pyhgf.updates.prediction_error.exponential.prediction_error_update_exponential_family_fixed

pyhgf.updates.prediction_error.exponential.prediction_error_update_exponential_family_fixed(attributes, node_idx, sufficient_stats_fn, **args)

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.

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.

Parameters:

• attributes (Dict)

• node_idx (int)

• sufficient_stats_fn (Callable)

Return type:

Dict[int | str, Dict]

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