matrixShapley {robustmatrix}

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 (Mayrhofer and Filzmoser 2023; double-blind 2024).

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

Mayrhofer M, Filzmoser P (2023). “Multivariate outlier explanations using Shapley values and Mahalanobis distances.” Econometrics and Statistics.

double-blind (2024). “Robust covariance estimation and explainable outlier detection for matrix-valued data.” [Manuscript submitted for publication].

See Also

mmd.

Examples

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)
distances <- mmd(X, mu, cov_row, cov_col)