nnpiv.linear.sparse_ridge_l1vsl1

class nnpiv.linear.sparse_ridge_l1vsl1(lambda_theta=0.01, B=100, eta_theta='auto', eta_w='auto', n_iter=2000, tol=0.01, sparsity=None, fit_intercept=True)

Sparse linear NPIV with empirical-L2 learner regularization.

Let \(Q_X=\mathbb E_n[XX^\top]\) and \(m(\alpha)=\mathbb E_n[Z(X^\top\alpha-Y)]\). This estimator solves

\[\min_{\|\alpha\|_1\leq B}\max_{\|\theta\|_1\leq 1} \theta^\top m(\alpha) +\frac{\lambda}{2}\alpha^\top Q_X\alpha.\]

duality_gap_ uses the exact quadratic learner best response over the \(\ell_1\) ball, including the active-boundary case.

Parameters

_SparseLinearAdversarialGMM. (Same as) –

fit(Z, X, Y)

Fit the model.

Parameters

• Z (array-like) – Instrumental variables.

• X (array-like) – Covariates.

• Y (array-like) – Outcomes.

Returns

Fitted estimator.

Return type

self

predict(X)

Predict.

Parameters

X (array-like) – Feature or treatment matrix.

Returns

Fitted linear function evaluated at X.

Return type

ndarray