matrixShapley: Outlier explanation based on Shapley values for...

In robustmatrix: Robust Matrix-Variate Parameter Estimation

Outlier explanation based on Shapley values for matrix-variate data

Description

matrixShapley decomposes the squared matrix Mahalanobis distance (mmd) into additive outlyingness contributions of the rows, columns, or cell of a matrix \insertCitemayrhofer2023multivariate,mayrhofer2024robustmatrix.

Usage

matrixShapley(X, mu = NULL, cov_row, cov_col, inverted = FALSE, type = "cell")

Arguments

X	a 3d array of dimension (p,q,n), containing n matrix-variate samples of p rows and q columns in each slice.
mu	a p \times q matrix containing the means.
cov_row	a p \times p positive-definite symmetric matrix specifying the rowwise covariance matrix
cov_col	a q \times q positive-definite symmetric matrix specifying the columnwise covariance matrix
inverted	Logical. FALSE by default. If TRUE cov_row and cov_col are supposed to contain the inverted rowwise and columnwise covariance matrices, respectively.
type	Character. Either "row", "col", or "cell" (default) to compute rowwise, columnwise, or cellwise Shapley values.

Value

Rowwise, columnwise, or cellwise Shapley value(s).

References

\insertAllCited

See Also

mmd.

Examples

set.seed(123)
n = 1000; p = 2; q = 3
mu = matrix(rep(0, p*q), nrow = p, ncol = q)
cov_row = matrix(c(5,2,2,4), nrow = p, ncol = p)
cov_col = matrix(c(3,2,1,2,3,2,1,2,3), nrow = q, ncol = q)
X <- rmatnorm(n = 1000, mu, cov_row, cov_col)
X[1:2,1,1] <- c(-10, 10)
X[2,2,1] <- 20

# Cellwise Shapley values additively decompose the squared Mahalanobis distance
# into outlyingness contributions of each cell:
cellwise_shv <- matrixShapley(X, mu, cov_row, cov_col)
cellwise_shv[,,1]
distances <- mmd(X, mu, cov_row, cov_col)
# verify that sum of cellwise Shapley values is equal to squared MMDs:
all.equal(target = apply(cellwise_shv, 3, sum), current = distances)
# For plots and more details see vignette("MMCD_examples").

robustmatrix documentation built on June 8, 2025, 10:34 a.m.