Revision as of 00:52, 5 October 2013
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Information Theory
The DKL Analysis
In information theory the Kullback-Leibler-Divergence (DKL[1]) describes and quantifies the distance between
two distributions P and Q. Where P denotes an experimental distribution, it is compared with Q, a reference distribution. DKL is also known as ‘relative entropy’ as well as ‘mutual information’.
Although DKL is often used as a metric or distance measurement, it is not a true measurement because it is not symmetric.
Here, P(i) and Q(i) denote the densities of P and Q at a position i. In our study, we use the DKL to describe the distances of the survey datasets from the human practice project. Therefore, we have to calculate a histogram out of the different datasets. Here, it is important to perform a constant binsize. In this approach we assume that a hypothetical distribution Q is uniformly distributed. To achieve this, we grate an appropriate test data set with the random generator runif in R.
Results
References
Kullback, S.; Leibler, R.A. (1951). "On Information and Sufficiency". Annals of Mathematical Statistics 22 (1): 79–86. doi:10.1214/aoms/1177729694. MR 39968.
