ExpectedLikelihood

class ExpectedLikelihood(exact: bool = True)

Bases: KG2ESimilarity

Compute the similarity based on expected likelihood.

Denoting \(\mu = \mu_e - \mu_r\) and \(\Sigma = \Sigma_e + \Sigma_t\), it is given by

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

Initialize the similarity module.

Parameters:

exact (bool) – Whether to return the exact similarity, or leave out constant offsets for slightly improved speed.

Methods Summary

forward(h, r, t)

Calculate the similarity.

Methods Documentation

forward(h: GaussianDistribution, r: GaussianDistribution, t: GaussianDistribution) → Tensor

Calculate the similarity.

# noqa: DAR401

Parameters:

• h (GaussianDistribution) – shape: (*batch_dims, d) The head entity Gaussian distribution.

• r (GaussianDistribution) – shape: (*batch_dims, d) The relation Gaussian distribution.

• t (GaussianDistribution) – shape: (*batch_dims, d) The tail entity Gaussian distribution.

Returns:

torch.Tensor, shape: (*batch_dims) # noqa: DAR202 The similarity.

Return type:

Tensor