boltzkit.evaluation.density_based.evidence

Functions

`get_elbo`(log_weights)	Compute the Evidence Lower Bound (ELBO) using samples from q(x).
`get_eubo`(log_weights)	Compute the Evidence Upper Bound (EUBO) using samples from p(x).
`get_nll`(model_log_prob)	Compute the negative log-likelihood under q(x) using samples from p(x).

boltzkit.evaluation.density_based.evidence.get_elbo(log_weights: ndarray) → float[source]

Compute the Evidence Lower Bound (ELBO) using samples from q(x).

For \(x \sim q(x)\),

\[\log w(x) = \log \tilde{p}(x) - \log q(x), \quad \mathrm{ELBO} = \mathbb{E}_q[\log w].\]

Parameters:: log_weights (np.ndarray) – Log weights, i.e., \(\log \tilde{p}(x) - \log q(x)\) for samples \(x \sim q(x)\).
Returns:: Estimate of the ELBO.
Return type:: float

boltzkit.evaluation.density_based.evidence.get_eubo(log_weights: ndarray) → float[source]

Compute the Evidence Upper Bound (EUBO) using samples from p(x).

For \(x \sim p(x)\),

\[\log w(x) = \log \tilde{p}(x) - \log q(x), \quad \mathrm{EUBO} = \mathbb{E}_p[\log w].\]

Parameters:: log_weights (np.ndarray) – Log weights, i.e., \(\log \tilde{p}(x) - \log q(x)\) for samples \(x \sim p(x)\).
Returns:: Estimate of the EUBO.
Return type:: float

boltzkit.evaluation.density_based.evidence.get_nll(model_log_prob: ndarray) → float[source]

Compute the negative log-likelihood under q(x) using samples from p(x).

For \(x \sim p(x)\),

\[\mathrm{NLL} = -\mathbb{E}_p[\log q(x)].\]

Parameters:: model_log_prob (np.ndarray) – Log-probabilities \(\log q(x)\) evaluated at samples \(x \sim p(x)\).
Returns:: Estimate of the negative log-likelihood.
Return type:: float