adelie.data.dense

adelie.data.dense(n: int, p: int, G: int, *, K: int = 1, glm: str = 'gaussian', equal_groups=False, rho: float = 0, sparsity: float = 0.95, zero_penalty: float = 0, snr: float = 1, seed: int = 0)

Creates a dense dataset.

• The groups and group sizes are generated randomly such that G groups are created and the sum of the group sizes is p.

• The data matrix X is generated from a normal distribution where each feature is equicorrelated with the other features by rho.

• The true coefficients \(\beta\) are such that sparsity proportion of the entries are set to \(0\).

• The response y is generated from the GLM specified by glm.

• The penalty factors are by default set to np.sqrt(group_sizes), however if zero_penalty > 0, a random set of penalties will be set to zero, in which case, penalty is rescaled such that the \(\ell_2\) norm squared equals p.

Parameters:

nint

Number of data points.

pint

Number of features.

Gint

Number of groups.

Kint, optional

Number of classes for multi-response GLMs. Default is 1.

glmstr, optional

GLM name. It must be one of the following:

• "binomial"

• "cox"

• "gaussian"

• "multigaussian"

• "multinomial"

• "poisson"

Default is "gaussian".

equal_groupsbool, optional

If True, group sizes are made as equal as possible. Default is False.

rhofloat, optional

Feature (equi)-correlation. Default is 0 so that the features are independent.

sparsityfloat, optional

Proportion of \(\beta\) entries to be zeroed out. Default is 0.95.

zero_penaltyfloat, optional

Proportion of penalty entries to be zeroed out. Default is 0.

snrfloat, optional

Signal-to-noise ratio. Default is 1.

seedint, optional

Random seed. Default is 0.

Returns:

datadict

A dictionary containing the generated data:

• "X": feature matrix.

• "y": response vector.

• "groups": mapping of group index to the starting column index of X.

• "group_sizes": mapping of group index to the group size.

• "penalty": penalty factor for each group index.