tick.prox.ProxGroupL1

class tick.prox.ProxGroupL1(strength: float, blocks_start, blocks_length, range: tuple = None, positive: bool = False)[source]

Proximal operator of group-L1, a.k.a group-Lasso. It applies ProxL2 in each group, or block. Blocks (non-overlapping) are specified by the blocks_start and blocks_length parameters.

Parameters

strength : float

Level of penalization. Note that ProxL2 which is applied in each group multiplies strength by the square-root of the group size. This allows to consider strengths that have the same order as with ProxL1 or other separable proximal operators.

blocks_start : list or numpy.array, shape=(n_blocks,)

First entry of each block

blocks_length : list or numpy.array, shape=(n_blocks,)

Size of each block

range : tuple of two int, default=`None`

Range on which the prox is applied. If None then the prox is applied on the whole vector

positive : bool, default=`False`

If True, apply the penalization together with a projection onto the set of vectors with non-negative entries

Attributes

n_blocks : int

Number of blocks

dtype : {'float64', 'float32'}

Type of the arrays used.

__init__(strength: float, blocks_start, blocks_length, range: tuple = None, positive: bool = False)[source]

Initialize self. See help(type(self)) for accurate signature.

call(coeffs, step=1.0, out=None)

Apply proximal operator on a vector. It computes:

\[argmin_x \big( f(x) + \frac{1}{2} \|x - v\|_2^2 \big)\]
Parameters

coeffs : numpy.ndarray, shape=(n_coeffs,)

Input vector on which is applied the proximal operator

step : float or np.array, default=1.

The amount of penalization is multiplied by this amount

  • If float, the amount of penalization is multiplied by this amount

  • If np.array, then each coordinate of coeffs (within the given range), receives an amount of penalization multiplied by t (available only for separable prox)

out : numpy.ndarray, shape=(n_params,), default=None

If not None, the output is stored in the given out. Otherwise, a new vector is created.

Returns

output : numpy.ndarray, shape=(n_coeffs,)

Same object as out

Notes

step must have the same size as coeffs whenever range is None, or a size matching the one given by the range otherwise

value(coeffs: numpy.ndarray)

Returns the value of the penalization at coeffs

Parameters

coeffs : numpy.array, shape=(n_coeffs,)

The value of the penalization is computed at this point

Returns

output : float

Value of the penalization at coeffs

Examples using tick.prox.ProxGroupL1