Multi-task LS estimators¶

Multi-response least squares with joint feature selection across tasks. Unlike the scalar LS family — where every output column of Y would be regressed independently — these estimators penalize a feature’s whole row of the coefficient matrix B ∈ ℝ^(p × K), so that feature j is either “active in every task” or “inactive in every task.” Useful for genomics, finance, and any setting where related outcomes are expected to share a sparse support.

All 8 classes follow the same shape:

Lasso (convex): MultiTaskLassoRegressor, MultiTaskLassoPathRegressor.
MCP (LLA-wrapped non-convex): MultiTaskMCPRegressor, MultiTaskMCPPathRegressor.
SCAD (LLA-wrapped non-convex): MultiTaskSCADRegressor, MultiTaskSCADPathRegressor.
Elastic net (convex): MultiTaskElasticNetRegressor, MultiTaskElasticNetPathRegressor.

Single-λ classes are useful when you’ve already chosen λ; path classes are the workhorse when picking λ post-hoc. CV wrappers live on the CV page.

Inputs and outputs¶

fit(X, Y) takes X ∈ ℝ^(n, p) (dense ndarray or scipy.sparse CSC) and Y ∈ ℝ^(n, K). After fitting:

coef_ has shape (K, p) — matches sklearn’s MultiTaskLasso.
intercept_ has shape (K,).
predict(X) → (n_pred, K).

Path classes have analogous coefs_ of shape (n_lambdas, K, p) and intercepts_ of shape (n_lambdas, K).

Convention vs sklearn¶

skein uses the natural per-sample objective from the stacked formulation: (1/(2nK)) ‖Y - X·B‖²_F + λ · P(B) where P(B) = Σ_j w_j ‖B[j, :]‖_2 for the lasso. sklearn’s MultiTaskLasso uses (1/(2n)) ‖Y - X·W^T‖²_F + α · ‖W‖_{2,1}. The same minimizer is reached at λ_skein = α_sklearn / K. Verified by a regression test in the suite.

This convention difference does not apply to MCP/SCAD’s shape parameters (gamma, a) — those mean the same thing as in scalar MCP/SCAD because they’re applied to the per-row L2 norm of B[j, :], which is on the same scale as the natural formulation.

See Concepts → Multi-task for the algebraic reduction (multi-task LS reduces exactly to a group-lasso problem on a virtual block-replicated design) and the K-rescale derivation.

Sparse + standardize¶

The MultiTaskLasso/MCP/SCAD/ElasticNet estimators dispatch transparently on scipy.sparse.issparse(X) — pass a CSC matrix and the path solver routes through the sparse MultiTaskDesign backend. standardize=True works for both dense (physical center+scale) and sparse (lazy Standardized wrapper composed with the augmented intercept column).

Lasso — single λ + path¶

class skein_glm.multitask.MultiTaskLassoRegressor(lambda_=0.1, *, weights=None, max_iter=100, tol=1e-06, fit_intercept=True, standardize=False, screening='strong', acceleration=5, parallel=False)[source]¶

Bases: BaseEstimator, RegressorMixin

Multi-task lasso at a single λ. Penalty is λ Σ_j w_j ‖B[j, :]‖_2 — feature j is selected jointly across all tasks. coef_ has shape (K, p), intercept_ shape (K,), predict(X) returns (n, K).

Parameters:

lambda_ (float)
weights (NDArray[np.float64] | None)
max_iter (int)
tol (float)
fit_intercept (bool)
standardize (bool)
screening (str)
acceleration (int | None)
parallel (bool)

set_fit_request(*, x='$UNCHANGED$')¶

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

x (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for x parameter in fit.
self (MultiTaskLassoRegressor)

Returns:

self – The updated object.

Return type:

Multi-task LS estimators¶

Inputs and outputs¶

Convention vs sklearn¶

Sparse + standardize¶

Lasso — single λ + path¶

MCP — single λ + path¶

SCAD — single λ + path¶

Elastic net — single λ + path¶