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Control of ZIPLNnetwork fit

Source: R/ZIPLNnetwork.R
ZIPLNnetwork_param.Rd

Helper to define list of parameters to control the ZIPLNnetwork fit. All arguments have defaults.

Usage

ZIPLNnetwork_param(
  backend = c("builtin", "nlopt"),
  inception_cov = c("full", "spherical", "diagonal"),
  trace = 1,
  n_penalties = 30,
  min_ratio = 0.1,
  penalize_diagonal = FALSE,
  penalty_weights = NULL,
  penalty_scale = c("correlation", "covariance"),
  latent_floor = 0.001,
  config_post = list(),
  config_optim = list(),
  inception = NULL
)

Arguments

backend

optimization backend, either "builtin" (default, joint Newton on (M,\(\psi\),R), combined with the partial E-step maxit_ve = 1) or "nlopt" (CCSAQ). "builtin" consistently finds a better ELBO across the penalty path at the cost of being slower.

inception_cov

Covariance structure used for the inception ZIPLN, which starts the penalty path and sets its top: "full" (default), "diagonal" or "spherical". The top of the grid of penalties is computed as in PLNnetwork_param(). Unlike for PLNnetwork(), a full inception is the default: a diagonal one makes the top of the path exactly the empty network, but was found to lead to a lower BIC along the path, at a higher cost.

trace

a integer for verbosity.

n_penalties

an integer that specifies the number of values for the penalty grid when internally generated. Ignored when penalties is non NULL

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 FALSE. Penalizing the diagonal inflates the latent variances (\(\Sigma_{ii} = S_{ii} + \rho\) on the covariance scale, \(\Sigma_{ii} = S_{ii} (1 + \rho)\) on the correlation scale), which the VE step then feeds back into the residual covariance \(S\): along the path, the network may then never become empty, and the latent variances diverge (#180).

penalty_weights

either a single or a list of p x p matrix of weights (default: all weights equal to 1) to adapt the amount of shrinkage to each pairs of node. Must be symmetric with positive values.

penalty_scale

character, the scale on which the l1 penalty applies. "correlation" (default) penalizes the entries of the precision matrix on the scale of the variables, with a penalty \(\lambda \sqrt{S_{ii} S_{jj}}\) on the pair \((i, j)\), where \(S\) is the current residual covariance. This amounts to applying the graphical-Lasso to the residual correlation matrix and rescaling the result, the correlation-based estimator of Rothman, Bickel, Levina and Zhu (2008), and makes the penalties dimensionless, between 0 and 1. "covariance", the only behavior until version 1.3.2, penalizes the entries of the precision matrix as they are. These are not scale invariant: a species with a large latent variance then has nearly free edges, and one that is often absent but abundant when present ends up connected to most of the others (see the field degenerate_species of a PLNfit). See the section on the scale of the penalty.

latent_floor

a positive number \(\epsilon\) (default 1e-3), or NULL for no floor: a floor on the variational means of the degenerate species. As soon as the latent variance of a species exceeds the threshold of the field degenerate_species of a PLNfit (100, see options(PLNmodels.latent_variance_threshold = )) during the optimization, its variational means are kept above \(\log \epsilon - O\), that is \(\exp(O + M) \geq \epsilon\), in this fit and in the following ones along the penalty path. The species concerned are in the field floored_species of the fits. This needs no preparation of the data: the species are found by the optimization itself. The floor restricts the variational family, not the model, and stops the latent variances from diverging. It leaves a fit without degenerate species exactly as it is.

config_post

a list for controlling the post-treatments (optional bootstrap, jackknife, R2, etc.). See details

config_optim

a list for controlling the optimizer (either "nlopt" or "torch" backend). See details

inception

Set up the parameters initialization: by default, the model is initialized with a multivariate linear model applied on log-transformed data, and with the same formula as the one provided by the user. However, the user can provide a PLNfit (typically obtained from a previous fit), which sometimes speeds up the inference.

Value

list of parameters configuring the fit.

Details

See PLNnetwork_param() for a full description of the optimization parameters. Note that some defaults values are different than those used in PLNnetwork_param():

  • "ftol_out" (outer loop convergence tolerance the objective function) is set by default to 1e-6

  • "maxit_out" (max number of iterations for the outer loop) is set by default to 50

References

Rothman, A. J., Bickel, P. J., Levina, E. and Zhu, J. (2008). Sparse permutation invariant covariance estimation. Electronic Journal of Statistics, 2, 494–515. doi:10.1214/08-EJS176

See also

PLNnetwork_param() and PLN_param()