4.1.5.1.1. statsmodels.base.l1_slsqp.fit_l1_slsqp

statsmodels.base.l1_slsqp.fit_l1_slsqp(f, score, start_params, args, kwargs, disp=False, maxiter=1000, callback=None, retall=False, full_output=False, hess=None)

Solve the l1 regularized problem using scipy.optimize.fmin_slsqp().

Specifically: We convert the convex but non-smooth problem

\[\min_\beta f(\beta) + \sum_k\alpha_k |\beta_k|\]

via the transformation to the smooth, convex, constrained problem in twice as many variables (adding the “added variables” \(u_k\))

\[\min_{\beta,u} f(\beta) + \sum_k\alpha_k u_k,\]

subject to

\[-u_k \leq \beta_k \leq u_k.\]

Parameters:

All the usual parameters from LikelhoodModel.fit

alpha : non-negative scalar or numpy array (same size as parameters)

The weight multiplying the l1 penalty term

trim_mode : ‘auto, ‘size’, or ‘off’

If not ‘off’, trim (set to zero) parameters that would have been zero

if the solver reached the theoretical minimum.

If ‘auto’, trim params using the Theory above. If ‘size’, trim params if they have very small absolute value

size_trim_tol : float or ‘auto’ (default = ‘auto’)

For use when trim_mode === ‘size’

auto_trim_tol : float

For sue when trim_mode == ‘auto’. Use

qc_tol : float

Print warning and don’t allow auto trim when (ii) in “Theory” (above) is violated by this much.

qc_verbose : Boolean

If true, print out a full QC report upon failure

acc : float (default 1e-6)

Requested accuracy as used by slsqp