pyhgf.updates.posterior.exponential.posterior_update_exponential_family

pyhgf.updates.posterior.exponential.posterior_update_exponential_family(attributes: Dict, edges: Tuple[AdjacencyLists, ...], node_idx: int, sufficient_stats_fn: Callable, **args) → Dict[int, Dict]

Update the parameters of an exponential family distribution.

Assuming that \(nu\) is fixed, updating the hyperparameters of the distribution is given by:

\[\xi \leftarrow \xi + \frac{1}{\nu + 1}(t(x)-\xi)\]

Parameters:

attributes

The attributes of the probabilistic nodes.

edges

The edges of the probabilistic nodes as a tuple of pyhgf.typing.Indexes. The tuple has the same length as the node number. For each node, the index lists the value and volatility parents and children.

node_idx

Pointer to the value parent node that will be updated.

sufficient_stats_fn

Compute the sufficient statistics of the probability distribution. This should be one of the method implemented in the distribution class in pyhgf.math.Normal, for a univariate normal.

Returns:

attributes

The updated attributes of the probabilistic nodes.

References

[1]

Mathys, C., & Weber, L. (2020). Hierarchical Gaussian Filtering of Sufficient Statistic Time Series for Active Inference. In Active Inference (pp. 52–58). Springer International Publishing. https://doi.org/10.1007/978-3-030-64919-7_7