bayesflow.losses module

bayesflow.losses.kl_latent_space_gaussian(z, log_det_J)

Computes the Kullback-Leibler divergence between true and approximate posterior assuming a Gaussian latent space as a source distribution.

Parameters:

ztf.Tensor of shape (batch_size, …)

The (latent transformed) target variables

log_det_Jtf.Tensor of shape (batch_size, …)

The logartihm of the Jacobian determinant of the transformation.

Returns:

losstf.Tensor

A single scalar value representing the KL loss, shape (,)

Examples

Parameter estimation

>>> kl_latent_space_gaussian(z, log_det_J)

bayesflow.losses.kl_latent_space_student(v, z, log_det_J)

Computes the Kullback-Leibler divergence between true and approximate posterior assuming latent student t-distribution as a source distribution.

Parameters:

vtf Tensor of shape (batch_size, …)

The degrees of freedom of the latent student t-distribution

ztf.Tensor of shape (batch_size, …)

The (latent transformed) target variables

log_det_Jtf.Tensor of shape (batch_size, …)

The logarithm of the Jacobian determinant of the transformation.

Returns:

losstf.Tensor

A single scalar value representing the KL loss, shape (,)

bayesflow.losses.kl_dirichlet(model_indices, alpha)

Computes the KL divergence between a Dirichlet distribution with parameter vector alpha and a uniform Dirichlet.

Parameters:

model_indicestf.Tensor of shape (batch_size, n_models)

one-hot-encoded true model indices

alphatf.Tensor of shape (batch_size, n_models)

positive network outputs in [1, +inf]

Returns:

kltf.Tensor

A single scalar representing \(D_{KL}(\mathrm{Dir}(\alpha) | \mathrm{Dir}(1,1,\ldots,1) )\), shape (,)

bayesflow.losses.mmd_summary_space(summary_outputs, z_dist=<function random_normal>, kernel='gaussian')

Computes the MMD(p(summary_otuputs) | z_dist) to re-shape the summary network outputs in an information-preserving manner.

Parameters:

summary_outputstf Tensor of shape (batch_size, …)

The outputs of the summary network.

z_distcallable, default tf.random.normal

The latent data distribution towards which the summary outputs are optimized.

kernelstr in (‘gaussian’, ‘inverse_multiquadratic’), default ‘gaussian’

The kernel function to use for MMD computation.

bayesflow.losses.log_loss(model_indices, preds, evidential=False, label_smoothing=0.01)

Computes the logarithmic loss given true model_indices and approximate model probabilities either according to [1] if evidential is True or according to [2] if evidential is False.

[1] Radev, S. T., D’Alessandro, M., Mertens, U. K., Voss, A., Köthe, U., & Bürkner, P. C. (2021). Amortized bayesian model comparison with evidential deep learning. IEEE Transactions on Neural Networks and Learning Systems.

[2] Elsemüller, L., Schnuerch, M., Bürkner, P. C., & Radev, S. T. (2023). A Deep Learning Method for Comparing Bayesian Hierarchical Models. arXiv preprint arXiv:2301.11873.

Parameters:

model_indicestf.Tensor of shape (batch_size, num_models)

one-hot-encoded true model indices

predstf.Tensor of shape (batch_size, num_models)

If evidential is True these should be the concentration parameters of a Dirichlet density bounded between [1, +inf]. Else, these should be normalized probability values.

evidentialboolean, optional, default: False

Whether to first normalize preds (True) or assume normalized (False, default)

label_smoothingfloat or None, optional, default: 0.01

Optional label smoothing factor.

Returns:

losstf.Tensor

A single scalar Monte-Carlo approximation of the log-loss, shape (,)

bayesflow.losses.norm_diff(tensor_a, tensor_b, axis=None, ord='euclidean')

Wrapper around tf.norm that computes the norm of the difference between two tensors along the specified axis.

Parameters:

tensor_aA Tensor.

tensor_bA Tensor. Must be the same shape as tensor_a.

axisAny or None

Axis along which to compute the norm of the difference. Default is None.

ordint or str

Order of the norm. Supports ‘euclidean’ and other norms supported by tf.norm. Default is ‘euclidean’.