graph_tool.inference.EpidemicsBlockState#
- class graph_tool.inference.EpidemicsBlockState(g, s, beta, r, r_v=None, global_beta=None, active=None, t=[], exposed=False, aE=nan, nested=True, state_args={}, bstate=None, self_loops=False, **kwargs)[source]#
Bases:
DynamicsBlockStateBase
Inference state for network reconstruction based on epidemic dynamics, using the stochastic block model as a prior.
- Parameters:
- g
Graph
Initial graph state.
- s
list
ofVertexPropertyMap
Collection of time-series with node states over time. Each entry in this list must be a
VertexPropertyMap
with typevector<int>
containing the states of each node in each time step. A value of1
means infected and0
susceptible. Other values are allowed (e.g. for recovered), but their actual value is unimportant for reconstruction.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.- beta
float
orEdgePropertyMap
Initial value of the global or local transmission probability for each edge.
- r
float
Spontaneous infection probability.
- r_v
VertexPropertyMap
(optional, default:None
) If given, this will set the initial spontaneous infection probability for each node, and trigger the use of a model where this quantity is in principle different for each node.
- global_beta
float
(optional, default:None
) If provided, and
beta is None
this will trigger the use of a model where all transmission probabilities on edges are the same, and given (initially) by this value.- t
list
ofVertexPropertyMap
(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 aVertexPropertyMap
with typevector<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 parameters
.- active
list
ofVertexPropertyMap
(optional, default:None
) If given, this specifies the points in time where each node is “active”, and prepared to change its state according to the state of its neighbors. Each entry in this list must be a
VertexPropertyMap
with typevector<int>
containing the states of each node in each time step. A value of1
means active and0
inactive.- exposed
boolean
(optional, default:False
) If
True
, the data is supposed to come from a SEI, SEIR, etc. model, where a susceptible node (valued0
) first transits to an exposed state (valued-1
) upon transmission, before transiting to the infective state (valued1
).- aE
float
(optional, default:NaN
) Expected total number of edges used in prior. If
NaN
, a flat prior will be used instead.- nested
boolean
(optional, default:True
) If
True
, aNestedBlockState
will be used, otherwiseBlockState
.- state_args
dict
(optional, default:{}
) Arguments to be passed to
NestedBlockState
orBlockState
.- bstate
NestedBlockState
orBlockState
(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.
- g
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 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.
Return the underlying block state, which can be either
BlockState
orNestedBlockState
.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 \((E,2)\).
Return the current inferred graph.
get_x
()Return latent edge transmission probabilities.
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()
withmultiflip=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:
- g
Graph
(optional, default:None
) Previous marginal graph.
- g
- Returns:
- g
Graph
New marginal graph, with internal edge
EdgePropertyMap
"eprob"
, containing the marginal probabilities for each edge.
- g
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:
- g
Graph
(optional, default:None
) Previous marginal multigraph.
- g
- Returns:
- g
Graph
New marginal graph, with internal edge
EdgePropertyMap
"w"
and"wcount"
, containing the edge multiplicities and their respective counts.
- g
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.
- 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
orNestedBlockState
.
- 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.
- 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 parameterh
controls the relative probability with which moves for the parametersr_v
will be attempted, andhstep
is the size of the step. The parameterp
controls the relative probability with which moves for the parametersglobal_beta
andr
will be attempted, andpstep
is the size of the step. The paramterxstep
determines the size of the attempted steps for the edge transmission probabilities.The remaining keyword parameters will be passed to
mcmc_sweep()
ormultiflip_mcmc_sweep()
, ifmultiflip=True
.
- multiflip_mcmc_sweep(**kwargs)#
Alias for
mcmc_sweep()
withmultiflip=True
.
- set_state(g, w)#
- virtual_add_edge(u, v, entropy_args={})#
- virtual_remove_edge(u, v, entropy_args={})#