In the above equation (1) 
is the
contingency independent term while the two other terms are in practice
strongly contingency dependent, and it is clearly appropriate to build
the regression models in a single-contingency approach so as to
exploit the latter specificity.
Thus, for a given contingency we select its learning set (
) as the
relevant operating states (denoted 
below) for this contingency
among the 
first of the data base. Each state is characterized
by : (i) 
candidate attributes 
describing its topology (e.g. in/out indicators) and electrical state
(e.g. voltages, power flows, generation levels, reactive reserves
...) which are deemed to influence the severity of the contingency
and in terms of which it is desired to express the regression models;
(ii) its difference 
of its pre-computed values
of 
and 
.
Then the learning objective is to build an approximate model,
where the function 
is determined so as to ``explain'' as much as
possible the variance of 
observed in the learning
set, e.g. such that the Mean Square Error (MSE)
is as small as possible. Notice that this calls for the identification among the candidate attributes of a subset of attributes which are actually relevant, i.e. which actually influence the severity of the particular contingency under consideration. We conjecture that for each contingency it is possible to identify a small number of attributes able to explain most of the variance of its severity. Obviously, these salient attributes are liable to change significantly from one contingency to another.
