`heat.regression.lasso`

Implementation of the LASSO regression

Module Contents

class Lasso(lam: float | None = 0.1, max_iter: int | None = 100, tol: float | None = 1e-06)

Bases: heat.RegressionMixin, heat.BaseEstimator

``Least absolute shrinkage and selection operator``(LASSO), a linear model with L1 regularization. The optimization objective for Lasso is:

\[E(w) = \frac{1}{2 m} ||y - Xw||^2_2 + \lambda ||w\_||_1\]

with

\[w\_=(w_1,w_2,...,w_n), w=(w_0,w_1,w_2,...,w_n),\]

\[y \in M(m \times 1), w \in M(n \times 1), X \in M(m \times n)\]

Parameters:

lam (float, optional) – Constant that multiplies the L1 term. Default value: 0.1 lam = 0. is equivalent to an ordinary least square (OLS). For numerical reasons, using lam = 0., with the Lasso object is not advised.
max_iter (int, optional) – The maximum number of iterations. Default value: 100
tol (float, optional. Default value: 1e-8) – The tolerance for the optimization.

Variables:

__theta (array, shape (n_features + 1,), first element is the interception parameter vector w.)
coef (array, shape (n_features,) | (n_targets, n_features)) – parameter vector (w in the cost function formula)
intercept (float | array, shape (n_targets,)) – independent term in decision function.
n_iter (int or None | array-like, shape (n_targets,)) – number of iterations run by the coordinate descent solver to reach the specified tolerance.

Examples

>>> X = ht.random.randn(10, 4, split=0)
>>> y = ht.random.randn(10,1, split=0)
>>> estimator = ht.regression.lasso.Lasso(max_iter=100, tol=None)
>>> estimator.fit(X, y)