learn_kcomp_heavytail_graph {fingraph}

Laplacian matrix of a k-component graph with heavy-tailed data Computes the Laplacian matrix of a graph on the basis of an observed data matrix, where we assume the data to be Student-t distributed.

Description

Laplacian matrix of a k-component graph with heavy-tailed data

Computes the Laplacian matrix of a graph on the basis of an observed data matrix, where we assume the data to be Student-t distributed.

Usage

learn_kcomp_heavytail_graph(
  X,
  k = 1,
  heavy_type = "gaussian",
  nu = NULL,
  w0 = "naive",
  d = 1,
  beta = 1e-08,
  update_beta = TRUE,
  early_stopping = FALSE,
  rho = 1,
  update_rho = FALSE,
  maxiter = 10000,
  reltol = 1e-05,
  verbose = TRUE,
  record_objective = FALSE
)

Arguments

X

an n x p data matrix, where n is the number of observations and p is the number of nodes in the graph.

k

the number of components of the graph.

heavy_type

a string which selects the statistical distribution of the data . Valid values are "gaussian" or "student".

nu

the degrees of freedom of the Student-t distribution. Must be a real number greater than 2.

w0

initial vector of graph weights. Either a vector of length p(p-1)/2 or a string indicating the method to compute an initial value.

d

the nodes' degrees. Either a vector or a single value.

beta

hyperparameter that controls the regularization to obtain a k-component graph

update_beta

whether to update beta during the optimization.

early_stopping

whether to stop the iterations as soon as the rank constraint is satisfied.

rho

constraint relaxation hyperparameter.

update_rho

whether or not to update rho during the optimization.

maxiter

maximum number of iterations.

reltol

relative tolerance as a convergence criteria.

verbose

whether to show a progress bar during the iterations.

record_objective

whether to record the objective function per iteration.

Value

A list containing possibly the following elements:

laplacian

estimated Laplacian matrix

adjacency

estimated adjacency matrix

theta

estimated Laplacian matrix slack variable

maxiter

number of iterations taken to reach convergence

convergence

boolean flag to indicate whether or not the optimization conv erged

beta_seq

sequence of values taken by the hyperparameter beta until convergence

primal_lap_residual

primal residual for the Laplacian matrix per iteratio n

primal_deg_residual

primal residual for the degree vector per iteration

dual_residual

dual residual per iteration

lagrangian

Lagrangian value per iteration

elapsed_time

Time taken to reach convergence