ridgeBasic#

swordfish.function.ridgeBasic()#

Perform Ridge regression.

Minimize the following objective function:

\[\begin{align*} \lVert y - X w \rVert_2^2 + \alpha \, \lVert w \rVert_2^2 \end{align*}\]
Parameters:

  • Y (Constant) – A numeric vector indicating the dependent variable.

  • X (Constant) –

    Aa numeric vector/tuple/matrix/table indicating the independent variable.

    • When X is a vector/tuple, it must be of the same length as Y.

    • When X is a matrix/table, the number of rows must be the same as the length of Y.

  • mode (Constant, optional) –

    An integer indicating the contents in the output. It can be:

    • 0 (default): a vector of the coefficient estimates.

    • 1: a table with coefficient estimates, standard error, t-statistics, and p-values.

    • 2: a dictionary with the following keys: ANOVA, RegressionStat, Coefficient, and Residual.

  • alpha (Constant, optional) – A floating number representing the constant that multiplies the L1-norm. The default value is 1.0.

  • intercept (Constant, optional) – A Boolean value indicating whether to include the intercept in the regression. The default value is true.

  • normalize (Constant, optional) – 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 (Constant, optional) – A positive integer indicating the maximum number of iterations. The default value is 1000.

  • tolerance (Constant, optional) – 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 (Constant, optional) – 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’.

  • swColName (Constant, optional) – A STRING indicating a column name of ds. The specified column is used as the sample weight. If it is not specified, the sample weight is treated as 1.

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