dodiscover.ci.kernel_utils.f_divergence_score

dodiscover.ci.kernel_utils.f_divergence_score(y_stat_q, y_stat_p)

Compute f-divergence upper bound on KL-divergence.

See definition 4 in [1], where the function is reversed to give an upper-bound for the sake of gradient descent.

The f-divergence bound gives an upper bound on KL-divergence:

$$D_{KL}(p||q)\le \underset{f}{sup}{E}_{x\sim q}[exp(f(x)-1)]-E_{x\sim p}[f(x)]$$

Parameters:

y_stat_qarray_like of shape (n_samples_q,)

Samples from the distribution Q, the variational class.

y_stat_p: array_like of shape (n_samples_p,)

Samples from the distribution P, the joint distribution.

Returns:

f_divfloat

The f-divergence score.