Ridge

from SymbolicDSGE.regression.ridge import RidgeResult, ridge, ridge_gs

ridge(
    x: ndarray,
    y: ndarray,
    alpha: float,
    variables: list[str] | None = None,
    intercept: bool = True,
) -> RidgeResult

Run ridge regression with an L2 penalty.

Inputs:

Name	Description
x	Design matrix. Shape (n, k).
y	Response vector. Shape (n,).
alpha	Non-negative L2 penalty weight.
variables	Optional names for the columns of x. Defaults to x0, x1, ...
intercept	If True, prepend an unpenalized intercept column to the returned design matrix.

Returns:

Type	Description
RidgeResult	Regression result with ridge penalty diagnostics.

 

ridge_gs(
    x: ndarray,
    y: ndarray,
    start: float,
    stop: float,
    num: int,
    criterion: Literal["aic", "bic", "loss"] = "aic",
    variables: list[str] | None = None,
    intercept: bool = True,
) -> RidgeResult

Run ridge regression over a logarithmic alpha grid and return the best result under the selected criterion.

Inputs:

Name	Description
start	Positive lower endpoint for the alpha grid.
stop	Positive upper endpoint for the alpha grid.
num	Number of grid points.
criterion	Grid-search objective: AIC, BIC, or residual loss.
x, y, variables, intercept	Same contract as ridge(...).

 

@dataclass(frozen=True)
class RidgeResult(RegressionResult)

Additional Fields and Properties:

Name	Type	Description
alpha	float64	Selected L2 penalty weight.
effective_dof	float64	Effective degrees of freedom used by grid-search criteria.
intercept	bool	Whether the returned design includes an intercept column.
objective	RidgeObjective | None	Grid-search criterion used to select alpha, if applicable.
objective_value	float64 | None	Realized grid-search criterion value, if applicable.
l2_penalty	float64	Realized ridge penalty excluding the intercept term.

Penalty Convention

When intercept=True, the intercept is not included in l2_penalty and is not regularized by the solver.