mixggm (version 1.0)

control-parameters: Set control parameters for various purposes

Description

Set control parameters for graphical model estimation, graph structure search via stepwise or genetic algorithm, mixture model fitting via structural-EM algorithm, and Bayesian regularization.

Usage

ctrlICF(tol = 1e-04, maxiter = 1e03)
ctrlSTEP(occamAdd = Inf, occamRem = Inf, start = NULL)
ctrlGA(popSize = 50, pcrossover = 0.8, pmutation = 0.1,
       maxiter = 100, run = maxiter/2,
       elitism = base::max(1, round(popSize*0.05)))
ctrlEM(tol = 1e-05, maxiter = 1e02, subset = NULL, printMsg = FALSE)
ctrlREG(data, K, scaleType = c("full", "fixed", "one", "diag"),
        scale = NULL, psi = NULL)

Arguments

tol

Tolerance value for judging when convergence has been reached. Used in estimation of a Gaussian graphical model and in the structural-EM algorithm.

maxiter

Maximum number of iterations in the Gaussian graphical model estimation algorithm, the genetic algorithm for structure search, and the structural-EM algorithm.

occamAdd, occamRem

Set the bounds of the Occam's window for stepwise search. See "Details". Default is Inf, corresponding to the case of no deletion of candidate graph structures through the search.

start

Provide in input a user-defined starting adjacency matrix for stepwise structure search.

popSize

Population size. This number corresponds to the number of different graph structures to be considered at each iteration of the genetic algorithm.

run

Number of consecutive generations without any improvement in the best fitness value of the structure search procedure before the genetic algorithm is stopped.

pcrossover

Probability of crossover between pairs of binary adjacency matrices.

pmutation

Probability of mutation in a parent adjacency matrix.

elitism

Number of best fitness graph structures to survive at each iteration of the genetic algorithm in the graph structure search procedure.

subset

A logical or numeric vector specifying a subset of the data to be used in the initial hierarchical clustering phase employed in the initialization of the structural-EM algorithm. By default no subset is used.

printMsg

A logical value indicating whether or not certain warnings (usually related to singularity) should be issued.

data

A matrix or data frame of observations. Categorical variables are not allowed. Rows correspond to observations and columns correspond to variables.

K

The number of mixture components.

scaleType

The type of scale hyperparameter for the prior on the covariance matrix in the case of Bayesian regularization for Gaussian covariance graph model. See "Details". Default is "full".

scale

The scale hyperparameter for the prior on the covariance matrix in the case of Bayesian regularization for Gaussian covariance graph model.

psi

The degrees of freedom hyperparameter for the prior on the covariance matrix in the case of Bayesian regularization for Gaussian covariance graph model.

Value

A list of parameters values.

Details

Function ctrlICF is used to set control parameters of the algorithms employed to estimate a Gaussian covariance or concentration graph model.

Function ctrlSTEP mainly controls the Occam's window used in the stepwise graph structure search. Default is Inf, corresponding to no Occam's window reduction is implemented. The rationale of the Occam's window is too reduce the space of candidate adjacency matrices during the search by discarding those with a value of the penalized objective function that is too distant from the current optimal value. Graph candidate structures whose penalized objective function value is within occamAdd from the current optimal value are considered in the next edge-add step of the search. Likewise, graph candidate structures whose penalized objective function value is within occamRem from the current optimal value are considered in the next edge-remove step of the search. Small values for occamRem and occamAdd significantly reduce the space of candidate solutions and the computational cost of the greedy search.

Function ctrlGA sets parameters of the genetic algorithm used for graph structure search. Arguments correspond to those of function ga in the GA package.

Function ctrlEM controls standard parameters of the structural-EM algorithm.

Function ctrlREG is used to set hyperparameters of the conjugate prior on the covariance matrix for Bayesian regularization in Gaussian covariance graph models. The function creates a list of hyperparameters to be given in input in argument regHyperPar of functions fitGGM, searchGGM and mixGGM. If not provided in input, the scale hyperparameter is computed on the data via the sample covariance matrix according to the argument scaleType. If scaleType = "full", the scale matrix is proportional to the data covariance matrix; if scaleType = "fixed", the scale matrix has determinant equal to \((\frac{0.001}{K})^{(1/V)}\) (Baudry, Celeux, 2015; Fop et al. 2018); if scaleType = "one" the scale matrix has determinant 1; if scaleType = "diag" the scale matrix is diagonal. Note that in the case V > N, if not provided in input the scale matrix is forced to be diagonal. The hyperparameter psi controlling the degrees of freedom is set to V + 2 by default.

References

Baudry, J.P. and Celeux, G. (2015). EM for mixtures: Initialization requires special care. Statistics and Computing, 25(4):713-726.

Fop, M., Murphy, T.B., and Scrucca, L. (2018). Model-based clustering with sparse covariance matrices. Statistics and Computing. To appear.

Examples

# NOT RUN {
# }
# NOT RUN {
# ga search with increased mutation probability
data(banknote, package = "mclust")
mod1 <- searchGGM(banknote[,-1], model = "concentration", search = "ga",
                  ctrlGa = ctrlGA(pmutation = 0.3))


# regularization
library(MASS)
V <- 10
N <- 20
mu <- rep(0, V)
sigma <- matrix(0.9, V,V)
diag(sigma) <- 1
x <- cbind( MASS::mvrnorm(N, mu, sigma),
            MASS::mvrnorm(N, mu, sigma),
            MASS::mvrnorm(N, mu, sigma))  # high-dimensional data V = 30, N = 20
#
hyperPar <- ctrlREG(x, K = 1, scaleType = "diag")
mod2 <- searchGGM(x, model = "covariance", penalty = "ebic")   # throws an error
mod2 <- searchGGM(x, model = "covariance", penalty = "ebic",   # regularization
                  regularize = TRUE, regHyperPar = hyperPar)
plot(mod2, "adjacency")


# occam's window
library(MASS)
V <- 20
N <- 500
mu <- rep(0, V)
sigma <- matrix(0.9, V,V)
diag(sigma) <- 1
edges <- rbinom(choose(V,2), 1, 0.3)
A <- matrix(0, V,V)
A[lower.tri(A)] <- edges
A <- A + t(A)
fit <- fitGGM(S = sigma, N = N, graph = A, model = "concentration",
              ctrlIcf = ctrlICF(tol = 1e-06))
sigma <- fit$sigma
#
x <- MASS:::mvrnorm(N, mu, sigma)
#
mod3 <- searchGGM(x, model = "concentration", search = "step-back",
                  ctrlStep = ctrlSTEP(occamAdd = 5, occamRem = 5))
par(mfrow = c(1,2))
plot(fit, what = "adjacency")
plot(mod3, what = "adjacency")

# }
# NOT RUN {
# }