skglm.penalties.MCPenalty

class skglm.penalties.MCPenalty(alpha, gamma, positive=False)

Minimax Concave Penalty (MCP), a non-convex sparse penalty.

Notes

With ${\displaystyle x\ge 0}$:

${\displaystyle \text{pen}\left(x\right)=\{\begin{array}{ll}\alpha x-\frac{x^2}{2\gamma }& ifx\le \alpha \gamma \\ \gamma \frac{{\alpha }^2}{2}& ifx>\alpha \gamma \end{array}}$

${\displaystyle \text{value}=\sum _{j=1}^{n_{\text{features}}}\text{pen}\left(\left|w_j\right|\right)}$

__init__(alpha, gamma, positive=False)

Methods

__init__(alpha, gamma[, positive])
alpha_max(gradient0)	Return penalization value for which 0 is solution.
generalized_support(w)	Return a mask with non-zero coefficients.
get_spec()	Specify the numba types of the class attributes.
is_penalized(n_features)	Return a binary mask with the penalized features.
params_to_dict()	Get the parameters to initialize an instance of the class.
prox_1d(value, stepsize, j)	Compute the proximal operator of MCP.
subdiff_distance(w, grad, ws)	Compute distance of negative gradient to the subdifferential at w.
value(w)	Value of penalty at vector w.