SCD: Detecting cellwise outliers using Shapley values.

In ShapleyOutlier: Multivariate Outlier Explanations using Shapley Values and Mahalanobis Distances

Detecting cellwise outliers using Shapley values.

Description

The SCD function indicates outlying cells for a data vector with p entries or data matrix with n \times p entries containing only numeric entries x for a given center mu and covariance matrix Sigma using the Shapley value \insertCiteMayrhofer2022ShapleyOutlier.

Usage

SCD(
  x,
  mu,
  Sigma,
  Sigma_inv = NULL,
  step_size = 0.1,
  min_deviation = 0,
  max_step = NULL,
  max_iter = 1000,
  q = 0.99,
  method = "cellMCD",
  check = TRUE,
  cells = NULL
)

Arguments

x	Data vector with p entries or data matrix with n \times p entries containing only numeric entries.
mu	Either NULL (default) or mean vector of x. If NULL, method is used for parameter estimation.
Sigma	Either NULL (default) or covariance matrix p \times p of x. If NULL, method is used for parameter estimation.
Sigma_inv	Either NULL (default) or Sigma's inverse p \times p matrix. If NULL, the inverse of Sigma is computed using solve(Sigma).
step_size	Numeric. Step size for the imputation of outlying cells, with step_size \in [0,1]. Defaults to 0.1.
min_deviation	Numeric. Detection threshold, with min_deviation \in [0,1]. Defaults to 0.2
max_step	Either NULL (default) or an integer. The maximum number of steps in each iteration. If NULL, max_step = p.
max_iter	Integer. The maximum number of iterations.
q	Numeric. The quantile of the Chi-squared distribution for detection and imputation of outliers. Defaults to 0.99.
method	Either "cellMCD" (default) or "MCD". Specifies the method used for parameter estimation if mu and/or Sigma are not provided.
check	Logical. If TRUE (default), inputs are checked before running the function and an error message is returned if one of the inputs is not as expected.
cells	Either NULL (default) or a vector/matrix of the same dimension as x, indicating the outlying cells. The matrix must contain only zeros and ones, or TRUE/FALSE.

Value

A list of class shapley_algorithm (new_shapley_algorithm) containing the following:

x	A p-dimensional vector (or a n \times p matrix) containing the imputed data.
phi	A p-dimensional vector (or a n \times p matrix) containing the Shapley values (outlyingness-scores) of x; see shapley.
x_original	A p-dimensional vector (or a n \times p matrix) containing the original data.
x_history	The path of how the original data vector was modified.
phi_history	The Shapley values corresponding to x_history.
S_history	The indices of the outlying cells in each iteration.

References

\insertAllCited

Examples

p <- 5
mu <- rep(0,p)
Sigma <- matrix(0.9, p, p); diag(Sigma) = 1
Sigma_inv <- solve(Sigma)
x <- c(0,1,2,2.3,2.5)
SCD_x <- SCD(x = x, mu = mu, Sigma = Sigma)
plot(SCD_x)

library(MASS)
set.seed(1)
n <- 100; p <- 10
mu <- rep(0,p)
Sigma <- matrix(0.9, p, p); diag(Sigma) = 1
X <- mvrnorm(n, mu, Sigma)
X[sample(1:(n*p), 100, FALSE)] <- rep(c(-5,5),50)
SCD_X <- SCD(X, mu, Sigma)
plot(SCD_X, subset = 20)

ShapleyOutlier documentation built on Oct. 17, 2024, 5:08 p.m.