File size: 1,593 Bytes
d6c8a4f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | import numpy as np
from src.cka.compute import linear_cka, linear_cka_feature
def hsic_biased(k, l):
h = np.eye(k.shape[0], dtype=k.dtype) - 1 / k.shape[0]
return float(np.trace(k @ h @ l @ h))
def hsic_unbiased(k, l):
m = k.shape[0]
k_tilde = k.copy()
l_tilde = l.copy()
np.fill_diagonal(k_tilde, 0.0)
np.fill_diagonal(l_tilde, 0.0)
hsic_value = (
(np.sum(k_tilde * l_tilde.T))
+ (np.sum(k_tilde) * np.sum(l_tilde) / ((m - 1) * (m - 2)))
- (2 * np.sum(k_tilde @ l_tilde) / (m - 2))
)
hsic_value /= m * (m - 3)
return float(hsic_value)
def ref_cka(a, b, unbiased=False):
k = a @ a.T
l = b @ b.T
hsic_fn = hsic_unbiased if unbiased else hsic_biased
hsic_kk = hsic_fn(k, k)
hsic_ll = hsic_fn(l, l)
hsic_kl = hsic_fn(k, l)
return float(hsic_kl / (np.sqrt(hsic_kk * hsic_ll) + 1e-6))
def main():
rng = np.random.default_rng(0)
a = rng.standard_normal((64, 128)).astype(np.float64)
b = rng.standard_normal((64, 128)).astype(np.float64)
our_biased = linear_cka(a, b, unbiased=False)
ref_biased = ref_cka(a, b, unbiased=False)
our_unbiased = linear_cka(a, b, unbiased=True)
ref_unbiased = ref_cka(a, b, unbiased=True)
our_feature = linear_cka_feature(a, b)
print("biased:", our_biased, ref_biased, "diff", abs(our_biased - ref_biased))
print("unbiased:", our_unbiased, ref_unbiased, "diff", abs(our_unbiased - ref_unbiased))
print("feature:", our_feature, ref_biased, "diff", abs(our_feature - ref_biased))
if __name__ == "__main__":
main()
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