brainmass.objectives.ks_distance

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brainmass.objectives.ks_distance#

brainmass.objectives.ks_distance(p, q)[source]#

Kolmogorov-Smirnov statistic between two 1-D densities / histograms.

Each cumulative sum is normalised to a proper CDF before the supremum is taken, so the result lies in [0, 1] independent of bin width and is directly comparable to scipy.stats.ks_2samp().

\[D = \sup_x \left| F_p(x) - F_q(x) \right|.\]
Parameters:

  • p (array) – Densities or (unnormalised) histograms on a shared, ordered grid.

  • q (array) – Densities or (unnormalised) histograms on a shared, ordered grid.

Returns:

Scalar KS statistic in [0, 1].

Return type:

jax.Array

Notes

The supremum (max) makes this non-smooth: its gradient is the indicator at the argmax, so prefer wasserstein_1d() (and fcd_wasserstein()) when the distance is a fitting loss. Use KS for evaluation / reporting, where literature comparability matters.

See also

wasserstein_1d

smooth, gradient-friendly distributional distance.

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