Description Usage Arguments Details Value References Examples
Runs a Natural Gradient Ascent algorithm to maximise the variational objective for a Sparse LPM.
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X 
Rectangular adjacency matrix with nonnegative entries. 
K 
The number of latent dimension of the model. 
var_pars_init 
List of variational parameters to be used as starting point for the optimisation. See Details for more specific indications. 
hyper_pars 
List defining the hyperparameters of the model. The list should contain three vectors of 
tol 
Positive number setting the stop condition: the algorithm stops if one entire iteration yields an increase in the objective function smaller than this value. 
n_iter_max 
Maximum number of iterations the algorithm should be run for. 
natural_gradient 

learning_rate_factor_up 
Before any natural gradient ascent update, the current step size is multiplied by this number to ensure that the algorithms tries new solutions which are relatively far from the current one. 
learning_rate_factor_down 
During any natural gradient ascent update, if a certain step size leads to a decrease in the objective function, then the step is divided by this number repeatedly until an increase is ensured. 
verbose 

var_pars
and var_pars_init
are lists with components:
M*K
matrix representing the Gaussian means for the latent positions of senders.
N*K
matrix representing the Gaussian means for the latent positions of receivers.
M*K
matrix representing the Gaussian variances for the latent positions of senders.
N*K
matrix representing the Gaussian variances for the latent positions of receivers.
M*N*K
array with entries corresponding to the posterior probabilities of assigning each edge to each latent dimension.
Vector of K
positive values representing the Dirichlet parameters generating the mixing proportions.
Vector of K
positive values corresponding to the shapes of the variational Gamma distribution on the precisions.
Vector of K
positive values corresponding to the rates of the variational Gamma distribution on the precisions.
A list with components:
computing_time 
Number of seconds required for the optimisation process. 
var_pars 
List containing the optimal values for the variational parameters. 
learning_rates_u 
Current stepsize for the update of the variational parameters of each Gaussian distribution on the latent positions of senders. 
learning_rates_v 
Current stepsize for the update of the variational parameters of each Gaussian distribution on the latent positions of receivers. 
elbo_values 
Values of the variational objective at the end of each of the iterations. 
elbo_init 
Value of the variational objective for the initial configuration. 
elbo_final 
Value of the variational objective for the optimal solution found. 
Rastelli, R. (2018) "The Sparse Latent Position Model for nonnegative weighted networks", https://arxiv.org/abs/1808.09262
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