thesIt » variance http://lakm.us/thesit computer science research log in semi microbloging style Tue, 24 Aug 2010 21:34:55 +0000 http://wordpress.org/?v=2.9 en hourly 1 Bias-variance dilemma (Geman et al., 199 … http://lakm.us/thesit/330/bias-variance-dilemma-geman-et-al-199/ http://lakm.us/thesit/330/bias-variance-dilemma-geman-et-al-199/#comments Tue, 24 Aug 2010 15:07:29 +0000 Arif http://xp-racy.lan/s2/?p=330 Bias-variance dilemma (Geman et al., 1992). It can be demonstrated that the mean square value of the estimation error between the function to be modelled and the neural network consists of the sum of the (squared) bias and variance. With a neural network using a training set of fixed size, a small bias can only be achieved with a large variance (Haykin, 1994). This dilemma can be circumvented if the training set is made very large, but if the total amount of data is limited, this may not be possible.

]]> http://lakm.us/thesit/330/bias-variance-dilemma-geman-et-al-199/feed/ 0 Easiest description standard deviation http://lakm.us/thesit/288/easiest-standard-deviation-is-distance-f/ http://lakm.us/thesit/288/easiest-standard-deviation-is-distance-f/#comments Mon, 28 Jun 2010 22:27:38 +0000 Arif http://xp-racy.lan/s2/?p=287 Easiest description for standard deviation definition is distance from mean (expected value) as shown in this graphical depiction


where all the values fall at σ distance within the dotted circle radius. Of course a more real-life situation is shown as


where σ is the square root of the following mean
\sigma^2 =\frac{\sum_{i=1}^{n}{\sigma_{i}^2}}{n}

σ² a.k.a. variance is averaged quadratic distances. Explanation:

Distance may have several concepts, in this variance description, distance shows “how far” a value is from its population expected value (mean). Quadratic form of this “how far” is

\sigma_i=(x_i-\bar{x} )^2

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