hoi.metrics.GradientOinfo

hoi.metrics.GradientOinfo#

class hoi.metrics.GradientOinfo(x, y, multiplets=None, base_model=<class 'hoi.metrics.oinfo.Oinfo'>, verbose=None)[source]#

First order Gradient O-information.

The Gradient O-information is defined as the difference between the O-information with the target variable minus the O-information without the target variable :

\[\begin{split}\partial_{i}\Omega(X^{n}) &= \Omega(X^{n}) - \Omega(X^{n}_{-i}) \\ &= (2 - n)I(X_{i}; X^{n}_{-i}) + \sum_{ k=1, k\neq i}^{n} I(X_{k}; X^{n}_{-ik})\end{split}\]

Warning

\(\partial_{i}\Omega(X^{n}) > 0 \Rightarrow Redundancy\)
\(\partial_{i}\Omega(X^{n}) < 0 \Rightarrow Synergy\)

Parameters:

xarray_like: Standard NumPy arrays of shape (n_samples, n_features) or (n_samples, n_features, n_variables)
yarray_like: The feature of shape (n_samples,) for estimating task-related O-info
multipletslist | None: List of multiplets to compute. Should be a list of multiplets, for example [(0, 1, 2), (2, 7, 8, 9)]. By default, all multiplets are going to be computed.

Attributes:

entropies: Entropies of shape (n_mult,)
multiplets: Indices of the multiplets of shape (n_mult, maxsize).
order: Order of each multiplet of shape (n_mult,).
undersampling: Under-sampling threshold.

Methods

`compute_entropies`([method, minsize, ...])	Compute entropies for all multiplets.
`fit`([minsize, maxsize, method, samples])	Compute the Gradient O-information.
`get_combinations`(minsize[, maxsize, astype])	Get combinations of features.

References

Scagliarini et al., 2023 [26]

__iter__()#: Iteration over orders.

compute_entropies(method='gc', minsize=1, maxsize=None, samples=None, **kwargs)#

Compute entropies for all multiplets.

Parameters:

method{‘gc’, ‘binning’, ‘knn’, ‘kernel}

Name of the method to compute entropy. Use either :

‘gc’: gaussian copula entropy [default]. See hoi.core.entropy_gc()

‘binning’: binning-based estimator of entropy. Note that to use this estimator, the data have be to discretized. See hoi.core.entropy_bin()

‘knn’: k-nearest neighbor estimator. See hoi.core.entropy_knn()

‘kernel’: kernel-based estimator of entropy see hoi.core.entropy_kernel()

samplesnp.ndarray

List of samples to use to compute HOI. If None, all samples are going to be used.

minsizeint, optional

Minimum size of the multiplets. Default is 1.

maxsizeint, optional

Maximum size of the multiplets. Default is None.

kwargsdict, optional

Additional arguments to pass to the entropy function.

Returns:

h_xarray_like: Entropies of shape (n_mult, n_variables)
h_idxarray_like: Indices of the multiplets of shape (n_mult, maxsize)
orderarray_like: Order of each multiplet of shape (n_mult,)

property entropies#: Entropies of shape (n_mult,)

fit(minsize=2, maxsize=None, method='gc', samples=None, **kwargs)[source]#

Compute the Gradient O-information.

Parameters:

minsize, maxsizeint | 2, None

Minimum and maximum size of the multiplets

method{‘gc’, ‘binning’, ‘knn’, ‘kernel’, callable}

Name of the method to compute entropy. Use either :

‘gc’: gaussian copula entropy [default]. See hoi.core.entropy_gc()

‘gauss’: gaussian entropy. See hoi.core.entropy_gauss()

‘binning’: binning-based estimator of entropy. Note that to use this estimator, the data have be to discretized. See hoi.core.entropy_bin()

‘knn’: k-nearest neighbor estimator. See hoi.core.entropy_knn()

‘kernel’: kernel-based estimator of entropy see hoi.core.entropy_kernel()

A custom entropy estimator can be provided. It should be a callable function written with Jax taking a single 2D input of shape (n_features, n_samples) and returning a float.

samplesnp.ndarray

List of samples to use to compute HOI. If None, all samples are going to be used.

kwargsdict | {}

Additional arguments are sent to each entropy function

Returns:

hoiarray_like: The NumPy array containing values of higher-order interactions of shape (n_multiplets, n_variables)

get_combinations(minsize, maxsize=None, astype='jax')#

Get combinations of features.

Parameters:

minsizeint: Minimum size of the multiplets
maxsizeint | None: Maximum size of the multiplets. If None, minsize is used.
astype{‘jax’, ‘numpy’, ‘iterator’}: Specify the output type. Use either ‘jax’ get the data as a jax array [default], ‘numpy’ for NumPy array or ‘iterator’.

Returns: