graph_tool.inference.MCMCState

class graph_tool.inference.MCMCState

Bases: ABC

Base state that implements single-flip MCMC sweeps

Methods

mcmc_sweep([beta, c, d, niter, ...])

Perform niter sweeps of a Metropolis-Hastings acceptance-rejection MCMC to sample network partitions.

mcmc_sweep(beta=1.0, c=0.5, d=0.01, niter=1, entropy_args={}, allow_vacate=True, sequential=True, deterministic=False, vertices=None, verbose=False, **kwargs)

Perform niter sweeps of a Metropolis-Hastings acceptance-rejection MCMC to sample network partitions.

Parameters:

betafloat (optional, default: 1.)

Inverse temperature.

cfloat (optional, default: .5)

Sampling parameter c for move proposals: For \(c\to 0\) the blocks are sampled according to the local neighborhood of a given node and their block connections; for \(c\to\infty\) the blocks are sampled randomly. Note that only for \(c > 0\) the MCMC is guaranteed to be ergodic.

dfloat (optional, default: .01)

Probability of selecting a new (i.e. empty) group for a given move.

niterint (optional, default: 1)

Number of sweeps to perform. During each sweep, a move attempt is made for each node.

entropy_argsdict (optional, default: {})

Entropy arguments, with the same meaning and defaults as in graph_tool.inference.BlockState.entropy().

allow_vacatebool (optional, default: True)

Allow groups to be vacated.

sequentialbool (optional, default: True)

If sequential == True each vertex move attempt is made sequentially, where vertices are visited in random order. Otherwise the moves are attempted by sampling vertices randomly, so that the same vertex can be moved more than once, before other vertices had the chance to move.

deterministicbool (optional, default: False)

If sequential == True and deterministic == True the vertices will be visited in deterministic order.

verticeslist of ints (optional, default: None)

If provided, this should be a list of vertices which will be moved. Otherwise, all vertices will.

verbosebool (optional, default: False)

If verbose == True, detailed information will be displayed.

Returns:

dSfloat

Entropy difference after the sweeps.

nattemptsint

Number of vertex moves attempted.

nmovesint

Number of vertices moved.

Notes

This algorithm has an \(O(E)\) complexity, where \(E\) is the number of edges (independent of the number of groups).

References

[peixoto-efficient-2014]

Tiago P. Peixoto, “Efficient Monte Carlo and greedy heuristic for the inference of stochastic block models”, Phys. Rev. E 89, 012804 (2014), DOI: 10.1103/PhysRevE.89.012804 [sci-hub, @tor], arXiv: 1310.4378