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x HingeMaster = x" # y . [6]
2
To obtain λ, we minimized the quantity ( x " ! y)
. The least squares regression
methodology is a standard one[82] which will not be derived here. The result is that:
T ! 1 T
" = ( x x)
x y
[7]
The above Equation 7 can be said to train " based on predictor output and gold standard
annotation over some set of residues i. The best available value of
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fitted using the set of all residues in all proteins in the HAG, which we designate as
179
" is likely to be one
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{HAG}. That is to say, in Equation 7 we use x, y(i | i " {HAG}) and obtain a particular
value of " which we call " HAG .
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Cross-validating HingeMaster parameters
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The HingeMaster cannot be tested on the same dataset used to train it. This is because
given sufficient predictors it is possible to fit the test results perfectly to the data, with no
guarantee that similar performance will be obtained on different proteins. This is referred
to as overfitting. To avoid this, we train and validate the predictor by first randomly
separating the 20 homologous pairs of proteins in HAG into a training set consisting of
15 of these pairs (30 total proteins) and a test set consisting of the remaining 5
pairs. The set of all residues in all proteins in the training set we call {TRAINING} ,
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