`mapie.metrics`.hsic¶

mapie.metrics.hsic(y_true: numpy.ndarray[Any, numpy.dtype[numpy._typing._generic_alias.ScalarType]], y_intervals: numpy.ndarray[Any, numpy.dtype[numpy._typing._generic_alias.ScalarType]], kernel_sizes: Union[numpy._typing._array_like._SupportsArray[numpy.dtype], numpy._typing._nested_sequence._NestedSequence[numpy._typing._array_like._SupportsArray[numpy.dtype]], bool, int, float, complex, str, bytes, numpy._typing._nested_sequence._NestedSequence[Union[bool, int, float, complex, str, bytes]]] = (1, 1)) → numpy.ndarray[Any, numpy.dtype[numpy._typing._generic_alias.ScalarType]][source]¶

Compute the square root of the hsic coefficient. HSIC is Hilbert-Schmidt independence criterion that is a correlation measure. Here we use it as proposed in [4], to compute the correlation between the indicator of coverage and the interval size.

If hsic is 0, the two variables (the indicator of coverage and the interval size) are independant.

Warning: This metric should be used only with non constant intervals (intervals of different sizes), with constant intervals the result may be misinterpreted.

[4] Feldman, S., Bates, S., & Romano, Y. (2021). Improving conditional coverage via orthogonal quantile regression. Advances in Neural Information Processing Systems, 34, 2060-2071.

Parameters

y_true: NDArray of shape (n_samples,): True labels.
y_intervals: NDArray of shape (n_samples, 2, n_alpha) or (n_samples, 2): Prediction sets given by booleans of labels.
kernel_sizes: ArrayLike of size (2,): The variance (sigma) for each variable (the indicator of coverage and the interval size), this coefficient controls the width of the curve.

Returns

NDArray of shape (n_alpha,): One hsic correlation coefficient by alpha.

Raises

ValueError: If kernel_sizes has a length different from 2 and if it has negative or null values.
Examples

>>> from mapie.metrics import hsic
    ..

>>> import numpy as np
    ..

>>> y_true = np.array([9.5, 10.5, 12.5])
    ..

>>> y_intervals = np.array([
    ..

… [[9, 9], [10.0, 10.0]],
… [[8.5, 9], [12.5, 12]],
… [[10.5, 10.5], [12.0, 12]]
… ])

>>> print(hsic(y_true, y_intervals))
    ..

[0.31787614 0.2962914 ]

mapie.metrics.hsic¶

`mapie.metrics`.hsic¶