matrixShapley: 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 mayrhofer2023multivariate,mayrhofer2024robustmatrix.

Usage

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

Value

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

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.

References

Examples

Run this code

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)