Intel® oneAPI Data Analytics Library Developer Guide and Reference
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Ridge Regression
The ridge regression method is similar to the least squares procedure except that it penalizes the sizes of the regression coefficients. Ridge regression is one of the most commonly used methods to overcome data multicollinearity.
Details
Let be a vector of input variables and
be the response. For each
, the ridge regression model has the form similar to the linear regression model [Hoerl70], except that the coefficients are estimated by minimizing a different objective function [James2013]:

Here ,
, are referred to as independent variables, and
are referred to as dependent variables or responses.
Training Stage
Let be a set of training data,
. The matrix X of size
contains observations
,
,
, of independent variables.
For each ,
, the ridge regression estimates
by minimizing the objective function:

where are ridge parameters [Hoerl70], [James2013].
Prediction Stage
Ridge regression based prediction is done for input vector using the equation
for each
.