LatentClosureBlockState#

class graph_tool.inference.LatentClosureBlockState(g, L=1, b=None, aE=nan, nested=True, state_args={}, g_orig=None, ew=None, ex=None, entropy_args={}, **kwargs)[source]#

Bases: LatentLayerBaseState

Inference state of the stochastic block model with latent triadic closure edges.

Parameters:

gGraph: Observed graph.
Lint (optional, default: 1): Maximum number of triadic closure generations.
bVertexPropertyMap (optional, default: None): Inital partition (or hierarchical partition nested=True).
aEfloat (optional, default: NaN): Expected total number of edges used in prior. If NaN, a flat prior will be used instead.
nestedboolean (optional, default: True): If True, a NestedBlockState will be used, otherwise BlockState.
state_argsdict (optional, default: {}): Arguments to be passed to NestedBlockState or BlockState.
g_origGraph (optional, default: None): Original graph, if g is used to initialize differently from a graph with no triadic closure edges.
ewlist of EdgePropertyMap (optional, default: None): List of edge property maps of g, containing the initial weights (counts) at each triadic generation.
exlist of EdgePropertyMap (optional, default: None): List of edge property maps of g, each containing a list of integers with the ego graph memberships of every edge, for every triadic generation.
entropy_args: ``dict`` (optional, default: ``{}``): Override default arguments for entropy() method and releated operations.

References

[peixoto-disentangling-2022]

Tiago P. Peixoto, “Disentangling homophily, community structure and triadic closure in networks”, Phys. Rev. X 12, 011004 (2022), DOI: 10.1103/PhysRevX.12.011004 [sci-hub, @tor], arXiv: 2101.02510

Methods

`collect_marginal`([gs])	Collect marginal inferred network during MCMC runs.
`collect_marginal_multigraph`([gs])	Collect marginal latent multigraphs during MCMC runs.
`copy`(**kwargs)	Return a copy of the state.
`entropy`([latent_edges, density, aE, sbm])	Return the entropy, i.e. negative log-likelihood.
`get_ec`([ew])	Return edge property map with layer membership.
`get_entropy_args`()	Return the current default values for the parameters of the function `entropy()`, together with other operations that depend on them.
`mcmc_sweep`([r, multiflip])	Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample network partitions and latent edges.
`multiflip_mcmc_sweep`(**kwargs)	Alias for `mcmc_sweep()` with `multiflip=True`.
`reset_entropy_args`()	Reset the current default values for the parameters of the function `entropy()`, together with other operations that depend on them.
`sample_graph`([sample_sbm, canonical_sbm, ...])	Sample graph from inferred model.
`update_entropy_args`(**kwargs)	Update the default values for the parameters of the function `entropy()` from the keyword arguments, in a stateful way, together with other operations that depend on them.

collect_marginal(gs=None)[source]#

Collect marginal inferred network during MCMC runs.

Parameters:

glist of Graph (optional, default: None): Previous marginal graphs.

Returns:

glist Graph: New list of marginal graphs, each with internal EdgePropertyMap "eprob", containing the marginal probabilities for each edge, as well as VertexPropertyMap "t", "m", "c", containing the average number of closures, open triads, and fraction of closed triads on each node.

Notes

The posterior marginal probability of an edge \((i,j)\) is defined as

\[\pi_{ij} = \sum_{\boldsymbol A}A_{ij}P(\boldsymbol A|\boldsymbol D)\]

where \(P(\boldsymbol A|\boldsymbol D)\) is the posterior probability given the data.

This function returns a list with the marginal graphs for every layer.

collect_marginal_multigraph(gs=None)#

Collect marginal latent multigraphs during MCMC runs.

Parameters:

glist of Graph (optional, default: None): Previous marginal multigraphs.

Returns:

glist of Graph: New marginal multigraphs, each with internal edge EdgePropertyMap "w" and "wcount", containing the edge multiplicities and their respective counts.

Notes

The mean posterior marginal multiplicity distribution of a multi-edge \((i,j)\) is defined as

\[\pi_{ij}(w) = \sum_{\boldsymbol G}\delta_{w,G_{ij}}P(\boldsymbol G|\boldsymbol D)\]

where \(P(\boldsymbol G|\boldsymbol D)\) is the posterior probability of a multigraph \(\boldsymbol G\) given the data.

This function returns a list with the marginal graphs for every layer.

copy(**kwargs)[source]#: Return a copy of the state.

entropy(latent_edges=True, density=False, aE=1.0, sbm=True, **kwargs)#: Return the entropy, i.e. negative log-likelihood.

Warning

The default arguments of this function are overriden by those obtained from get_entropy_args(). To update the defaults in a stateful way, update_entropy_args() should be called.

get_ec(ew=None)#: Return edge property map with layer membership.

get_entropy_args()#: Return the current default values for the parameters of the function entropy(), together with other operations that depend on them.

mcmc_sweep(r=0.5, multiflip=True, **kwargs)#: Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample network partitions and latent edges. The parameter r controls the probability with which edge move will be attempted, instead of partition moves. The remaining keyword parameters will be passed to mcmc_sweep() or multiflip_mcmc_sweep(), if multiflip=True.

multiflip_mcmc_sweep(**kwargs)#: Alias for mcmc_sweep() with multiflip=True.

reset_entropy_args()#: Reset the current default values for the parameters of the function entropy(), together with other operations that depend on them.

sample_graph(sample_sbm=True, canonical_sbm=False, sample_params=True, canonical_closure=True)[source]#

Sample graph from inferred model.

Parameters:

sample_sbmboolean (optional, default: True): If True, the substrate network will be sampled anew from the SBM parameters. Otherwise, it will be the same as the current posterior state.
canonical_sbmboolean (optional, default: False): If True, the canonical SBM will be used, otherwise the microcanonical SBM will be used.
sample_paramsbool (optional, default: True): If True, and canonical_sbm == True the count parameters (edges between groups and node degrees) will be sampled from their posterior distribution conditioned on the actual state. Otherwise, their maximum-likelihood values will be used.
canonical_closureboolean (optional, default: True): If True, the canonical version of triadic clousre will be used (i.e. conditioned on a probability), otherwise the microcanonical version will be used (i.e. conditional on the count number).

Returns:

ulist Graph: Sampled graph, with internal edge EdgePropertyMap "gen", containing the triadic generation of each edge.

update_entropy_args(**kwargs)#

Update the default values for the parameters of the function entropy() from the keyword arguments, in a stateful way, together with other operations that depend on them.

Values updated in this manner are preserved by the copying or pickling of the state.

LatentClosureBlockState

Contents

LatentClosureBlockState#