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minor update on docstring
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kzkadc committed Sep 8, 2024
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Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions ignite/metrics/hsic.py
Original file line number Diff line number Diff line change
Expand Up @@ -18,14 +18,14 @@ class HSIC(Metric):
+ \frac{\mathbf{1}^\top \tilde{\mathbf{K}} \mathbf{11}^\top \tilde{\mathbf{L}} \mathbf{1}}{(B-1)(B-2)}
-\frac{2}{B-2}\mathbf{1}^\top \tilde{\mathbf{K}}\tilde{\mathbf{L}} \mathbf{1} \right]
where :math:`\tilde{\mathbf{K}}` and :math:`\tilde{\mathbf{L}}` are the Gram matrices of
where :math:`B` is the batch size, and :math:`\tilde{\mathbf{K}}` and :math:`\tilde{\mathbf{L}}` are the Gram matrices of
the Gaussian RBF kernel with their diagonal entries being set to zero.
HSIC measures non-linear statistical independence between features :math:`X` and :math:`Y`.
HSIC becomes zero if and only if :math:`X` and :math:`Y` are independent.
This metric computes the unbiased estimator of HSIC proposed in
`Song et al., 2012 <https://jmlr.csail.mit.edu/papers/v13/song12a.html>`_
`Song et al. (2012) <https://jmlr.csail.mit.edu/papers/v13/song12a.html>`_
for each batch and accumulates the average.
Each batch must contain at least four samples.
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