thesIt » error 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 Stone 1974 is referenced in: Michaelsen … http://lakm.us/thesit/316/stone-1974-is-referenced-inmichaelsen/ http://lakm.us/thesit/316/stone-1974-is-referenced-inmichaelsen/#comments Sun, 22 Aug 2010 12:41:37 +0000 Arif http://xp-racy.lan/s2/?p=316 Stone 1974 is referenced in:
Michaelsen J. 1987. Cross-validation in statistical climate forecast models. J Climate Applied Meteorology, 26:1589-1600

1520-0450(1987)026-1589-cviscf-2.0.co;2.pdf

Set Z = z_{1}, z_{2},... , z_{1} consists of predictions and targets z_{i}=(x_{i}, y_{i})

A set of prediction rule \eta (x,Z) will be used to predict y0 from \eta (x_{0},Z)

Let Q(y_{i},\eta_{i}) be the accuracy.
by least squares this will usually (y_{i}-\eta_{i})^{2}
in other words expected Err is
Err= E[Q(y_{i},\eta(x_{0},Z))]

MSE

MSE= \sum_{i=1}^{n}Q(y_{i},\eta(x_{i},Z))/n

In cross validation
MSE_{(CV)}= \sum_{i=1}^{n}Q(y_{i},\eta(x_{i},Z_{(i)}))/n

]]> http://lakm.us/thesit/316/stone-1974-is-referenced-inmichaelsen/feed/ 0 If we assume a normally distributed popu … http://lakm.us/thesit/315/if-we-assume-a-normally-distributed-popu/ http://lakm.us/thesit/315/if-we-assume-a-normally-distributed-popu/#comments Sun, 22 Aug 2010 12:19:08 +0000 Arif http://xp-racy.lan/s2/?p=315 If we assume a normally distributed population with mean μ and standard deviation σ, and take sample

x_{1}, x_{2},..., x_{n}\sim N(\mu,\sigma^{2})

statistical error is then
\varepsilon_{i}=x_{i}-\mu

Residual

while residual is
\hat{\varepsilon}_{i}=x_{i}-\bar{x}

hat over the letter ε indicates an observable estimate of an unobservable quantity called ε.

]]> http://lakm.us/thesit/315/if-we-assume-a-normally-distributed-popu/feed/ 0