# ridge

Syntax

ridge(ds, yColName, xColNames, [alpha=1.0], [intercept=true], [normalize=false], [maxIter=1000], [tolerance=0.0001], [solver=’svd’])

Arguments

ds is an in-memory table, or a data source, or a list of data sources.

yColName is a string indicating the column name of the dependent variable in ds.

xColNames is a string scalar/vector indicating the column names of the independent variables in ds.

alpha is a floating number representing the constant that multiplies the L1-norm. The default value is 1.0.

intercept is a Boolean value indicating whether to include the intercept in the regression. The default value is true.

normalize is a Boolean value. If true, the regressors will be normalized before regression by subtracting the mean and dividing by the L2-norm. If intercept=false, this parameter will be ignored. The default value is false.

maxIter is a positive integer indicating the maximum number of iterations. The default value is 1000.

tolerance is a floating number. The iterations stop when the improvement in the objective function value is smaller than tolerance. The default value is 0.0001.

solver is a string indicating the solver to use in the computation. It can be either ‘svd’ or ‘cholesky’. It ds is a list of data sources, solver must be ‘cholesky’.

Details

Linear least squares with l2 regularization.

Minimize the following objective function:

$$\Bigl\lVert{y - Xw} \Bigr\rVert_2^2 + alpha * \Bigl\lVert{w}\Bigr\rVert_2^2$$

Examples

$y = [225.720746,-76.195841,63.089878,139.44561,-65.548346,2.037451,22.403987,-0.678415,37.884102,37.308288]$ x0 = [2.240893,-0.854096,0.400157,1.454274,-0.977278,-0.205158,0.121675,-0.151357,0.333674,0.410599]
$x1 = [0.978738,0.313068,1.764052,0.144044,1.867558,1.494079,0.761038,0.950088,0.443863,-0.103219]$ t = table(y, x0, x1);

$ridge(t, y, x0x1);  If t is a DFS table, then the input should be a data source: $ ridge(sqlDS(<select * from t>), y, x0x1);