Fit the sparse inverse covariance variant of the Poisson lognormal with a variational algorithm. Use the (g)lm syntax for model specification (covariates, offsets).
an object of class "formula": a symbolic description of the model to be fitted.
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.
an optional vector specifying a subset of observations to be used in the fitting process.
an optional vector of observation weights to be used in the fitting process.
an optional vector of positive real number controlling the level of sparsity of the underlying network. if NULL (the default), will be set internally. See
control_main options for additional tuning of the penalty.
a list for controlling the optimization of the PLN model used at initialization, and how the vector of
penalties is generated. See details.
a list for controlling the main optimization process. Can be used to specify adaptive penalty weights. See details.
The list of parameters
control_main controls the optimization of the main process, with the following entries:
"ftol_rel" stop when an optimization step changes the objective function by less than ftol multiplied by the absolute value of the parameter. Default is 1e-6 when n < p, 1e-8 otherwise.
"ftol_abs" stop when an optimization step changes the objective function by less than ftol multiplied by the absolute value of the parameter. Default is 0
"xtol_rel" stop when an optimization step changes every parameters by less than xtol_rel multiplied by the absolute value of the parameter. Default is 1e-6
"xtol_abs" stop when an optimization step changes every parameters by less than xtol_abs. Default is 0
"maxeval" stop when the number of iteration exceeds maxeval. Default is 10000
"algorithm" the optimization method used by NLOPT among LD type, i.e. "CCSAQ", "MMA", "LBFGS", "VAR1", "VAR2". See NLOPT documentation for further details. Default is "CCSAQ".
"trace" integer for verbosity. Useless when
cores > 1
"ftol_out" outer solver stops when an optimization step changes the objective function by less than xtol multiply by the absolute value of the parameter. Default is 1e-6
"maxit_out" outer solver stops when the number of iteration exceeds out.maxit. Default is 50
The list of parameters
control_init controls the optimization process in the initialization and in the function
PLN(), plus some additional parameters:
"nPenalties" an integer that specified the number of values for the penalty grid when internally generated. Ignored when penalties is non
"min.ratio" the penalty grid ranges from the minimal value that produces a sparse to this value multiplied by
min.ratio. Default is 0.1.
"penalize_diagonal" boolean: should the diagonal terms be penalized in the graphical-Lasso? Default is TRUE
"penalty_weights" either a single or a list of p x p matrix of weights (default filled with 1) to adapt the amount of shrinkage to each pairs of node. Must be symmetric with positive values.
data(trichoptera) trichoptera <- prepare_data(trichoptera$Abundance, trichoptera$Covariate) fits <- PLNnetwork(Abundance ~ 1, data = trichoptera) #> #> Initialization... #> Adjusting 30 PLN with sparse inverse covariance estimation #> Joint optimization alternating gradient descent and graphical-lasso #> sparsifying penalty = 7.510862 sparsifying penalty = 6.937564 sparsifying penalty = 6.408026 sparsifying penalty = 5.918907 sparsifying penalty = 5.467121 sparsifying penalty = 5.049821 sparsifying penalty = 4.664372 sparsifying penalty = 4.308345 sparsifying penalty = 3.979492 sparsifying penalty = 3.675741 sparsifying penalty = 3.395175 sparsifying penalty = 3.136024 sparsifying penalty = 2.896654 sparsifying penalty = 2.675555 sparsifying penalty = 2.471332 sparsifying penalty = 2.282698 sparsifying penalty = 2.108461 sparsifying penalty = 1.947524 sparsifying penalty = 1.798871 sparsifying penalty = 1.661565 sparsifying penalty = 1.534739 sparsifying penalty = 1.417594 sparsifying penalty = 1.30939 sparsifying penalty = 1.209446 sparsifying penalty = 1.11713 sparsifying penalty = 1.03186 sparsifying penalty = 0.953099 sparsifying penalty = 0.8803498 sparsifying penalty = 0.8131535 sparsifying penalty = 0.7510862 #> Post-treatments #> DONE!