learn_kcomp_heavytail_graph: Laplacian matrix of a k-component graph with heavy-tailed...

In fingraph: Learning Graphs for Financial Markets

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

fingraph documentation built on Feb. 16, 2023, 9:50 p.m.