cross_validation {abcrlda}

Cross Validation for separate sampling adjusted for cost.

Description

This function implements Cross Validation for separate sampling adjusted for cost.

Usage

cross_validation(
  x,
  y,
  gamma = 1,
  cost = c(0.5, 0.5),
  nfolds = 10,
  bias_correction = TRUE
)

Arguments

x

Input matrix or data.frame of dimension nobs x nvars; each row is an feature vector.

y

A numeric vector or factor of class labels. Factor should have either two levels or be a vector with two distinct values. If y is presented as a vector, it will be coerced into a factor. Length of y has to correspond to number of samples in x.

gamma

Regularization parameter \gamma in the ABC-RLDA discriminant function given by:

W_{ABC}^{RLDA} = \gamma (x-\frac{\bar{x}_0 + \bar{x}_1}{2})^T H (\bar{x}_0 - \bar{x}_1) - log(\frac{C_{01}}{C_{10}}) + \hat{\omega}_{opt}

H = (I_p + \gamma \hat{\Sigma})^{-1}

Formulas and derivations for parameters used in above equation can be found in the article under reference section.

cost

Parameter that controls the overall misclassification costs. This is a vector of length 1 or 2 where the first value is C_{10} (represents the cost of assigning label 1 when the true label is 0) and the second value, if provided, is C_{01} (represents the cost of assigning label 0 when the true label is 1). The default setting is c(0.5, 0.5), so both classes have equal misclassification costs

If a single value is provided, it should be normalized to lie between 0 and 1 (but not including 0 or 1). This value will be assigned to C_{10} while C_{01} will be equal to (1 - C_{10}).

nfolds

Number of folds to use with cross-validation. Default is 10. In case of imbalanced data, nfolds should not be greater than the number of observations in smaller class.

bias_correction

Takes in a boolean value. If bias_correction is TRUE, then asymptotic bias correction will be performed. Otherwise, (if bias_correction is FALSE) asymptotic bias correction will not be performed and the ABCRLDA is the classical RLDA. The default is TRUE.

Value

Returns list of parameters.

risk_cross

Returns risk estimation where \Re = \varepsilon_0 * C_{10} + \varepsilon_1 * C_{01}

e_0

Error estimate for class 0.

e_1

Error estimate for class 1.

Reference

Braga-Neto, Ulisses & Zollanvari, Amin & Dougherty, Edward. (2014). Cross-Validation Under Separate Sampling: Strong Bias and How to Correct It. Bioinformatics (Oxford, England). 30. 10.1093/bioinformatics/btu527. URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4296143/pdf/btu527.pdf

See Also

Other functions in the package: abcrlda(), da_risk_estimator(), grid_search(), predict.abcrlda(), risk_calculate()

Examples

data(iris)
train_data <- iris[which(iris[, ncol(iris)] == "virginica" |
                         iris[, ncol(iris)] == "versicolor"), 1:4]
train_label <- factor(iris[which(iris[, ncol(iris)] == "virginica" |
                                 iris[, ncol(iris)] == "versicolor"), 5])
cross_validation(train_data, train_label, gamma = 10)