Initial Active Set

User-specified initial active set

We believe that it worth allowing given an initial active set so that the splicing process starts from this set for each sparsity. It might come from prior analysis, whose result is not quite precise but better than random selection, so the algorithm can run more efficiently. Or you just want to give different initial sets to test the stability of the algorithm.

Note that this is NOT equivalent to always_select, since they can be exchanged to inactive set when splicing.

To specify initial active set, an additive argument A_init should be given in fit().

import numpy as np
from abess.datasets import make_glm_data
from abess.linear import LinearRegression
n = 100
p = 10
k = 3
np.random.seed(2)

data = make_glm_data(n=n, p=p, k=k, family='gaussian')

model = LinearRegression(support_size=range(0, 5), A_init=[0, 1, 2])
model.fit(data.x, data.y)

LinearRegression(A_init=[0, 1, 2], support_size=range(0, 5))

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Some strategies for initial active set are:

• If sparsity = len(A_init), the splicing process would start from A_init.

• If sparsity > len(A_init), the initial set includes A_init and other variables with larger forward sacrifices chooses.

• If sparsity < len(A_init), the initial set includes part of A_init.

• If both A_init and always_select are given, always_select first.

• For warm-start, A_init will only affect splicing under the first sparsity in support_size.

• For CV, A_init will affect each fold but not the re-fitting on full data.

The abess R package also supports user-defined initial active set. For R tutorial, please view https://abess-team.github.io/abess/articles/v07-advancedFeatures.html.