graph_tool.inference.IsingBaseBlockState#

class graph_tool.inference.IsingBaseBlockState(g, s, beta, x=None, h=None, t=None, aE=nan, nested=True, state_args={}, bstate=None, self_loops=False, has_zero=False, **kwargs)[source]#

Bases: DynamicsBlockStateBase

Base state for network reconstruction based on the Ising model, using the stochastic block model as a prior. This class is not supposed to be instantiated directly. Instead one of its specialized subclasses must be used, which have the same signature: IsingGlauberBlockState, PseudoIsingBlockState, CIsingGlauberBlockState, PseudoCIsingBlockState.

Parameters:
gGraph

Initial graph state.

slist of VertexPropertyMap or VertexPropertyMap

Collection of time-series with node states over time, or a single time-series. Each time-series must be a VertexPropertyMap with type vector<int> containing the Ising states (-1 or +1) of each node in each time step.

If the parameter t below is given, each property map value for a given node should contain only the states for the same points in time given by that parameter.

betafloat

Initial value of the global inverse temperature.

xEdgePropertyMap (optional, default: None)

Initial value of the local coupling for each edge. If not given, a uniform value of 1 will be used.

hVertexPropertyMap (optional, default: None)

If given, this will set the initial local fields of each node. Otherwise a value of 0 will be used.

tlist of VertexPropertyMap (optional, default: [])

If nonempty, this allows for a compressed representation of the time-series parameter s, corresponding only to points in time where the state of each node changes. Each entry in this list must be a VertexPropertyMap with type vector<int> containing the points in time where the state of each node change. The corresponding state of the nodes at these times are given by parameter s.

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.

bstateNestedBlockState or BlockState (optional, default: None)

If passed, this will be used to initialize the block state directly.

self_loopsbool (optional, default: False)

If True, it is assumed that the inferred graph can contain self-loops.

has_zerobool (optional, default: False)

If True, the three-state “Ising” model with values {-1,0,1} is used.

References

[peixoto-network-2019]

Tiago P. Peixoto, “Network reconstruction and community detection from dynamics”, Phys. Rev. Lett. 123 128301 (2019), DOI: 10.1103/PhysRevLett.123.128301 [sci-hub, @tor], arXiv: 1903.10833

Methods

collect_marginal([g])

Collect marginal inferred network during MCMC runs.

collect_marginal_multigraph([g])

Collect marginal latent multigraph during MCMC runs.

copy(**kwargs)

Return a copy of the state.

entropy([latent_edges, density])

Return the entropy, i.e. negative log-likelihood.

get_block_state()

Return the underlying block state, which can be either BlockState or NestedBlockState.

get_edge_prob(u, v, x[, entropy_args, epsilon])

Return conditional posterior log-probability of edge \((u,v)\).

get_edges_prob(elist[, entropy_args, epsilon])

Return conditional posterior log-probability of an edge list, with shape \((E,2)\).

get_graph()

Return the current inferred graph.

get_x()

Return edge couplings.

mcmc_sweep([r, p, pstep, h, hstep, xstep, ...])

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.

set_params(params)

Sets the model parameters via the dictionary params.

set_state(g, w)

virtual_add_edge(u, v[, entropy_args])

virtual_remove_edge(u, v[, entropy_args])

collect_marginal(g=None)#

Collect marginal inferred network during MCMC runs.

Parameters:
gGraph (optional, default: None)

Previous marginal graph.

Returns:
gGraph

New marginal graph, with internal edge EdgePropertyMap "eprob", containing the marginal probabilities for each edge.

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.

collect_marginal_multigraph(g=None)#

Collect marginal latent multigraph during MCMC runs.

Parameters:
gGraph (optional, default: None)

Previous marginal multigraph.

Returns:
gGraph

New marginal graph, 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.

copy(**kwargs)#

Return a copy of the state.

entropy(latent_edges=True, density=True, **kwargs)#

Return the entropy, i.e. negative log-likelihood.

get_block_state()#

Return the underlying block state, which can be either BlockState or NestedBlockState.

get_edge_prob(u, v, x, entropy_args={}, epsilon=1e-08)#

Return conditional posterior log-probability of edge \((u,v)\).

get_edges_prob(elist, entropy_args={}, epsilon=1e-08)#

Return conditional posterior log-probability of an edge list, with shape \((E,2)\).

get_graph()#

Return the current inferred graph.

get_x()[source]#

Return edge couplings.

mcmc_sweep(r=0.5, p=0.1, pstep=0.1, h=0.1, hstep=1, xstep=0.1, multiflip=True, **kwargs)[source]#

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 parameter h controls the relative probability with which moves for the parameters r_v will be attempted, and hstep is the size of the step. The parameter p controls the relative probability with which moves for the parameters global_beta and r will be attempted, and pstep is the size of the step. The paramter xstep determines the size of the attempted steps for the edge coupling parameters.

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.

set_params(params)#

Sets the model parameters via the dictionary params.

set_state(g, w)#
virtual_add_edge(u, v, entropy_args={})#
virtual_remove_edge(u, v, entropy_args={})#