R/signal.R

In Tlasso: Non-Convex Optimization and Statistical Inference for Sparse Tensor Graphical Models

#' Regression Parameter of Conditional Linear Model
#'
#' Compute regression parameter of conditional linear model of separable tensor normal distribution described in \href{https://arxiv.org/abs/1609.04522}{Lyu et al. (2019)}.
#'
#' @param Omega.list list of precision matrices of tensor, i.e., \code{Omega.list[[k]]} is the kth precision matrix.
#' Omega.list can be either true precision matrices or output of \code{Tlasso.fit}.   
#' for the kth tensor mode, \eqn{k \in \{1 , \ldots, K\}}{ 1 <= k <= K }.   
#' @param i index of interested regression parameter, default is 1. See details in \href{https://arxiv.org/abs/1609.04522}{Lyu et al. (2019)}.
#' @param k index of interested mode, default is 1.
#' 
#' @details This function computes regression parameter and is fundamental for sample covariance of residuals and 
#' bias correction. See details in \href{https://arxiv.org/abs/1609.04522}{Lyu et al. (2019)}.
#' 
#' @return A vector of regression paramter.  
#'
#' @author Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu, Jian Yang, Guang Cheng. 
#' @seealso \code{\link{covres}}, \code{\link{biascor}}
#'
#' @examples
#' 
#' m.vec = c(5,5,5)  # dimensionality of a tensor 
#' n = 5   # sample size 
#' k=1 # index of interested mode
#' lambda.thm = 20*c( sqrt(log(m.vec[1])/(n*prod(m.vec))), 
#'                    sqrt(log(m.vec[2])/(n*prod(m.vec))), 
#'                    sqrt(log(m.vec[3])/(n*prod(m.vec))))
#' DATA=Trnorm(n,m.vec,type='Chain') 
#' # obersavations from tensor normal distribution
#' out.tlasso = Tlasso.fit(DATA,T=1,lambda.vec = lambda.thm)   
#' # output is a list of estimation of precision matrices
#' signal(out.tlasso, i=2 , k=k )
#' # the regression parameter for conditional linear model of 2rd row in 1st mode
#' 
#' @export
#' 
signal = function(Omega.list, i=1, k = 1) {

  
  if (!is.list(Omega.list)){
    stop('argument Omega.list should be a list')
  } else if (any(!sapply(Omega.list,is.matrix))) {
    stop('argument Omega.list should be a list of precision matrices')
  } else if ( !(((k==1) | (k > 1 ))& (k==length(Omega.list) | k < length(Omega.list))) ) {
    stop('argument k should be a positive integer between 1 and the length of argument Omega.list')
  } else if ( !(((i==1) | (i > 1 ))& (i==dim(Omega.list[[k]])[1] | i < dim(Omega.list[[k]])[1])) ){
    stop('argument i should be a positive integer between 1 and the dimension of kth matrix in arguemnt Omega.list')
  }
  
  est = Omega.list[[k]]
  return(- est[i,i]^(-1) * est[i , -i])
  
}