# actual¶

Methods for computing actual causation of subsystems and mechanisms.

If you use this module, please cite the following papers:

Albantakis L, Marshall W, Hoel E, Tononi G (2019). What Caused What? A quantitative Account of Actual Causation Using Dynamical Causal Networks. Entropy, 21 (5), pp. 459. https://doi.org/10.3390/e21050459

Mayner WGP, Marshall W, Albantakis L, Findlay G, Marchman R, Tononi G. (2018). PyPhi: A toolbox for integrated information theory. PLOS Computational Biology 14(7): e1006343. https://doi.org/10.1371/journal.pcbi.1006343

pyphi.actual.log2(x)

Rounded version of log2.

class pyphi.actual.Transition(network, before_state, after_state, cause_indices, effect_indices, cut=None, noise_background=False)

A state transition between two sets of nodes in a network.

A Transition is implemented with two Subsystem objects: one representing the system at time $$t-1$$ used to compute effect coefficients, and another representing the system at time $$t$$ which is used to compute cause coefficients. These subsystems are accessed with the effect_system and cause_system attributes, and are mapped to the causal directions via the system attribute.

Parameters
• network (Network) – The network the subsystem belongs to.

• before_state (tuple[int]) – The state of the network at time $$t-1$$.

• after_state (tuple[int]) – The state of the network at time $$t$$.

• cause_indices (tuple[int] or tuple[str]) – Indices of nodes in the cause system. (TODO: clarify)

• effect_indices (tuple[int] or tuple[str]) – Indices of nodes in the effect system. (TODO: clarify)

Keyword Arguments

noise_background (bool) – If True, background conditions are noised instead of frozen.

node_indices

The indices of the nodes in the system.

Type

tuple[int]

network

The network the system belongs to.

Type

Network

before_state

The state of the network at time $$t-1$$.

Type

tuple[int]

after_state

The state of the network at time $$t$$.

Type

tuple[int]

effect_system

The system in before_state used to compute effect repertoires and coefficients.

Type

Subsystem

cause_system

The system in after_state used to compute cause repertoires and coefficients.

Type

Subsystem

cause_system
Type

Subsystem

system

A dictionary mapping causal directions to the system used to compute repertoires in that direction.

Type

dict

cut

The cut that has been applied to this transition.

Type

ActualCut

Note

During initialization, both the cause and effect systems are conditioned on before_state as the background state. After conditioning the effect_system is then properly reset to after_state.

property node_labels
to_json()

Return a JSON-serializable representation.

apply_cut(cut)

Return a cut version of this transition.

cause_repertoire(mechanism, purview)

Return the cause repertoire.

effect_repertoire(mechanism, purview)

Return the effect repertoire.

unconstrained_cause_repertoire(purview)

Return the unconstrained cause repertoire of the occurence.

unconstrained_effect_repertoire(purview)

Return the unconstrained effect repertoire of the occurence.

repertoire(direction, mechanism, purview)

Return the cause or effect repertoire function based on a direction.

Parameters

direction (str) – The temporal direction, specifiying the cause or effect repertoire.

state_probability(direction, repertoire, purview)

Compute the probability of the purview in its current state given the repertoire.

Collapses the dimensions of the repertoire that correspond to the purview nodes onto their state. All other dimension are already singular and thus receive 0 as the conditioning index.

Returns

A single probabilty.

Return type

float

probability(direction, mechanism, purview)

Probability that the purview is in it’s current state given the state of the mechanism.

unconstrained_probability(direction, purview)

Unconstrained probability of the purview.

purview_state(direction)

The state of the purview when we are computing coefficients in direction.

For example, if we are computing the cause coefficient of a mechanism in after_state, the direction isCAUSE and the purview_state is before_state.

mechanism_state(direction)

The state of the mechanism when computing coefficients in direction.

mechanism_indices(direction)

The indices of nodes in the mechanism system.

purview_indices(direction)

The indices of nodes in the purview system.

cause_ratio(mechanism, purview)

The cause ratio of the purview given mechanism.

effect_ratio(mechanism, purview)

The effect ratio of the purview given mechanism.

partitioned_repertoire(direction, partition)

Compute the repertoire over the partition in the given direction.

partitioned_probability(direction, partition)

Compute the probability of the mechanism over the purview in the partition.

find_mip(direction, mechanism, purview, allow_neg=False)

Find the ratio minimum information partition for a mechanism over a purview.

Parameters
Keyword Arguments

allow_neg (boolean) – If true, alpha is allowed to be negative. Otherwise, negative values of alpha will be treated as if they were 0.

Returns

The irreducibility analysis for the mechanism.

Return type

AcRepertoireIrreducibilityAnalysis

potential_purviews(direction, mechanism, purviews=False)

Return all purviews that could belong to the MaximallyIrreducibleCause/MaximallyIrreducibleEffect.

Filters out trivially-reducible purviews.

Parameters
Keyword Arguments

purviews (tuple[int]) – Optional subset of purviews of interest.

Return the maximally irreducible cause or effect ratio for a mechanism.

Parameters
• direction (str) – The temporal direction, specifying cause or effect.

• mechanism (tuple[int]) – The mechanism to be tested for irreducibility.

Keyword Arguments

purviews (tuple[int]) – Optionally restrict the possible purviews to a subset of the subsystem. This may be useful for _e.g._ finding only concepts that are “about” a certain subset of nodes.

Returns

The maximally-irreducible actual cause or effect.

Return type

find_actual_cause(mechanism, purviews=False)

Return the actual cause of a mechanism.

find_actual_effect(mechanism, purviews=False)

Return the actual effect of a mechanism.

find_mice(*args, **kwargs)

Backwards-compatible alias for find_causal_link().

pyphi.actual.directed_account(transition, direction, mechanisms=False, purviews=False, allow_neg=False)

Return the set of all CausalLink of the specified direction.

pyphi.actual.account(transition, direction=<Direction.BIDIRECTIONAL: 2>)

Return the set of all causal links for a Transition.

Parameters

transition (Transition) – The transition of interest.

Keyword Arguments

direction (Direction) – By default the account contains actual causes and actual effects.

pyphi.actual.account_distance(A1, A2)

Return the distance between two accounts. Here that is just the difference in sum(alpha)

Parameters
• A1 (Account) – The first account.

• A2 (Account) – The second account

Returns

The distance between the two accounts.

Return type

float

pyphi.actual.sia(transition, direction=<Direction.BIDIRECTIONAL: 2>)

Return the minimal information partition of a transition in a specific direction.

Parameters

transition (Transition) – The candidate system.

Returns

A nested structure containing all the data from the intermediate calculations. The top level contains the basic irreducibility information for the given subsystem.

Return type

AcSystemIrreducibilityAnalysis

class pyphi.actual.ComputeACSystemIrreducibility(iterable, *context)

Computation engine for AC SIAs.

description = 'Evaluating AC cuts'
empty_result(transition, direction, unpartitioned_account)

Return the default result with which to begin the computation.

static compute(cut, transition, direction, unpartitioned_account)

Map over a single object from self.iterable.

process_result(new_sia, min_sia)

Reduce handler.

Every time a new result is generated by compute, this method is called with the result and the previous (accumulated) result. This method compares or collates these two values, returning the new result.

Setting self.done to True in this method will abort the remainder of the computation, returning this final result.

pyphi.actual.transitions(network, before_state, after_state)

Return a generator of all possible transitions of a network.

pyphi.actual.nexus(network, before_state, after_state, direction=<Direction.BIDIRECTIONAL: 2>)

Return a tuple of all irreducible nexus of the network.

pyphi.actual.causal_nexus(network, before_state, after_state, direction=<Direction.BIDIRECTIONAL: 2>)

Return the causal nexus of the network.

pyphi.actual.nice_true_ces(tc)

Format a true CauseEffectStructure.

pyphi.actual.events(network, previous_state, current_state, next_state, nodes, mechanisms=False)

Find all events (mechanisms with actual causes and actual effects).

pyphi.actual.true_ces(subsystem, previous_state, next_state)

Set of all sets of elements that have true causes and true effects.

Note

Since the true CauseEffectStructure is always about the full system, the background conditions don’t matter and the subsystem should be conditioned on the current state.

pyphi.actual.true_events(network, previous_state, current_state, next_state, indices=None, major_complex=None)

Return all mechanisms that have true causes and true effects within the complex.

Parameters
• network (Network) – The network to analyze.

• previous_state (tuple[int]) – The state of the network at t - 1.

• current_state (tuple[int]) – The state of the network at t.

• next_state (tuple[int]) – The state of the network at t + 1.

Keyword Arguments
• indices (tuple[int]) – The indices of the major complex.

• major_complex (AcSystemIrreducibilityAnalysis) – The major complex. If major_complex is given then indices is ignored.

Returns

List of true events in the major complex.

Return type

tuple[Event]

pyphi.actual.extrinsic_events(network, previous_state, current_state, next_state, indices=None, major_complex=None)

Set of all mechanisms that are in the major complex but which have true causes and effects within the entire network.

Parameters
• network (Network) – The network to analyze.

• previous_state (tuple[int]) – The state of the network at t - 1.

• current_state (tuple[int]) – The state of the network at t.

• next_state (tuple[int]) – The state of the network at t + 1.

Keyword Arguments
• indices (tuple[int]) – The indices of the major complex.

• major_complex (AcSystemIrreducibilityAnalysis) – The major complex. If major_complex is given then indices is ignored.

Returns

List of extrinsic events in the major complex.

Return type

tuple(actions)