MultivariateNormalScore#

class bayesflow.scores.MultivariateNormalScore(dim: int = None, links: dict = None, **kwargs)[source]#

Bases: ParametricDistributionScore

\(S(\hat p_{\mu, \Sigma}, \theta; k) = \log( \mathcal N (\theta; \mu, \Sigma))\)

Scores a predicted mean and covariance matrix with the log-score of the probability of the materialized value.

get_config()[source]#

get_head_shapes_from_target_shape(target_shape: tuple[int, ...]) → dict[str, tuple[int, ...]][source]#: Request a dictionary of names and output shapes of required heads from the score.

log_prob(x: Tensor, mean: Tensor, covariance: Tensor) → Tensor[source]#

Compute the log probability density of a multivariate Gaussian distribution.

This function calculates the log probability density for each sample in x under a multivariate Gaussian distribution with the given mean and covariance.

The computation includes the determinant of the covariance matrix, its inverse, and the quadratic form in the exponential term of the Gaussian density function.

Parameters:

xTensor: A tensor of input samples for which the log probability density is computed. The shape should be compatible with broadcasting against mean.
meanTensor: A tensor representing the mean of the multivariate Gaussian distribution.
covarianceTensor: A tensor representing the covariance matrix of the multivariate Gaussian distribution.

Returns:

Tensor: A tensor containing the log probability densities for each sample in x under the given Gaussian distribution.

sample(batch_shape: tuple[int, ...], mean: Tensor, covariance: Tensor) → Tensor[source]#

Generate samples from a multivariate Gaussian distribution.

This function samples from a multivariate Gaussian distribution with the given mean and covariance using the Cholesky decomposition method. Independent standard normal samples are transformed using the Cholesky factor of the covariance matrix to generate correlated samples.

Parameters:

batch_shapeShape: A tuple specifying the batch size and the number of samples to generate.
meanTensor: A tensor representing the mean of the multivariate Gaussian distribution. Must have shape (batch_size, D), where D is the dimensionality of the distribution.
covarianceTensor: A tensor representing the covariance matrix of the multivariate Gaussian distribution. Must have shape (batch_size, D, D), where D is the dimensionality.

Returns:

Tensor: A tensor of shape (batch_size, num_samples, D) containing the generated samples.

aggregate(scores: Tensor, weights: Tensor = None) → Tensor#

Computes the mean of scores, optionally applying weights.

This function computes the mean value of the given scores. When weights are provided, it first multiplies the scores by the weights and then computes the mean of the result. If no weights are provided, it computes the mean of the scores.

Parameters:

scoresTensor: A tensor containing the scores to be aggregated.
weightsTensor, optional (default - None): A tensor of weights corresponding to each score. Must be the same shape as scores. If not provided, the function returns the mean of scores.

Returns:

Tensor: The aggregated score computed as a weighted mean if weights is provided, or as the simple mean of scores otherwise.

classmethod from_config(config)#

get_head(key: str, shape: tuple[int, ...]) → Sequential#

For a specified head key and shape, request corresponding head network.

Parameters:

keystr: Name of head for which to request a link.
shape: Shape: The necessary shape for the point estimators.

Returns:

headkeras.Sequential: Head network consisting of a learnable projection, a reshape and a link operation to parameterize estimates.

get_link(key: str) → Layer#

For a specified key, request a link from network output to estimation target.

Parameters:

keystr: Name of head for which to request a link.

Returns:

linkkeras.Layer: Activation function linking network output to estimation target.

get_subnet(key: str) → Layer#

For a specified key, request a subnet to be used for projecting the shared condition embedding before reshaping to the heads output shape.

Parameters:

keystr: Name of head for which to request a link.

Returns:

linkkeras.Layer: Subnet projecting the shared condition embedding.

score(estimates: dict[str, Tensor], targets: Tensor, weights: Tensor = None) → Tensor#

Computes the quantile-based scoring function.

This function extracts the “value” tensor from the estimates dictionary and computes the pointwise difference between the estimates and the targets, expanding the target dimensions as necessary.

The scoring function applies a quantile-based transformation to the difference, computing the mean score across a specified axis. The final score is then aggregated, optionally applying weights.

Parameters:

estimatesdict[str, Tensor]: A dictionary containing tensors of estimated values. The “value” key must be present.
targetsTensor: A tensor of true target values. The shape is adjusted to align with estimates.
weightsTensor, optional: A tensor of weights corresponding to each estimate-target pair. If provided, it is used to compute a weighted aggregate score.

Returns:

Tensor: The aggregated quantile-based score, computed using the absolute pointwise difference transformed by the quantile adjustment, optionally weighted.