PseudoNormalBlockState#
- class graph_tool.inference.PseudoNormalBlockState(s, g=None, fix_mean=True, positive=True, pslack=1e-06, **kwargs)[source]#
Bases:
BPBlockStateBase
State for network reconstruction based on the multivariate normal distribution, using the Pseudolikelihood approximation and the stochastic block model as a prior.
fix_mean == True
means thats
will be changed to become zero-mean.positive == True
ensures that the result is positive-semidefinite, according to slack given bypslack
.See documentation for
DynamicsBlockStateBase
for more details.Methods
add_edge
(u, v, x[, dm])Add edge \((u, v)\) with multiplicity
dm
and weightx
.bisect_t
(v[, maxiter, tol, entropy_args, ...])Perform a bisection search to find the best value of node
v
.bisect_x
(u, v[, maxiter, tol, entropy_args, ...])Perform a bisection search to find the best weight value for edge \((u, v)\).
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.
edge_MI
(u, v)Return the mutual information between nodes \(u\) and \(v\), according to their time-series.
edge_TE
(u, v)Return the transfer entropy between nodes \(u\) and \(v\), according to their time-series.
edge_cov
(u, v[, toffset, pearson])Return the covariance (or Pearson correlation if
pearson == True
) between nodes \(u\) and \(v\), according to their time-series.edge_mcmc_sweep
([beta, niter, k, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample latent edges.
edge_multiflip_mcmc_sweep
([beta, niter, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection merge-split MCMC to sample discrete edge weight categories.
entropy
([latent_edges, density, aE, sbm, ...])Return the description length, i.e. the negative joint log-likelihood.
get_S
()Get negative model likelihood according to pseudo-likelihood.
get_S_bp
(**kwargs)Get negative model likelihood according to BP.
Return the underlying block state, which can be either
BlockState
orNestedBlockState
.get_bp_state
(**kwargs)Return an
NormalBPState
instance corresponding to the inferred model.get_candidate_edges
([k, r, max_rk, epsilon, ...])Return the \(\lfloor\kappa N\rceil\) best edge candidates according to a stochastic second neighbor search.
get_dcov
()Return data covariance matrix.
get_dyn_state
([s])Return an
NormalState
instance corresponding to the inferred model, optionally with initial state given bys
.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_elist_grad
([h, entropy_args])Get edge list gradient.
Return the current default values for the parameters of the function
entropy()
, together with other operations that depend on them.Return the current inferred graph.
get_node_grad
([h, entropy_args])Get node gradient.
get_params
(params)Gets the model parameters via the dictionary
params
.Return precision matrix.
Return latent node values.
Return shifted node values to ensure positive semi-definiteness.
Return latent node categories.
get_x
()Return latent edge weights.
Return latent edge weight categories.
Return exact log-likelihood.
Return exact log-likelihood normalization constant.
mcmc_sweep
([beta, niter, edge, edge_swap, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample latent edges and network partitions.
quantize_x
(delta)Quantize weight values according to multiples of \(\Delta\).
remove_edge
(u, v[, dm])Remove edge \((u, v)\) with multiplicity
dm
.Reset the current default values for the parameters of the function
entropy()
, together with other operations that depend on them.sample_delta
(minval, maxval[, beta, ...])Sample from the conditional posterior of the \(\Delta\) parameter associated with the edge and node categories.
sample_t
(v[, beta, maxiter, tol, ...])Sample a value for node
v
according to the conditional posterior.sample_tl1
(minval, maxval[, beta, maxiter, ...])Sample from the conditional posterior of the \(\lambda\) parameter associated with the node categories.
sample_val_lprob
(x, xc[, beta])Compute probability of sampling value
x
from bisection historyxc
and inverse temperaturebeta
.sample_x
(u, v[, beta, maxiter, tol, ...])Sample a weight value for edge \((u, v)\) according to the conditional posterior.
sample_xl1
(minval, maxval[, beta, maxiter, ...])Sample from the conditional posterior of the \(\lambda\) parameter associated with the edge categories.
sbm_mcmc_sweep
([multiflip])Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample node partitions.
set_params
(params)Sets the model parameters via the dictionary
params
.set_state
(g, w)Set all edge multiplicities via
EdgePropertyMap
w
.swap_mcmc_sweep
([beta, niter, k, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to swap edge endpoints.
theta_mcmc_sweep
([beta, niter, pold, pnew, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample node parameters.
theta_multiflip_mcmc_sweep
([beta, pmerge, ...])Perform sweeps of a Metropolis-Hastings acceptance-rejection merge-split MCMC to sample discrete node value categories.
tvals_sweep
([beta, niter, maxiter, ...])Perform sweeps of a greedy update on the node category values, based on bisection search.
update_edge
(u, v, nx)update edge \((u, v)\) with weight
nx
.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.update_node
(v, nt)update node \((u, v)\) with value
nt
.virtual_add_edge
(u, v, x[, dm, entropy_args])Return the difference in description length if edge \((u, v)\) would be added with multiplicity
dm
and weightx
.virtual_remove_edge
(u, v[, dm, entropy_args])Return the difference in description length if edge \((u, v)\) with multiplicity
dm
would be removed.virtual_update_edge
(u, v, nx[, entropy_args])Return the difference in description length if edge \((u, v)\) would take a new weight
nx
.virtual_update_node
(v, nt[, entropy_args])Return the difference in description length if node
v
would take a new valuent
.xvals_sweep
([beta, niter, maxiter, tol, ...])Perform sweeps of a greedy update on the edge weight category values, based on bisection search.
- add_edge(u, v, x, dm=1)#
Add edge \((u, v)\) with multiplicity
dm
and weightx
.
- bisect_t(v, maxiter=0, tol=1e-07, entropy_args={}, reversible=False, fb=False)#
Perform a bisection search to find the best value of node
v
.- Parameters:
- u
int
orVertex
Source
- v
int
orVertex
Target
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- reversible
boolean
(optional, default:False
) Perform search in a manner that is usable for a reversible Makov chain.
- fb
boolean
(optional, default:False
) Perform a Fibonacci (a.k.a. golden ratio) search, instead of a random bisection search.
- u
- bisect_x(u, v, maxiter=0, tol=1e-07, entropy_args={}, reversible=False, fb=False)#
Perform a bisection search to find the best weight value for edge \((u, v)\).
- Parameters:
- u
int
orVertex
Source
- v
int
orVertex
Target
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- reversible
boolean
(optional, default:False
) Perform search in a manner that is usable for a reversible Makov chain.
- fb
boolean
(optional, default:False
) Perform a Fibonacci (a.k.a. golden ratio) search, instead of a random bisection search.
- u
- 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.
- copy(**kwargs)#
Return a copy of the state.
- edge_MI(u, v)#
Return the mutual information between nodes \(u\) and \(v\), according to their time-series.
- edge_TE(u, v)#
Return the transfer entropy between nodes \(u\) and \(v\), according to their time-series.
- edge_cov(u, v, toffset=True, pearson=False)#
Return the covariance (or Pearson correlation if
pearson == True
) between nodes \(u\) and \(v\), according to their time-series.
- edge_mcmc_sweep(beta=inf, niter=1, k=1, elist_args={}, keep_elist=False, pold=1, pnew=1, pxu=0.1, pm=1, premove=1, maxiter=0, tol=1e-07, binary=True, deterministic=False, sequential=True, parallel=True, verbose=False, entropy_args={}, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample latent edges.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- k
int
(optional, default:1
) \(\kappa\) parameter to be passed to
get_candidate_edges()
.- elist_args
dict
(optional, default:{}
) Paramters to pass to call
get_candidate_edges()
.- keep_elist
boolean
(optional, default:False
) If
True
, the candidate edge list from last call will be re-used (if it exists).- pold
float
(optional, default:1
) Relative probability of proposing a new edge weight from existing categories.
- pnew
float
(optional, default:1
) Relative probability of proposing a new edge weight from a new categories.
- pxu
float
(optional, default:.1
) Probability of choosing from an existing category uniformly at random (instead of doing a bisection search).
- pm
float
(optional, default:1
) Relative probability of doing edge multiplicity updates.
- premove
float
(optional, default:1
) Relative probability of removing edges.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- binary
boolean
(optional, default:True
) If
True
, the latent graph will be assumed to be a simple graph, otherwise a multigraph.- deterministic
boolean
(optional, default:False
) If
True
, the the order of edge updates will be determinisitc, otherwise uniformly at random.- sequential
boolean
(optional, default:True
) If
True
, a sweep will visit every edge candidate once, otherwise individiual updates will be chosen at random.- parallel
boolean
(optional, default:True
) If
True
, the updates are performed in parallel, using locks on edges candidate incident on the same node.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- edge_multiflip_mcmc_sweep(beta=inf, niter=1, pmerge=1, psplit=1, pmergesplit=1, pmovelabel=1, gibbs_sweeps=1, c=0.1, maxiter=0, tol=1e-07, accept_stats=None, verbose=False, entropy_args={}, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection merge-split MCMC to sample discrete edge weight categories.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- pmerge
float
(optional, default:1
) Relative probability of merging two discrete categories.
- psplit
float
(optional, default:1
) Relative probability of splitting two discrete categories.
- pmergesplit
float
(optional, default:1
) Relative probability of simultaneoulsly merging and splitting two discrete categories.
- pmovelabel
float
(optional, default:1
) Relative probability of moving the value of a discrete category.
- gibbs_sweeps
int
(optional, default:1
) Number of Gibbs sweeps performed to achieve a split proposal.
- c
double
(optional, default:.1
) Probability of choosing a category uniformly at random to perform a merge, otherwise an adjacent one is chosen.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- accept_stats
dict
(optional, default:None
) If provided, the dictionary will be updated with acceptance statistics.
- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- entropy(latent_edges=True, density=False, aE=1, sbm=True, xdist=True, tdist=True, xl1=1, tl1=1, alpha=1, delta=1e-08, normal=False, mu=0, sigma=1, **kwargs)#
Return the description length, i.e. the negative joint 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.- Parameters:
- latent_edges
boolean
(optional, default:True
) If
True
, the adjacency term of the description length will be included.- density
boolean
(optional, default:False
) If
True
, a geometric prior for the total number of edges will be included.- aE
double
(optional, default:1
) If
density=True
, this will correspond to the expected number of edges according to the geometric prior.- sbm
boolean
(optional, default:True
) If
True
, SBM description length will be included.- xdist
boolean
(optional, default:True
) If
True
, the quantized edge weight distribution description length will be included.- tdist
boolean
(optional, default:True
) If
True
, the quantized node parameter distribution description length will be included.- xl1
float
(optional, default:1
) Specifies the \(\lambda\) parameter for \(L_1\) regularization for the edge weights if
xdist == False
, or the Laplace hyperprior for the discrete categories ifxdist == True
.- tl1
float
(optional, default:1
) Specifies the \(\lambda\) parameter for \(L_1\) regularization for the node paraemters if
tdist == False
, or the Laplace hyperprior for the discrete categories iftdist == True
.- delta
float
(optional, default:1e-8
) Specifies the precision parameter for the discrete categories.
- normal
boolean
(optional, default:False
) If
True
, a normal distribution will be used for the weight priors.- mu
double
(optional, default:0
) If
normal == True
, this will be the mean of the normal distribution.- sigma
double
(optional, default:1
) If
normal == True
, this will be the standard deviation of the normal distribution.
- latent_edges
Notes
The “entropy” of the state is the negative log-likelihood of the generative model for the data \(\boldsymbol S\), that includes the inferred weighted adjacency matrix \(\boldsymbol{X}\), the node parameters \(\boldsymbol{\theta}\), and the SBM node partition \(\boldsymbol{b},\) given by
\[\begin{split}\begin{aligned} \Sigma(\boldsymbol{S},\boldsymbol{X},\boldsymbol{\theta}|\lambda_x,\lambda_{\theta},\Delta) = &- \ln P(\boldsymbol{S}|\boldsymbol{X},\boldsymbol{\theta})\\ &- \ln P(\boldsymbol{X}|\boldsymbol{A},\lambda_x, \Delta)\\ &- \ln P(\boldsymbol{A},\boldsymbol{b})\\ &- \ln P(\boldsymbol{\theta}, \lambda_{\theta}, \Delta). \end{aligned}\end{split}\]The term \(P(\boldsymbol{S}|\boldsymbol{X},\boldsymbol{\theta})\) is given by the particular generative model being used and \(P(\boldsymbol{A},\boldsymbol{b})\) by the SBM. The weight ditribution is given by the quantized model
\[P(\boldsymbol X|\boldsymbol A,\lambda_x,\Delta) = \frac{\prod_{k}m_{k}!\times \mathrm{e}^{-\lambda_x \sum_k |z_k|}(\mathrm{e}^{\lambda\Delta} - 1)^{K}} {E!{E-1 \choose K-1}2^{K}\max(E,1)}\]where \(\boldsymbol z\) are the \(K\) discrete weight categories, and analogously
\[P(\boldsymbol\theta|\lambda_{\theta},\Delta) =\frac{\prod_{k}n_{k}!\times \mathrm{e}^{-\lambda \sum_k |u_k|} \sinh(\lambda_{\theta}\Delta)^{K_{\theta}-\mathbb{1}_{0\in\boldsymbol u}} (1-\mathrm{e}^{-\lambda_{\theta}\Delta})^{\mathbb{1}_{0\in\boldsymbol u}}} {N!{N-1 \choose K_{\theta}-1}N},\]is the node parameter quantized distribution. For more details see [peixoto-network-2024].
References
[peixoto-network-2024]Tiago P. Peixoto, “Network reconstruction via the minimum description length principle”, arXiv: 2405.01015
[peixoto-scalable-2024]Tiago P. Peixoto, “Scalable network reconstruction in subquadratic time”, arXiv: 2401.01404
- get_S()#
Get negative model likelihood according to pseudo-likelihood.
- get_S_bp(**kwargs)#
Get negative model likelihood according to BP.
- get_block_state()#
Return the underlying block state, which can be either
BlockState
orNestedBlockState
.
- get_bp_state(**kwargs)[source]#
Return an
NormalBPState
instance corresponding to the inferred model.
- get_candidate_edges(k=1, r=1, max_rk='k', epsilon=0.01, c_stop=False, max_iter=0, knn=False, gradient=None, h=1e-06, f_max_iter=10, tol=1e-06, allow_edges=False, include_edges=True, use_hint=True, nrandom=0, keep_all=False, exact=False, return_graph=False, keep_iter=False, entropy_args={}, verbose=False)#
Return the \(\lfloor\kappa N\rceil\) best edge candidates according to a stochastic second neighbor search.
- Parameters:
- k
float
(optional, default:1
) \(\kappa\) parameter.
- r
float
(optional, default:1
) Fraction of second neighbors to consider during the search.
- max_rk
float
(optional, default:"k"
) Maximum number of second-neighbors to be considered per iteration. A string value
"k"
means that this will match the number of first neighbors.- epsilon
float
(optional, default:.01
) Convergence criterion.
- c_stop
boolean
(optional, default:False
) If
True
, the clustering coefficient will be used for the convergence criterion.- max_iter
int
(optional, default:0
) Maximum number of iterations allowed (
0
means unlimited).- knn
boolean
(optional, default:False
) If
True
, the KNN graph will be returned.- gradient
boolean
(optional, default:None
) Whether to use the gradient to rank edges. If
None
, it defaults toTrue
is the number of edge categories is empty.- h
float
(optional, default:1e-8
) Step length used to compute the gradient with central finite difference.
- allow_edges
boolean
(optional, default:False
) Permit currently present edges to be included in the search.
- use_hint
boolean
(optional, default:True
) Use current edges as a hint during the search.
- nrandom
int
(optional, default:0
) Add this many random entries to the list.
- keep_all
boolean
(optional, default:False
) Keep all entries seen during the search, not only the best.
- exact
boolean
(optional, default:False
) If
True
an exact quadratic algorithm will be used.- return_graph
boolean
(optional, default:False
) If
True
the result will be returned as graph and a property map.- keep_iter
boolean
(optional, default:False
) If
True
the result contain the iteration at which an entry has been found.- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- k
- Returns:
- elist:class:
~numpy.ndarray
of shape(E, 2)
Best entries.
- a:class:
~numpy.ndarray
Edge scores.
- elist:class:
- get_dyn_state(s=None)[source]#
Return an
NormalState
instance corresponding to the inferred model, optionally with initial state given bys
.
- 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_elist_grad(h=1e-06, entropy_args={})#
Get edge list gradient.
- get_entropy_args()#
Return the current default values for the parameters of the function
entropy()
, together with other operations that depend on them.
- get_graph()#
Return the current inferred graph.
- get_node_grad(h=1e-06, entropy_args={})#
Get node gradient.
- get_params(params)#
Gets the model parameters via the dictionary
params
.
- get_theta()#
Return latent node values.
- get_tvals()#
Return latent node categories.
- get_x()#
Return latent edge weights.
- get_xvals()#
Return latent edge weight categories.
- mcmc_sweep(beta=inf, niter=1, edge=True, edge_swap=True, edge_multiflip=True, theta=True, theta_multiflip=True, sbm=True, xvals=True, tvals=True, k=1, keep_elist=False, verbose=False, elist_args={}, edge_mcmc_args={}, edge_swap_mcmc_args={}, edge_multiflip_mcmc_args={}, xvals_mcmc_args={}, theta_mcmc_args={}, theta_multiflip_mcmc_args={}, tvals_mcmc_args={}, sbm_mcmc_args={}, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample latent edges and network partitions.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- k
int
(optional, default:1
) \(\kappa\) parameter to be passed to
get_candidate_edges()
.- elist_args
dict
(optiona, default:{}
) Paramters to pass to call
get_candidate_edges()
.- keep_elist
boolean
(optional, default:False
) If
True
, the candidate edge list from last call will be re-used (if it exists).- edge
boolean
(optiona, default:True
) Whether to call
edge_mcmc_sweep()
.- edge_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
edge_mcmc_sweep()
.- edge_swap
boolean
(optiona, default:True
) Whether to call
swap_mcmc_sweep()
.- edge_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
swap_mcmc_sweep()
.- edge_multiflip
boolean
(optiona, default:True
) Whether to call
edge_multiflip_mcmc_sweep()
.- edge_multiflip_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
edge_multiflip_mcmc_sweep()
.- theta
boolean
(optiona, default:True
) Whether to call
theta_mcmc_sweep()
.- theta_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
theta_mcmc_sweep()
.- theta_multiflip
boolean
(optiona, default:True
) Whether to call
theta_multiflip_mcmc_sweep()
.- theta_multiflip_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
theta_multiflip_mcmc_sweep()
.- sbm
boolean
(optiona, default:True
) Whether to call
sbm_mcmc_sweep()
.- sbm_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
sbm_mcmc_sweep()
.- xvals
boolean
(optiona, default:True
) Whether to call
xvals_sweep()
.- xvals_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
xvals_sweep()
.- tvals
boolean
(optiona, default:True
) Whether to call
tvals_sweep()
.- tvals_mcmc_args
dict
(optiona, default:{}
) Paramters to pass to call
tvals_sweep()
.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.- **kwargs
dict
(optional, default:{}
) Remaining keyword parameters will be passed to all individual MCMC functions.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- quantize_x(delta)#
Quantize weight values according to multiples of \(\Delta\).
- remove_edge(u, v, dm=1)#
Remove edge \((u, v)\) with multiplicity
dm
.
- reset_entropy_args()#
Reset the current default values for the parameters of the function
entropy()
, together with other operations that depend on them.
- sample_delta(minval, maxval, beta=inf, maxiter=0, tol=1e-07, entropy_args={})#
Sample from the conditional posterior of the \(\Delta\) parameter associated with the edge and node categories.
- Parameters:
- minval
float
Minimum value to consider.
- minval
float
Maximum value to consider.
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of iterations.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- minval
- Returns:
- delta
float
Sampled value of \(\Delta\).
- delta
- sample_t(v, beta=inf, maxiter=0, tol=1e-07, entropy_args={}, fb=False)#
Sample a value for node
v
according to the conditional posterior.- Parameters:
- u
int
orVertex
Source
- v
int
orVertex
Target
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- reversible
boolean
(optional, default:False
) Perform search in a manner that is usable for a reversible Makov chain.
- fb
boolean
(optional, default:False
) Perform a Fibonacci (a.k.a. golden ratio) search, instead of a random bisection search.
- u
- sample_tl1(minval, maxval, beta=inf, maxiter=0, tol=1e-07, entropy_args={})#
Sample from the conditional posterior of the \(\lambda\) parameter associated with the node categories.
- Parameters:
- minval
float
Minimum value to consider.
- minval
float
Maximum value to consider.
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of iterations.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- minval
- Returns:
- tl1
float
Sampled value of \(\lambda\).
- tl1
- sample_val_lprob(x, xc, beta=inf)#
Compute probability of sampling value
x
from bisection historyxc
and inverse temperaturebeta
.
- sample_x(u, v, beta=inf, maxiter=0, tol=1e-07, entropy_args={}, fb=False)#
Sample a weight value for edge \((u, v)\) according to the conditional posterior.
- Parameters:
- u
int
orVertex
Source
- v
int
orVertex
Target
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- reversible
boolean
(optional, default:False
) Perform search in a manner that is usable for a reversible Makov chain.
- fb
boolean
(optional, default:False
) Perform a Fibonacci (a.k.a. golden ratio) search, instead of a random bisection search.
- u
- sample_xl1(minval, maxval, beta=inf, maxiter=0, tol=1e-07, entropy_args={})#
Sample from the conditional posterior of the \(\lambda\) parameter associated with the edge categories.
- Parameters:
- minval
float
Minimum value to consider.
- minval
float
Maximum value to consider.
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of iterations.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- minval
- Returns:
- xl1
float
Sampled value of \(\lambda\).
- xl1
- sbm_mcmc_sweep(multiflip=True, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample node partitions. The remaining keyword parameters will be passed to
mcmc_sweep()
ormultiflip_mcmc_sweep()
, ifmultiflip=True
.
- set_params(params)#
Sets the model parameters via the dictionary
params
.
- set_state(g, w)#
Set all edge multiplicities via
EdgePropertyMap
w
.
- swap_mcmc_sweep(beta=inf, niter=1, k=1, elist_args={}, keep_elist=False, pmove=1, ptmove=1, pswap=1, deterministic=False, sequential=True, parallel=True, verbose=False, entropy_args={}, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to swap edge endpoints.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- k
int
(optional, default:1
) \(\kappa\) parameter to be passed to
get_candidate_edges()
.- elist_args
dict
(optional, default:{}
) Paramters to pass to call
get_candidate_edges()
.- keep_elist
boolean
(optional, default:False
) If
True
, the candidate edge list from last call will be re-used (if it exists).- pmove
float
(optional, default:1
) Relative probability of swaping the weights between two randomly chosen edges.
- ptmove
float
(optional, default:1
) Relative probability of moving a single edge endpoint of an edge with a candidate edge.
- pswap
float
(optional, default:1
) Relative probability of swapping the endpoints of two randomly selected edges.
- deterministic
boolean
(optional, default:False
) If
True
, the the order of edge updates will be determinisitc, otherwise uniformly at random.- sequential
boolean
(optional, default:True
) If
True
, a sweep will visit every edge candidate once, otherwise individiual updates will be chosen at random.- parallel
boolean
(optional, default:True
) If
True
, the updates are performed in parallel, using locks on edges candidate incident on the same node.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- theta_mcmc_sweep(beta=inf, niter=1, pold=1, pnew=1, maxiter=0, tol=1e-07, deterministic=False, sequential=True, parallel=True, verbose=False, entropy_args={}, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample node parameters.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- pold
float
(optional, default:1
) Relative probability of proposing a new node value from existing categories.
- pnew
float
(optional, default:1
) Relative probability of proposing a new node value from a new categories.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- deterministic
boolean
(optional, default:False
) If
True
, the the order of node updates will be determinisitc, otherwise uniformly at random.- sequential
boolean
(optional, default:True
) If
True
, a sweep will visit every node once, otherwise individiual updates will be chosen at random.- parallel
boolean
(optional, default:True
) If
True
, the updates are performed in parallel.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- theta_multiflip_mcmc_sweep(beta=inf, pmerge=1, psplit=1, pmergesplit=1, pmovelabel=0, gibbs_sweeps=1, c=0.1, niter=1, maxiter=0, tol=1e-07, entropy_args={}, accept_stats=None, verbose=False, **kwargs)#
Perform sweeps of a Metropolis-Hastings acceptance-rejection merge-split MCMC to sample discrete node value categories.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:1
) Number of sweeps.
- pmerge
float
(optional, default:1
) Relative probability of merging two discrete categories.
- psplit
float
(optional, default:1
) Relative probability of splitting two discrete categories.
- pmergesplit
float
(optional, default:1
) Relative probability of simultaneoulsly merging and splitting two discrete categories.
- pmovelabel
float
(optional, default:1
) Relative probability of moving the value of a discrete category.
- gibbs_sweeps
int
(optional, default:1
) Number of Gibbs sweeps performed to achieve a split proposal.
- c
double
(optional, default:.1
) Probability of choosing a category uniformly at random to perform a merge, otherwise an adjacent one is chosen.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- accept_stats
dict
(optional, default:None
) If provided, the dictionary will be updated with acceptance statistics.
- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- tvals_sweep(beta=inf, niter=100, maxiter=0, min_size=1, tol=1e-07, entropy_args={})#
Perform sweeps of a greedy update on the node category values, based on bisection search.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:100
) Number of categories to update.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- min_size
int
(optional, default:1
) Minimum size of node categories that will be updated.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS
- update_edge(u, v, nx)#
update edge \((u, v)\) with weight
nx
.
- 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.
- update_node(v, nt)#
update node \((u, v)\) with value
nt
.
- virtual_add_edge(u, v, x, dm=1, entropy_args={})#
Return the difference in description length if edge \((u, v)\) would be added with multiplicity
dm
and weightx
.
- virtual_remove_edge(u, v, dm=1, entropy_args={})#
Return the difference in description length if edge \((u, v)\) with multiplicity
dm
would be removed.
- virtual_update_edge(u, v, nx, entropy_args={})#
Return the difference in description length if edge \((u, v)\) would take a new weight
nx
.
- virtual_update_node(v, nt, entropy_args={})#
Return the difference in description length if node
v
would take a new valuent
.
- xvals_sweep(beta=inf, niter=100, maxiter=0, tol=1e-07, min_size=1, entropy_args={})#
Perform sweeps of a greedy update on the edge weight category values, based on bisection search.
- Parameters:
- beta
float
(optional, default:np.inf
) Inverse temperature parameter.
- niter
int
(optional, default:100
) Number of categories to update.
- maxiter
int
(optional, default:0
) Maximum number of iterations for bisection search (
0
means unlimited).- tol
float
(optional, default:1e-7
) Tolerance for bisection search.
- min_size
int
(optional, default:1
) Minimum size of edge categories that will be updated.
- entropy_args
dict
(optional, default:{}
) Entropy arguments, with the same meaning and defaults as in
entropy()
.- verbose
boolean
(optional, default:False
) If
verbose == True
, detailed information will be displayed.
- beta
- Returns:
- dS
float
Entropy difference after the sweeps.
- nmoves
int
Number of variables moved.
- dS