mlePath {countprop}

Maximum Likelihood Estimator Paths

Description

Calculates the maximum likelihood estimates of the parameters for the mutlinomial logit-Normal distribution under various values of the penalization parameter lambda. Parameter lambda controls the sparsity of the covariance matrix Sigma, and penalizes the false large correlations that may arise in high-dimensional data.

Usage

mlePath(
  y,
  max.iter = 10000,
  max.iter.nr = 100,
  tol = 1e-06,
  tol.nr = 1e-06,
  lambda.gl = NULL,
  lambda.min.ratio = 0.1,
  n.lambda = 1,
  n.cores = 1,
  gamma = 0.1
)

Arguments

y

Matrix of counts; samples are rows and features are columns.

max.iter

Maximum number of iterations

max.iter.nr

Maximum number of Newton-Raphson iterations

tol

Stopping rule

tol.nr

Stopping rule for the Newton Raphson algorithm

lambda.gl

Vector of penalization parameters lambda, for the graphical lasso penalty

lambda.min.ratio

Minimum lambda ratio of the maximum lambda, used for the sequence of lambdas

n.lambda

Number of lambdas to evaluate the model on

n.cores

Number of cores to use (for parallel computation)

gamma

Gamma value for EBIC calculation of the log-likelihood

Value

The MLE estimates of y for each element lambda of lambda.gl, (est); the value of the estimates which produce the minimum EBIC, (est.min); the vector of lambdas used for graphical lasso, (lambda.gl); the index of the minimum EBIC (extended Bayesian information criterion), (min.idx); vector containing the EBIC for each lambda, (ebic).

Note

If using parallel computing, consider setting n.cores to be equal to the number of lambdas being evaluated for, n.lambda.

The graphical lasso penalty is the sum of the absolute value of the elements of the covariance matrix Sigma. The penalization parameter lambda controls the sparsity of Sigma.

Examples

data(singlecell)
mle.sim <- mlePath(singlecell, tol=1e-4, tol.nr=1e-4, n.lambda = 2, n.cores = 1)

mu.hat <- mle.sim$est.min$mu
Sigma.hat <- mle.sim$est.min$Sigma