treeple.datasets.make_trunk_mixture_classification

treeple.datasets.make_trunk_mixture_classification(n_samples, n_dim=4096, n_informative=256, mu_0=0, mu_1=1, rho=0, band_type='ma', return_params=False, mix=0.5, scaling_factor=1.0, seed=None)

Generate trunk mixture binary classification dataset.

The first class is generated from a multivariate-Gaussians with mean vector of 0’s. The second class is generated from a mixture of Gaussians with mean vectors specified by mu_0 and mu_1. The mixture is specified by the mix parameter, which is the probability of the first Gaussian in the mixture.

For each dimension in the first distribution, there is a mean of \(1 / d\), where d is the dimensionality. The covariance is the identity matrix. The second distribution has a mean vector that is the negative of the first. As d increases, the two distributions become closer and closer.

Full details for the trunk simulation can be found in [1].

Instead of the identity covariance matrix, one can implement a banded covariance matrix that follows [2].

Parameters:

n_samplesint

Number of sample to generate. Must be an even number, else the total number of samples generated will be n_samples - 1.

n_dimint, optional

The dimensionality of the dataset and the number of unique labels, by default 4096.

n_informativeint, optional

The informative dimensions. All others for n_dim - n_informative are Gaussian noise. Default is 256.

mu_0int, optional

The mean of the first distribution. By default -1. The mean of the distribution will decrease by a factor of sqrt(i) for each dimension i.

mu_1int, optional

The mean of the second distribution. By default 1. The mean of the distribution will decrease by a factor of sqrt(i) for each dimension i.

rhofloat, optional

The covariance value of the bands. By default 0 indicating, an identity matrix is used.

band_typestr

The band type to use. For details, see Example 1 and 2 in [2]. Either ‘ma’, or ‘ar’.

return_paramsbool, optional

Whether or not to return the distribution parameters of the classes normal distributions.

mixint, optional

The probabilities associated with the mixture of Gaussians in the trunk-mix simulation. By default 0.5.

scaling_factorfloat, optional

The scaling factor for the covariance matrix. By default 1.

seedint, optional

Random seed, by default None.

Returns:

Xnp.ndarray of shape (n_samples, n_dim), dtype=np.float64

Trunk dataset as a dense array.

ynp.ndarray of shape (n_samples,), dtype=np.intp

Labels of the dataset.

meanslist of ArrayLike of shape (n_dim,), dtype=np.float64

The mean vector for each class starting with class 0. Returned if return_params is True.

covslist of ArrayLike of shape (n_dim, n_dim), dtype=np.float64

The covariance for each class. Returned if return_params is True.

X_mixturenp.ndarray of shape (n_samples, n_dim), dtype=np.float64

The mixture of Gaussians. Returned if return_params is True.

Notes

Trunk: The trunk simulation decreases the signal-to-noise ratio as the dimensionality increases. This is implemented by decreasing the mean of the distribution by a factor of sqrt(i) for each dimension i. Thus for instance if the means of distribution one and two are 1 and -1 respectively, the means for the first dimension will be 1 and -1, for the second dimension will be 1/sqrt(2) and -1/sqrt(2), and so on.

Trunk Mix: The trunk mix simulation generates two classes of data with the same covariance matrix. The first class (label 0) is generated from a multivariate-Gaussians with mean vector of zeros and the second class is generated from a mixture of Gaussians with mean vectors specified by mu_0 and mu_1. The mixture is specified by the mix parameter, which is the probability of the first Gaussian in the mixture.

Covariance: The covariance matrix among different dimensions is controlled by the rho parameter and the band_type parameter. The band_type parameter controls the type of band to use, while the rho parameter controls the specific scaling factor for the covariance matrix while going from one dimension to the next.

References

[1]

Gerard V. Trunk and J. O. Coleman. Repeated hypothesis testing on a growing data set. IEEE Trans. Pattern Anal. Mach. Intell., 4(3):343–345, 1982. URL: https://doi.org/10.1109/TPAMI.1982.4767256, doi:10.1109/TPAMI.1982.4767256.

[2] (1,2)

Peter J. Bickel and Elizaveta Levina. Regularized estimation of large covariance matrices. The Annals of Statistics, February 2008. URL: http://dx.doi.org/10.1214/009053607000000758, doi:10.1214/009053607000000758.

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