Lasso

from SymbolicDSGE.regression.lasso import LassoResult, lasso, lasso_gs

lasso(
    X: ndarray,
    y: ndarray,
    alpha: float,
    variables: list[str] | None = None,
    intercept: bool = True,
    max_iter: int = 1000,
    tol: float = 1e-10,
) -> LassoResult

Run Lasso regression with an L1 penalty using coordinate descent on the normalized Gram system.

Inputs:

Name	Description
X	Design matrix. Shape `(n, k)`.
y	Response vector. Shape `(n,)`.
alpha	Non-negative L1 penalty weight.
variables	Optional names for the columns of `X`. Defaults to `x0`, `x1`, ...
intercept	If `True`, fit an unpenalized intercept by centering and restore it in the returned design.
max_iter	Maximum coordinate-descent iterations.
tol	Coordinate-descent convergence tolerance.

Returns:

Type	Description
`LassoResult`	Regression result with L1 sparsity diagnostics.

lasso_gs(
    X: ndarray,
    y: ndarray,
    start: float,
    stop: float,
    num: int,
    variables: list[str] | None = None,
    intercept: bool = True,
    max_iter: int = 1000,
    tol: float = 1e-10,
) -> LassoResult

Evaluate a logarithmic alpha grid using the LARS-Lasso path and select the coefficient vector with the lowest residual loss.

Inputs:

Name	Description
start	Positive lower endpoint for the alpha grid.
stop	Positive upper endpoint for the alpha grid.
num	Number of grid points.
X, y, variables, intercept, max_iter, tol	Same contract as `lasso(...)`.

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

Additional Fields and Properties:

Name	Type	Description
alpha	`float64`	Selected L1 penalty weight.
effective_dof	`float64`	Active penalized coefficient count plus the intercept, when present.
intercept	`bool`	Whether the returned design includes an intercept column.
alpha_grid	`ndarray \| None`	Grid of alpha values evaluated by `lasso_gs(...)`.
coefficient_path	`ndarray \| None`	Coefficients evaluated on `alpha_grid`.
objective_trace	`ndarray \| None`	Residual-loss trace over `alpha_grid`.
knot_lambdas	`ndarray \| None`	LARS path knot locations from grid-search construction.
knot_coefficients	`ndarray \| None`	LARS path coefficients aligned to `knot_lambdas`.
penalized_coefficients	`ndarray`	Coefficients subject to the L1 penalty.
active_mask	`ndarray`	Boolean mask over penalized coefficients.
n_active	`int`	Number of active penalized coefficients.
selected_variables	`list[str]`	Variable names with active penalized coefficients.
l1_norm	`float64`	L1 norm of penalized coefficients.
l1_penalty	`float64`	Realized L1 penalty value.

Path Output

Path fields are populated by lasso_gs(...). Direct lasso(...) calls return only the selected coefficient vector and scalar L1 diagnostics.