DI: Detection-Imputation algorithm

Description

The Detection-Imputation algorithm computes cellwise robust estimates of the center and covariance matrix of a data set X. The algorithm alternates between the detection of cellwise outliers and their imputation combined with re-estimation of the center and covariance matrix. By default, it starts by calling checkDataSet to clean the data.

Usage

DI(X, initEst = "DDCWcov", crit = 0.01, maxits = 10, quant = 0.99,
maxCol = 0.25, checkPars = list())

Arguments

X is the input data, and must be an \(n\) by \(d\) matrix or a data frame.

initEst

An initial estimator for the center and covariance matrix. Should be one of "DDCWcov" or "TSGS", where the latter refers to the function TSGS. The default option "DDCWcov" uses the proposal of Raymaekers and Rousseeuw (2020) which is much faster for increasing dimension.

crit

The algorithm converges when the subsequent estimates of the center and covariance matrix do not differ more than crit in squared Euclidean norm.

maxits

Maximum number of DI-iterations.

quant

The cutoff used to detect cellwise outliers.

maxCol

The maximum number of cellwise outliers allowed in a column.

checkPars

Optional list of parameters used in the call to checkDataSet. The options are:

coreOnly If TRUE, skip the execution of checkDataset. Defaults to FALSE
numDiscrete A column that takes on numDiscrete or fewer values will be considered discrete and not retained in the cleaned data. Defaults to \(5\).
fracNA Only retain columns and rows with fewer NAs than this fraction. Defaults to \(0.15\).
precScale Only consider columns whose scale is larger than precScale. Here scale is measured by the median absolute deviation. Defaults to \(1e-12\).
silent Whether or not the function progress messages should be printed. Defaults to FALSE.

Value

A list with components:

center The final estimate of the center of the data.
cov The final estimate of the covariance matrix.
nbits Number of DI-iterations executed to reach convergence.
Ximp The imputed data.
indcells Indices of the cells which were flagged in the analysis.
indNAs Indices of the NAs in the data.
Zres Matrix with standardized cellwise residuals of the flagged cells. Contains zeroes in the unflagged cells.
Zres_denom Denominator of the standardized cellwise residuals.
cellPaths Matrix with the same dimensions as X, in which each row contains the path of least angle regression through the cells of that row, i.e. the order of the coordinates in the path (1=first, 2=second,...)
checkDataSet_out Output of the call to checkDataSet which is used to clean the data.

References

J. Raymaekers and P.J. Rousseeuw (2020). Handling cellwise outliers by sparse regression and robust covariance. Arxiv: 1912.12446. (link to open access pdf)

Examples

Run this code

# NOT RUN {
mu <- rep(0, 3)
Sigma <- diag(3) * 0.1 + 0.9
X <- MASS::mvrnorm(100, mu, Sigma)
DI.out <- DI(X)
DI.out$cov
# }