from __future__ import annotations
from copy import deepcopy
-from typing import TYPE_CHECKING , Callable , Dict , List , Optional , Tuple , Union
+from typing import TYPE_CHECKING , Callable , Dict , List , Optional , Tuple
import jax.numpy as jnp
@@ -476,6 +476,7 @@ Source code for pyhgf.model.add_nodes
coupling_fn : Tuple [ Optional [ Callable ], ... ],
):
"""Add continuous state node(s) to a network."""
+
node_type = 2
default_parameters = {
@@ -531,6 +532,7 @@ Source code for pyhgf.model.add_nodes
additional_parameters : Dict ,
):
"""Add binary state node(s) to a network."""
+
# define the type of node that is created
node_type = 1
@@ -572,9 +574,10 @@ Source code for pyhgf.model.add_nodes
n_nodes : int ,
node_parameters : Dict ,
additional_parameters : Dict ,
- value_children : Tuple = ( None , None ),
+ value_children : Optional [ Tuple [ Optional [ Tuple ]]],
):
"""Add exponential family state node(s) to a network."""
+
node_type = 3
default_parameters = {
@@ -629,6 +632,7 @@ Source code for pyhgf.model.add_nodes
network : Network , n_nodes : int , node_parameters : Dict , additional_parameters : Dict
) -> Network :
"""Add categorical state node(s) to a network."""
+
node_type = 5
if "n_categories" in node_parameters :
@@ -690,6 +694,7 @@ Source code for pyhgf.model.add_nodes
network : Network , n_nodes : int , node_parameters : Dict , additional_parameters : Dict
):
"""Add a Dirichlet Process node to a network."""
+
node_type = 4
if "batch_size" in additional_parameters . keys ():
@@ -732,12 +737,13 @@ Source code for pyhgf.model.add_nodes
[docs]
def get_couplings (
-
value_parents : Optional [ Union [ Tuple , List , int ]],
-
volatility_parents : Optional [ Union [ Tuple , List , int ]],
-
value_children : Optional [ Union [ Tuple , List , int ]],
-
volatility_children : Optional [ Union [ Tuple , List , int ]],
+
value_parents : Optional [ Tuple ],
+
volatility_parents : Optional [ Tuple ],
+
value_children : Optional [ Tuple ],
+
volatility_children : Optional [ Tuple ],
) -> Tuple [ Tuple , ... ]:
"""Transform coupling parameter into tuple of indexes and strenghts."""
+
couplings = []
for indexes in [
value_parents ,
@@ -759,7 +765,7 @@
Source code for pyhgf.model.add_nodes
coupling_idxs , coupling_strengths = None , None
couplings . append (( coupling_idxs , coupling_strengths ))
- return tuple ( couplings )
+
return couplings
@@ -768,7 +774,8 @@ Source code for pyhgf.model.add_nodes
def update_parameters (
node_parameters : Dict , default_parameters : Dict , additional_parameters : Dict
) -> Dict :
- """Update the default node parameters using keywords args and dictonary."""
+ """Update the default node parameters using keywords args and dictonary"""
+
if bool ( additional_parameters ):
# ensure that all passed values are valid keys
invalid_keys = [
@@ -808,9 +815,10 @@ Source code for pyhgf.model.add_nodes
volatility_parents : Tuple = ( None , None ),
value_children : Tuple = ( None , None ),
volatility_children : Tuple = ( None , None ),
- coupling_fn : Tuple [ Optional [ Callable ], ... ] = ( None ,),
+ coupling_fn : Optional [ Tuple [ Optional [ Callable ], ... ]] = ( None ,),
) -> Network :
"""Insert a set of parametrised node in a network."""
+
# ensure that the set of coupling functions match with the number of child nodes
if value_children [ 0 ] is not None :
if value_children [ 0 ] is None :
diff --git a/dev/_modules/pyhgf/model/network.html b/dev/_modules/pyhgf/model/network.html
index 0b1e73f88..82e1b7491 100644
--- a/dev/_modules/pyhgf/model/network.html
+++ b/dev/_modules/pyhgf/model/network.html
@@ -535,7 +535,7 @@ Source code for pyhgf.model.network
self . input_idxs = value
def create_belief_propagation_fn (
- self , overwrite : bool = True , update_type : str = "unbounded"
+ self , overwrite : bool = True , update_type : str = "eHGF"
) -> "Network" :
"""Create the belief propagation function.
@@ -549,16 +549,11 @@ Source code for pyhgf.model.network
preexisting values. Otherwise, do not create a new function if the attribute
`scan_fn` is already defined.
update_type :
- The type of update to perform for volatility coupling. Can be `"unbounded"`
- (defaults), `"ehgf"` or `"standard"`. The unbounded approximation was
- recently introduced to avoid negative precisions updates, which greatly
- improve sampling performance. The eHGF update step was proposed as an
+ The type of update to perform for volatility coupling. Can be `"eHGF"`
+ (defaults) or `"standard"`. The eHGF update step was proposed as an
alternative to the original definition in that it starts by updating the
mean and then the precision of the parent node, which generally reduces the
- occurence of negative precision updates, while not removing them entirely.
- .. note:
- The different update steps only apply to nodes having at least one
- volatility parents. In other cases, the regular HGF updates are applied.
+ errors associated with impossible parameter space and improves sampling.
"""
# create the update sequence if it does not already exist
@@ -1025,6 +1020,9 @@ Source code for pyhgf.model.network
+
+
+# Functions to be added
pyhgf.updates.posterior.continuous — pyhgf 0.2.0 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Source code for pyhgf.updates.posterior.continuous
+# Author: Nicolas Legrand <nicolas.legrand@cas.au.dk>
+
+from functools import partial
+from typing import Dict
+
+import jax.numpy as jnp
+from jax import grad , jit
+
+from pyhgf.typing import Edges
+
+
+
+
[docs]
+
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
+
def posterior_update_mean_continuous_node (
+
attributes : Dict ,
+
edges : Edges ,
+
node_idx : int ,
+
node_precision : float ,
+
) -> float :
+
r """Update the mean of a state node using the value prediction errors.
+
+
1. Mean update from value coupling.
+
+
The new mean of a state node :math:`b` value coupled with other input and/or state
+
nodes :math:`j` at time :math:`k` is given by:
+
+
For linear value coupling:
+
+
.. math::
+
\mu_b^{(k)} = \hat{\mu}_b^{(k)} + \sum_{j=1}^{N_{children}}
+
\frac{\kappa_j \hat{\pi}_j^{(k)}}{\pi_b} \delta_j^{(k)}
+
+
Where :math:`\kappa_j` is the volatility coupling strength between the child node
+
and the state node and :math:`\delta_j^{(k)}` is the value prediction error that
+
was computed beforehand by
+
:py:func:`pyhgf.updates.prediction_errors.continuous.continuous_node_value_prediction_error`.
+
+
For non-linear value coupling:
+
+
.. math::
+
\mu_b^{(k)} = \hat{\mu}_b^{(k)} + \sum_{j=1}^{N_{children}}
+
\frac{\kappa_j g'_{j,b}({\mu}_b^{(k-1)}) \hat{\pi}_j^{(k)}}{\pi_b}
+
\delta_j^{(k)}
+
+
+
2. Mean update from volatility coupling.
+
+
The new mean of a state node :math:`b` volatility coupled with other input and/or
+
state nodes :math:`j` at time :math:`k` is given by:
+
+
.. math::
+
\mu_b^{(k)} = \hat{\mu}_b^{(k)} + \frac{1}{2\pi_b}
+
\sum_{j=1}^{N_{children}} \kappa_j \gamma_j^{(k)} \Delta_j^{(k)}
+
+
where :math:`\kappa_j` is the volatility coupling strength between the volatility
+
parent and the volatility children :math:`j` and :math:`\Delta_j^{(k)}` is the
+
volatility prediction error is given by:
+
+
.. math::
+
+
\Delta_j^{(k)} = \frac{\hat{\pi}_j^{(k)}}{\pi_j^{(k)}} +
+
\hat{\pi}_j^{(k)} \left( \delta_j^{(k)} \right)^2 - 1
+
+
with :math:`\delta_j^{(k)}` the value prediction error
+
:math:`\delta_j^{(k)} = \mu_j^{k} - \hat{\mu}_j^{k}`.
+
+
:math:`\gamma_j^{(k)}` is the effective precision of the prediction, given by:
+
+
.. math::
+
+
\gamma_j^{(k)} = \Omega_j^{(k)} \hat{\pi}_j^{(k)}
+
+
with :math:`\Omega_j^{(k)}` the predicted volatility computed in the prediction
+
step :py:func:`pyhgf.updates.prediction.predict_precision`.
+
+
If the child node is a continuous state node, the volatility prediction error
+
:math:`\Delta_j^{(k)}` was computed by
+
:py:func:`pyhgf.updates.prediction_errors.continuous.continuous_node_volatility_prediction_error`.
+
+
Parameters
+
----------
+
attributes :
+
The attributes of the probabilistic nodes.
+
edges :
+
The edges of the probabilistic nodes as a tuple of
+
:py:class:`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.
+
node_precision :
+
The precision of the node. Depending on the kind of volatility update, this
+
value can be the expected precision (ehgf), or the posterior from the update
+
(standard).
+
+
Returns
+
-------
+
posterior_mean :
+
The new posterior mean.
+
+
Notes
+
-----
+
This update step is similar to the one used for the state node, except that it uses
+
the observed value instead of the mean of the child node, and the expected mean of
+
the parent node instead of the expected mean of the child node.
+
+
See Also
+
--------
+
posterior_update_precision_continuous_node
+
+
References
+
----------
+
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
+
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
+
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
+
+
"""
+
# sum the prediction errors from both value and volatility coupling
+
(
+
value_precision_weigthed_prediction_error ,
+
volatility_precision_weigthed_prediction_error ,
+
) = ( 0.0 , 0.0 )
+
+
# Value coupling updates - update the mean of a value parent
+
# ----------------------------------------------------------
+
if edges [ node_idx ] . value_children is not None :
+
for value_child_idx , value_coupling , coupling_fn in zip (
+
edges [ node_idx ] . value_children , # type: ignore
+
attributes [ node_idx ][ "value_coupling_children" ],
+
edges [ node_idx ] . coupling_fn ,
+
):
+
# get the value prediction error (VAPE)
+
# if this is jnp.nan (no observation) set the VAPE to 0.0
+
value_prediction_error = attributes [ value_child_idx ][ "temp" ][
+
"value_prediction_error"
+
]
+
+
# cancel the prediction error if the child value was not observed
+
value_prediction_error *= attributes [ value_child_idx ][ "observed" ]
+
+
# get differential of coupling function with value children
+
if coupling_fn is None : # linear coupling
+
coupling_fn_prime = 1
+
else : # non-linear coupling
+
# Compute the derivative of the coupling function
+
coupling_fn_prime = grad ( coupling_fn )( attributes [ node_idx ][ "mean" ])
+
+
# expected precisions from the value children
+
# sum the precision weigthed prediction errors over all children
+
value_precision_weigthed_prediction_error += (
+
(
+
(
+
value_coupling
+
* attributes [ value_child_idx ][ "expected_precision" ]
+
* coupling_fn_prime
+
)
+
/ node_precision
+
)
+
) * value_prediction_error
+
+
# Volatility coupling updates - update the mean of a volatility parent
+
# --------------------------------------------------------------------
+
if edges [ node_idx ] . volatility_children is not None :
+
for volatility_child_idx , volatility_coupling in zip (
+
edges [ node_idx ] . volatility_children , # type: ignore
+
attributes [ node_idx ][ "volatility_coupling_children" ],
+
):
+
# get the volatility prediction error (VOPE)
+
volatility_prediction_error = attributes [ volatility_child_idx ][ "temp" ][
+
"volatility_prediction_error"
+
]
+
+
# retrieve the effective precision (γ)
+
# computed during the prediction step
+
effective_precision = attributes [ volatility_child_idx ][ "temp" ][
+
"effective_precision"
+
]
+
+
# the precision weigthed prediction error
+
precision_weigthed_prediction_error = (
+
volatility_coupling * effective_precision * volatility_prediction_error
+
)
+
+
# weight using the node's precision
+
precision_weigthed_prediction_error *= 1 / ( 2 * node_precision )
+
+
# cancel the prediction error if the child value was not observed
+
precision_weigthed_prediction_error *= attributes [ volatility_child_idx ][
+
"observed"
+
]
+
+
# aggregate over volatility children
+
volatility_precision_weigthed_prediction_error += (
+
precision_weigthed_prediction_error
+
)
+
+
# Compute the new posterior mean
+
# using value prediction errors from both value and volatility coupling
+
posterior_mean = (
+
attributes [ node_idx ][ "expected_mean" ]
+
+ value_precision_weigthed_prediction_error
+
+ volatility_precision_weigthed_prediction_error
+
)
+
+
return posterior_mean
+
[docs]
+
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
+
def posterior_update_precision_continuous_node (
+
attributes : Dict ,
+
edges : Edges ,
+
node_idx : int ,
+
) -> float :
+
r """Update the precision of a state node using the volatility prediction errors.
+
+
#. Precision update from value coupling.
+
+
The new precision of a state node :math:`b` value coupled with other input and/or
+
state nodes :math:`j` at time :math:`k` is given by:
+
+
For linear coupling (default)
+
+
.. math::
+
+
\pi_b^{(k)} = \hat{\pi}_b^{(k)} + \sum_{j=1}^{N_{children}}
+
\kappa_j^2 \hat{\pi}_j^{(k)}
+
+
Where :math:`\kappa_j` is the volatility coupling strength between the child node
+
and the state node and :math:`\delta_j^{(k)}` is the value prediction error that
+
was computed before hand by
+
:py:func:`pyhgf.updates.prediction_errors.continuous.continuous_node_value_prediction_error`.
+
+
For non-linear value coupling:
+
+
.. math::
+
+
\pi_b^{(k)} = \hat{\pi}_b^{(k)} + \sum_{j=1}^{N_{children}}
+
\hat{\pi}_j^{(k)} * (\kappa_j^2 * g'_{j,b}(\mu_b^(k-1))^2 -
+
g''_{j,b}(\mu_b^(k-1))*\delta_j)
+
+
#. Precision update from volatility coupling.
+
+
The new precision of a state node :math:`b` volatility coupled with other input
+
and/or state nodes :math:`j` at time :math:`k` is given by:
+
+
.. math::
+
+
\pi_b^{(k)} = \hat{\pi}_b^{(k)} + \sum_{j=1}^{N_{children}}
+
\frac{1}{2} \left( \kappa_j \gamma_j^{(k)} \right) ^2 +
+
\left( \kappa_j \gamma_j^{(k)} \right) ^2 \Delta_j^{(k)} -
+
\frac{1}{2} \kappa_j^2 \gamma_j^{(k)} \Delta_j^{(k)}
+
+
where :math:`\kappa_j` is the volatility coupling strength between the volatility
+
parent and the volatility children :math:`j` and :math:`\Delta_j^{(k)}` is the
+
volatility prediction error given by:
+
+
.. math::
+
+
\Delta_j^{(k)} = \frac{\hat{\pi}_j^{(k)}}{\pi_j^{(k)}} +
+
\hat{\pi}_j^{(k)} \left( \delta_j^{(k)} \right)^2 - 1
+
+
with :math:`\delta_j^{(k)}` the value prediction error
+
:math:`\delta_j^{(k)} = \mu_j^{k} - \hat{\mu}_j^{k}`.
+
+
:math:`\gamma_j^{(k)}` is the effective precision of the prediction, given by:
+
+
.. math::
+
+
\gamma_j^{(k)} = \Omega_j^{(k)} \hat{\pi}_j^{(k)}
+
+
that was computed in the prediction step.
+
+
Parameters
+
----------
+
attributes :
+
The attributes of the probabilistic nodes.
+
edges :
+
The edges of the probabilistic nodes as a tuple of
+
:py:class:`pyhgf.typing.Indexes`. The tuple has the same length as node number.
+
For each node, the index list value and volatility parents and children.
+
node_idx :
+
Pointer to the value parent node that will be updated.
+
time_step :
+
The time elapsed between this observation and the previous one.
+
+
Returns
+
-------
+
posterior_precision :
+
The new posterior precision.
+
+
Notes
+
-----
+
This update step is similar to the one used for the state node, except that it uses
+
the observed value instead of the mean of the child node, and the expected mean of
+
the parent node instead of the expected mean of the child node.
+
+
See Also
+
--------
+
posterior_update_mean_continuous_node
+
+
References
+
----------
+
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
+
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
+
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
+
+
"""
+
# sum the prediction errors from both value and volatility coupling
+
precision_weigthed_prediction_error = 0.0
+
+
# Value coupling updates - update the precision of a value parent
+
# ---------------------------------------------------------------
+
if edges [ node_idx ] . value_children is not None :
+
for value_child_idx , value_coupling , coupling_fn in zip (
+
edges [ node_idx ] . value_children , # type: ignore
+
attributes [ node_idx ][ "value_coupling_children" ],
+
edges [ node_idx ] . coupling_fn ,
+
):
+
if coupling_fn is None : # linear coupling
+
coupling_fn_prime = 1
+
coupling_fn_second = 0
+
else : # non-linear coupling
+
coupling_fn_prime = grad ( coupling_fn )( attributes [ node_idx ][ "mean" ]) ** 2
+
value_prediction_error = attributes [ value_child_idx ][ "temp" ][
+
"value_prediction_error"
+
]
+
coupling_fn_second = (
+
grad ( grad ( coupling_fn ))( attributes [ node_idx ][ "mean" ])
+
* value_prediction_error
+
)
+
+
# cancel the prediction error if the child value was not observed
+
precision_weigthed_prediction_error += (
+
value_coupling ** 2
+
* attributes [ value_child_idx ][ "expected_precision" ]
+
* coupling_fn_prime
+
- coupling_fn_second
+
) * attributes [ value_child_idx ][ "observed" ]
+
+
# Volatility coupling updates - update the precision of a volatility parent
+
# -------------------------------------------------------------------------
+
if edges [ node_idx ] . volatility_children is not None :
+
for volatility_child_idx , volatility_coupling in zip (
+
edges [ node_idx ] . volatility_children , # type: ignore
+
attributes [ node_idx ][ "volatility_coupling_children" ],
+
):
+
# volatility weigthed precision for the volatility child (γ)
+
effective_precision = attributes [ volatility_child_idx ][ "temp" ][
+
"effective_precision"
+
]
+
+
# retrieve the volatility prediction error
+
volatility_prediction_error = attributes [ volatility_child_idx ][ "temp" ][
+
"volatility_prediction_error"
+
]
+
+
# sum over all volatility children
+
# cancel the prediction error if the child value was not observed
+
precision_weigthed_prediction_error += (
+
0.5 * ( volatility_coupling * effective_precision ) ** 2
+
+ ( volatility_coupling * effective_precision ) ** 2
+
* volatility_prediction_error
+
- 0.5
+
* volatility_coupling ** 2
+
* effective_precision
+
* volatility_prediction_error
+
) * attributes [ volatility_child_idx ][ "observed" ]
+
+
# Compute the new posterior precision
+
# using value prediction errors from both value and volatility coupling
+
posterior_precision = (
+
attributes [ node_idx ][ "expected_precision" ] + precision_weigthed_prediction_error
+
)
+
+
# ensure the new precision is greater than 0
+
observed_posterior_precision = jnp . where (
+
posterior_precision > 1e-128 , posterior_precision , jnp . nan
+
)
+
+
# additionnal steps for unobserved values
+
# ---------------------------------------
+
+
# List the node's volatility parents
+
volatility_parents_idxs = edges [ node_idx ] . volatility_parents
+
+
# Get the tonic volatility from the node
+
total_volatility = attributes [ node_idx ][ "tonic_volatility" ]
+
+
# Look at the (optional) volatility parents and add their value to the tonic
+
# volatility to get the total volatility
+
if volatility_parents_idxs is not None :
+
for volatility_parents_idx , volatility_coupling in zip (
+
volatility_parents_idxs ,
+
attributes [ node_idx ][ "volatility_coupling_parents" ],
+
):
+
total_volatility += (
+
volatility_coupling * attributes [ volatility_parents_idx ][ "mean" ]
+
)
+
+
# compute the predicted_volatility from the total volatility
+
time_step = attributes [ - 1 ][ "time_step" ]
+
predicted_volatility = time_step * jnp . exp ( total_volatility )
+
+
# Estimate the new precision for the continuous state node
+
unobserved_posterior_precision = 1 / (
+
( 1 / attributes [ node_idx ][ "precision" ]) + predicted_volatility
+
)
+
+
# for all children, look at the values of VAPE
+
# if all these values are NaNs, the node has not received observations
+
observations = []
+
if edges [ node_idx ] . value_children is not None :
+
for children_idx in edges [ node_idx ] . value_children : # type: ignore
+
observations . append ( attributes [ children_idx ][ "observed" ])
+
if edges [ node_idx ] . volatility_children is not None :
+
for children_idx in edges [ node_idx ] . volatility_children : # type: ignore
+
observations . append ( attributes [ children_idx ][ "observed" ])
+
observations = jnp . any ( jnp . array ( observations ))
+
+
posterior_precision = (
+
unobserved_posterior_precision * ( 1 - observations ) # type: ignore
+
+ observed_posterior_precision * observations
+
)
+
+
return posterior_precision
+
[docs]
+
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
+
def continuous_node_posterior_update (
+
attributes : Dict , node_idx : int , edges : Edges , ** args
+
) -> Dict :
+
"""Update the posterior of a continuous node using the standard HGF update.
+
+
The standard HGF posterior update is a two-step process:
+
1. Update the posterior precision.
+
2. Update the posterior mean and assume that the posterior precision is the value
+
updated in the first step.
+
+
Parameters
+
----------
+
attributes :
+
The attributes of the probabilistic nodes.
+
node_idx :
+
Pointer to the node that needs to be updated. After continuous updates, the
+
parameters of value and volatility parents (if any) will be different.
+
edges :
+
The edges of the probabilistic nodes as a tuple of
+
:py:class:`pyhgf.typing.Indexes`. The tuple has the same length as node number.
+
For each node, the index list value and volatility parents and children.
+
+
Returns
+
-------
+
attributes :
+
The updated attributes of the probabilistic nodes.
+
+
See Also
+
--------
+
posterior_update_precision_continuous_node, posterior_update_mean_continuous_node
+
+
References
+
----------
+
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
+
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
+
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
+
+
"""
+
# update the posterior mean and precision
+
attributes [ node_idx ][ "precision" ] = posterior_update_precision_continuous_node (
+
attributes , edges , node_idx
+
)
+
+
attributes [ node_idx ][ "mean" ] = posterior_update_mean_continuous_node (
+
attributes , edges , node_idx , node_precision = attributes [ node_idx ][ "precision" ]
+
)
+
+
return attributes
+
[docs]
+
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
+
def continuous_node_posterior_update_ehgf (
+
attributes : Dict , node_idx : int , edges : Edges , ** args
+
) -> Dict :
+
"""Update the posterior of a continuous node using the eHGF update.
+
+
The eHGF posterior update is a two-step process:
+
1. Update the posterior mean and assume that the posterior precision is equal to
+
the expected precision.
+
2. Update the posterior precision.
+
+
.. note::
+
By updating the mean first, and approximating the precision using the expected,
+
precision, this update step often perform better than the regular update and
+
limit the occurence of negative precision that cause the model to fail under
+
some circumstances
+
+
Parameters
+
----------
+
attributes :
+
The attributes of the probabilistic nodes.
+
node_idx :
+
Pointer to the node that needs to be updated. After continuous updates, the
+
parameters of value and volatility parents (if any) will be different.
+
edges :
+
The edges of the probabilistic nodes as a tuple of
+
:py:class:`pyhgf.typing.Indexes`. The tuple has the same length as node number.
+
For each node, the index list value and volatility parents and children.
+
+
Returns
+
-------
+
attributes :
+
The updated attributes of the probabilistic nodes.
+
+
See Also
+
--------
+
posterior_update_precision_continuous_node, posterior_update_mean_continuous_node
+
+
References
+
----------
+
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
+
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
+
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
+
+
"""
+
# update the posterior mean and precision using the eHGF update step
+
# we start with the mean update using the expected precision as an approximation
+
posterior_mean = posterior_update_mean_continuous_node (
+
attributes ,
+
edges ,
+
node_idx ,
+
node_precision = attributes [ node_idx ][ "expected_precision" ],
+
)
+
attributes [ node_idx ][ "mean" ] = posterior_mean
+
+
posterior_precision = posterior_update_precision_continuous_node (
+
attributes ,
+
edges ,
+
node_idx ,
+
)
+
attributes [ node_idx ][ "precision" ] = posterior_precision
+
+
return attributes
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
pyhgf.updates.posterior.continuous.continuous_node_posterior_update — pyhgf 0.2.0 documentation
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- Source code for pyhgf.updates.posterior.continuous.continuous_node_posterior_update
-# Author: Nicolas Legrand <nicolas.legrand@cas.au.dk>
-
-from functools import partial
-from typing import Dict
-
-from jax import jit
-
-from pyhgf.typing import Edges
-
-from .posterior_update_mean_continuous_node import posterior_update_mean_continuous_node
-from .posterior_update_precision_continuous_node import (
- posterior_update_precision_continuous_node ,
-)
-
-
-
-
[docs]
-
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
-
def continuous_node_posterior_update (
-
attributes : Dict , node_idx : int , edges : Edges , ** args
-
) -> Dict :
-
"""Update the posterior of a continuous node using the standard HGF update.
-
-
The standard HGF posterior update is a two-step process:
-
1. Update the posterior precision.
-
2. Update the posterior mean and assume that the posterior precision is the value
-
updated in the first step.
-
-
Parameters
-
----------
-
attributes :
-
The attributes of the probabilistic nodes.
-
node_idx :
-
Pointer to the node that needs to be updated. After continuous updates, the
-
parameters of value and volatility parents (if any) will be different.
-
edges :
-
The edges of the probabilistic nodes as a tuple of
-
:py:class:`pyhgf.typing.Indexes`. The tuple has the same length as node number.
-
For each node, the index list value and volatility parents and children.
-
-
Returns
-
-------
-
attributes :
-
The updated attributes of the probabilistic nodes.
-
-
See Also
-
--------
-
posterior_update_precision_continuous_node, posterior_update_mean_continuous_node
-
-
References
-
----------
-
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
-
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
-
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
-
-
"""
-
# update the posterior mean and precision
-
attributes [ node_idx ][ "precision" ] = posterior_update_precision_continuous_node (
-
attributes , edges , node_idx
-
)
-
-
attributes [ node_idx ][ "mean" ] = posterior_update_mean_continuous_node (
-
attributes , edges , node_idx , node_precision = attributes [ node_idx ][ "precision" ]
-
)
-
-
return attributes
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
pyhgf.updates.posterior.continuous.continuous_node_posterior_update_ehgf — pyhgf 0.2.0 documentation
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-
-
- Source code for pyhgf.updates.posterior.continuous.continuous_node_posterior_update_ehgf
-# Author: Nicolas Legrand <nicolas.legrand@cas.au.dk>
-
-from functools import partial
-from typing import Dict
-
-from jax import jit
-
-from pyhgf.typing import Edges
-
-from .posterior_update_mean_continuous_node import posterior_update_mean_continuous_node
-from .posterior_update_precision_continuous_node import (
- posterior_update_precision_continuous_node ,
-)
-
-
-
-
[docs]
-
@partial ( jit , static_argnames = ( "edges" , "node_idx" ))
-
def continuous_node_posterior_update_ehgf (
-
attributes : Dict , node_idx : int , edges : Edges , ** args
-
) -> Dict :
-
"""Update the posterior of a continuous node using the eHGF update.
-
-
The eHGF posterior update is a two-step process:
-
1. Update the posterior mean and assume that the posterior precision is equal to
-
the expected precision.
-
2. Update the posterior precision.
-
-
.. note::
-
By updating the mean first, and approximating the precision using the expected,
-
precision, this update step often perform better than the regular update and
-
limit the occurence of negative precision that cause the model to fail under
-
some circumstances
-
-
Parameters
-
----------
-
attributes :
-
The attributes of the probabilistic nodes.
-
node_idx :
-
Pointer to the node that needs to be updated. After continuous updates, the
-
parameters of value and volatility parents (if any) will be different.
-
edges :
-
The edges of the probabilistic nodes as a tuple of
-
:py:class:`pyhgf.typing.Indexes`. The tuple has the same length as node number.
-
For each node, the index list value and volatility parents and children.
-
-
Returns
-
-------
-
attributes :
-
The updated attributes of the probabilistic nodes.
-
-
See Also
-
--------
-
posterior_update_precision_continuous_node, posterior_update_mean_continuous_node
-
-
References
-
----------
-
.. [1] Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., &
-
Mathys, C. (2023). The generalized Hierarchical Gaussian Filter (Version 1).
-
arXiv. https://doi.org/10.48550/ARXIV.2305.10937
-
-
"""
-
# update the posterior mean and precision using the eHGF update step
-
# we start with the mean update using the expected precision as an approximation
-
posterior_mean = posterior_update_mean_continuous_node (
-
attributes ,
-
edges ,
-
node_idx ,
-
node_precision = attributes [ node_idx ][ "expected_precision" ],
-
)
-
attributes [ node_idx ][ "mean" ] = posterior_mean
-
-
posterior_precision = posterior_update_precision_continuous_node (
-
attributes ,
-
edges ,
-
node_idx ,
-
)
-
attributes [ node_idx ][ "precision" ] = posterior_precision
-
-
return attributes
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Source code for pyhgf.utils.get_update_sequence <
from pyhgf.updates.posterior.continuous import (
continuous_node_posterior_update ,
continuous_node_posterior_update_ehgf ,
-
continuous_node_posterior_update_unbounded ,
)
from pyhgf.updates.prediction.binary import binary_state_node_prediction
from pyhgf.updates.prediction.continuous import continuous_node_prediction
@@ -585,12 +584,7 @@
Source code for pyhgf.utils.get_update_sequence <
if all ([ i not in nodes_without_prediction_error for i in all_children ]):
no_update = False
if network . edges [ idx ] . node_type == 2 :
-
if update_type == "unbounded" :
-
if network . edges [ idx ] . volatility_children is not None :
-
update_fn = continuous_node_posterior_update_unbounded
-
else :
-
update_fn = continuous_node_posterior_update
-
elif update_type == "eHGF" :
+
if update_type == "eHGF" :
if network . edges [ idx ] . volatility_children is not None :
update_fn = continuous_node_posterior_update_ehgf
else :
diff --git a/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_mean_continuous_node.rst.txt b/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_mean_continuous_node.rst.txt
index 162e06368..aee5477e8 100644
--- a/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_mean_continuous_node.rst.txt
+++ b/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_mean_continuous_node.rst.txt
@@ -1,12 +1,6 @@
pyhgf.updates.posterior.continuous.posterior\_update\_mean\_continuous\_node
============================================================================
-.. automodule:: pyhgf.updates.posterior.continuous.posterior_update_mean_continuous_node
+.. currentmodule:: pyhgf.updates.posterior.continuous
-
- .. rubric:: Functions
-
- .. autosummary::
-
- posterior_update_mean_continuous_node
-
\ No newline at end of file
+.. autofunction:: posterior_update_mean_continuous_node
\ No newline at end of file
diff --git a/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_precision_continuous_node.rst.txt b/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_precision_continuous_node.rst.txt
index e2f6dbf2c..1e922433b 100644
--- a/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_precision_continuous_node.rst.txt
+++ b/dev/_sources/generated/pyhgf.updates.posterior.continuous/pyhgf.updates.posterior.continuous.posterior_update_precision_continuous_node.rst.txt
@@ -1,12 +1,6 @@
pyhgf.updates.posterior.continuous.posterior\_update\_precision\_continuous\_node
=================================================================================
-.. automodule:: pyhgf.updates.posterior.continuous.posterior_update_precision_continuous_node
+.. currentmodule:: pyhgf.updates.posterior.continuous
-
- .. rubric:: Functions
-
- .. autosummary::
-
- posterior_update_precision_continuous_node
-
\ No newline at end of file
+.. autofunction:: posterior_update_precision_continuous_node
\ No newline at end of file
diff --git a/dev/api.html b/dev/api.html
index 53a9d5498..cd25f6c39 100644
--- a/dev/api.html
+++ b/dev/api.html
@@ -505,11 +505,11 @@
Categorical nodes
+
The results above indicate that given the responses provided by the participant, the most likely values for the parameter \(\omega_2\) are between -4.9 and -3.1, with a mean at -3.9 (you can find slightly different values if you sample different actions from the decisions function). We can consider this as an excellent estimate given the sparsity of the data, and the complexity of the model.
@@ -980,24 +980,24 @@ System configuration
-
diff --git a/dev/notebooks/3-Multilevel_HGF.html b/dev/notebooks/3-Multilevel_HGF.html
index f2a42ab78..9e4d37ae4 100644
--- a/dev/notebooks/3-Multilevel_HGF.html
+++ b/dev/notebooks/3-Multilevel_HGF.html
@@ -52,7 +52,7 @@
-
+
@@ -806,7 +806,7 @@
Plot the computational graph
@@ -832,17 +832,23 @@
Sampling
@@ -923,25 +929,25 @@
System configuration
-
diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index 8d3bc104b..3a6606d42 100644
--- a/dev/notebooks/4-Parameter_recovery.html
+++ b/dev/notebooks/4-Parameter_recovery.html
@@ -50,7 +50,7 @@
-
+
@@ -676,12 +676,12 @@
Inference from the simulated behaviours Visualizing parameters recovery System configuration
-
diff --git a/dev/notebooks/5-Non_linear_value_coupling.html b/dev/notebooks/5-Non_linear_value_coupling.html
index d4b94d43c..d63e92aee 100644
--- a/dev/notebooks/5-Non_linear_value_coupling.html
+++ b/dev/notebooks/5-Non_linear_value_coupling.html
@@ -978,23 +978,23 @@
System configuration
-
diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index 3eb48f358..52063d41a 100644
--- a/dev/notebooks/Example_1_Heart_rate_variability.html
+++ b/dev/notebooks/Example_1_Heart_rate_variability.html
@@ -50,7 +50,7 @@
-
+
@@ -574,16 +574,16 @@
Loading and preprocessing physiological recording Model<
+
Model<
-
+
@@ -729,7 +732,7 @@
Model<
-
+
@@ -744,23 +747,23 @@
System configuration
-
System configuration
-
diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index f7bafb407..51db783f8 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
-
+
@@ -1085,14 +1085,11 @@
Bayesian inference
+
-
-
@@ -1108,7 +1105,7 @@
Bayesian inference
@@ -1123,26 +1120,26 @@
System configuration
-
diff --git a/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html b/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
index d98d7e1c3..1ee24b12d 100644
--- a/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
+++ b/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
@@ -1034,23 +1034,23 @@
System configuration
-
diff --git a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
index 7db0cdd18..e694c4380 100644
--- a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
+++ b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
@@ -52,7 +52,7 @@
-
+
@@ -726,8 +726,8 @@
Parameters optimization
+
@@ -743,7 +743,7 @@
Parameters optimization
-
+
@@ -785,14 +785,14 @@
Parameters optimization
-
+
@@ -853,7 +853,7 @@
Biased random Assess model fitting, here using leave-one-out cross-validation from the Arviz library.
@@ -921,16 +921,16 @@
Rescorla-Wagner Rescorla-Wagner
@@ -1036,8 +1036,8 @@
Two-level HGF
+
@@ -1053,7 +1053,7 @@
Two-level HGF We have saved the pointwise log probabilities as a variable, here we simply move this variable to the log_likelihoo field of the idata Arviz knows that this can be used later for model comparison.
@@ -1147,12 +1147,12 @@
Three-level HGF
+
-
Three-level HGF Move pointwise estimate into the likelihood field.
@@ -1240,11 +1240,11 @@ Model comparison Looking at the final result, we can see that the three-level HGF had the best predictive performance on the participant decision, suggesting that higher-level uncertainty is important here to understand the agent’s behaviour.
@@ -1413,7 +1413,7 @@
Beliefs trajectories The resulting samples show belief trajectories for 10 samples for each model (we are not depicting the biased random here for clarity). The trajectories are highly similar, but we can see that the two and three-level HGF are slightly adjusting their learning rates in a way that was more consistent with the observed behaviours.
@@ -1476,25 +1476,25 @@ System configuration
-
diff --git a/dev/objects.inv b/dev/objects.inv
index 30b20a616..60ab3b8fe 100644
Binary files a/dev/objects.inv and b/dev/objects.inv differ
diff --git a/dev/py-modindex.html b/dev/py-modindex.html
deleted file mode 100644
index 90f941454..000000000
--- a/dev/py-modindex.html
+++ /dev/null
@@ -1,521 +0,0 @@
-
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Python Module Index — pyhgf 0.2.0 documentation
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diff --git a/dev/searchindex.js b/dev/searchindex.js
index 99864d792..1efae6547 100644
--- a/dev/searchindex.js
+++ b/dev/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"": [[80, "exercise1.1"], [80, "exercise1.2"], [80, "exercise1.3"], [80, "exercise1.4"], [80, "exercise1.5"], [80, "exercise1.6"], [81, "exercise2.1"], [81, "exercise2.2"]], "API": [[0, "api"]], "Acknowledgments": [[65, "acknowledgments"]], "Add data": [[70, "add-data"], [70, "id4"], [72, "add-data"], [72, "id3"]], "Adding a drift to the random walk": [[67, "adding-a-drift-to-the-random-walk"]], "Autoregressive processes": [[67, "autoregressive-processes"]], "Bayesian inference": [[79, "bayesian-inference"]], "Beliefs trajectories": [[81, "beliefs-trajectories"]], "Biased random": [[81, "biased-random"]], "Binary nodes": [[0, "binary-nodes"]], "Bivariate normal distribution": [[69, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id1"]], "Continuous value coupling": [[68, "continuous-value-coupling"]], "Continuous volatility coupling": [[68, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[68, "coupling-with-binary-nodes"]], "Create the model": [[70, "create-the-model"], [70, "id3"], [72, "create-the-model"], [72, "id2"]], "Creating a new response function": [[73, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[73, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[68, null]], "Creating custom update functions": [[68, "creating-custom-update-functions"]], "Creating custom update sequences": [[68, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[68, "creating-probabilistic-nodes"]], "Creating the decision rule": [[73, "creating-the-decision-rule"]], "Creating the model": [[70, "creating-the-model"], [70, "id7"], [72, "creating-the-model"], [72, "id5"]], "Creating the probabilistic network": [[71, "creating-the-probabilistic-network"]], "Decision rule": [[79, "decision-rule"]], "Dirichlet processes": [[0, "dirichlet-processes"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[68, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[67, "dynamic-beliefs-updating"]], "Example 1: Bayesian filtering of cardiac volatility": [[77, null]], "Example 2: Estimating the mean and precision of a time-varying Gaussian distributions": [[78, null]], "Example 3: A multi-armed bandit task with independent rewards and punishments": [[79, null]], "Exercises": [[66, "exercises"]], "Filtering the Sufficient Statistics of a Non-Stationary Distribution": [[69, "filtering-the-sufficient-statistics-of-a-non-stationary-distribution"]], "Filtering the Sufficient Statistics of a Stationary Distribution": [[69, "filtering-the-sufficient-statistics-of-a-stationary-distribution"]], "Fitting behaviours to different RL models": [[81, "fitting-behaviours-to-different-rl-models"]], "Fitting the binary HGF with fixed parameters": [[70, "fitting-the-binary-hgf-with-fixed-parameters"]], "Fitting the continuous HGF with fixed parameters": [[72, "fitting-the-continuous-hgf-with-fixed-parameters"]], "Fitting the model forwards": [[71, "fitting-the-model-forwards"]], "Frequency tracking": [[76, "frequency-tracking"]], "From Reinforcement Learning to Generalised Bayesian Filtering": [[69, null]], "Gaussian Random Walks": [[67, "gaussian-random-walks"], [80, "gaussian-random-walks"]], "Getting started": [[65, "getting-started"]], "Glossary": [[67, "glossary"], [73, "glossary"]], "Group-level inference": [[74, "group-level-inference"]], "Hierarchical Bayesian modelling with probabilistic neural networks": [[74, null]], "How does it work?": [[65, "how-does-it-work"]], "How to cite?": [[1, null]], "Imports": [[70, "imports"]], "Inference from the simulated behaviours": [[75, "inference-from-the-simulated-behaviours"]], "Inference using MCMC sampling": [[71, "inference-using-mcmc-sampling"]], "Installation": 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