CODEWITHSUNDEEP
evolutionary-algorithmstandard-errordifferential-evolution
Bazman
Bazman

Reputation: 2150

Standard Errors for Differential Evolution

Is it possible to calculate standard errors for Differential Evolution?

From the Wikipedia entry:

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

It's not derivative based (indeed that is one of its strengths) but how then so you calculate the standard errors?

I would have thought some kind of bootstrapping strategy might have been applicable but can't seem to find any sources than apply bootstrapping to DE?

Baz

Upvotes: 2

Views: 588

Answers (1)

manlio
manlio

Reputation: 18962

Concerning the standard errors, differential evolution is just like any other evolutionary algorithm.

Using a bootstrapping strategy seems a good idea: the usual formulas assume a normal (Gaussian) distribution for the underlying data. That's almost never true for evolutionary computation (exponential distributions being far more common, probably followed by bimodal distributions).

The simplest bootstrap method involves taking the original data set of N numbers and sampling from it to form a new sample (a resample) that is also of size N. The resample is taken from the original using sampling with replacement. This process is repeated a large number of times (typically 1000 or 10000 times) and for each of these bootstrap samples we compute its mean / median (each of these are called bootstrap estimates).

Use the original sample to represent the population. Take repeated re-samples from the ordinal sample. Use these re-samples to calculate an estimate for the population statistic (mean or median)

The standard deviation (SD) of the means is the bootstrapped standard error (SE) of the mean and the SD of the medians is the bootstrapped SE of the median (the 2.5th and 97.5th centiles of the means are the bootstrapped 95% confidence limits for the mean).

Warnings:

  • the word population is used with different meanings in different contexts (bootstrapping vs evolutionary algorithm)
  • in any GA or GP, the average of the population tells you almost nothing of interest. Use the mean/median of the best-of-run
  • the average of a set that is not normally distributed produces a value that behaves non-intuitively. Especially if the probability distribution is skewed: large values in "tail" can dominate and average tends to reflect the typical value of the "worst" data not the typical value of the data in general. In this case it's better the median

Some interesting links are:

Upvotes: 1

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