expected_likelihood

expected_likelihood(h, r, t, exact=True)[source]

Compute the similarity based on expected likelihood.

\[D((\mu_e, \Sigma_e), (\mu_r, \Sigma_r))) = \frac{1}{2} \left( (\mu_e - \mu_r)^T(\Sigma_e + \Sigma_r)^{-1}(\mu_e - \mu_r) + \log \det (\Sigma_e + \Sigma_r) + d \log (2 \pi) \right) = \frac{1}{2} \left( \mu^T\Sigma^{-1}\mu + \log \det \Sigma + d \log (2 \pi) \right)\]

with \(\mu_e = \mu_h - \mu_t\) and \(\Sigma_e = \Sigma_h + \Sigma_t\).

Parameters
  • h (GaussianDistribution) – shape: (batch_size, num_heads, 1, 1, d) The head entity Gaussian distribution.

  • r (GaussianDistribution) – shape: (batch_size, 1, num_relations, 1, d) The relation Gaussian distribution.

  • t (GaussianDistribution) – shape: (batch_size, 1, 1, num_tails, d) The tail entity Gaussian distribution.

  • exact (bool) – Whether to return the exact similarity, or leave out constant offsets.

Return type

FloatTensor

Returns

torch.Tensor, shape: (batch_size, num_heads, num_relations, num_tails) The similarity.