npcs {npcs}

Fit a multi-class Neyman-Pearson classifier with error controls via cost-sensitive learning.

Description

Fit a multi-class Neyman-Pearson classifier with error controls via cost-sensitive learning. This function implements two algorithms proposed in Tian, Y. & Feng, Y. (2021). The problem is minimize a linear combination of P(hat(Y)(X) != k| Y=k) for some classes k while controlling P(hat(Y)(X) != k| Y=k) for some classes k. See Tian, Y. & Feng, Y. (2021) for more details.

Usage

npcs(
  x,
  y,
  algorithm = c("CX", "ER"),
  classifier,
  seed = 1,
  w,
  alpha,
  trControl = list(),
  tuneGrid = list(),
  split.ratio = 0.5,
  split.mode = c("by-class", "merged"),
  tol = 1e-06,
  refit = TRUE,
  protect = TRUE,
  opt.alg = c("Hooke-Jeeves", "Nelder-Mead")
)

Arguments

x

the predictor matrix of training data, where each row and column represents an observation and predictor, respectively.

y

the response vector of training data. Must be integers from 1 to K for some K >= 2. Can be either a numerical or factor vector.

algorithm

the NPMC algorithm to use. String only. Can be either "CX" or "ER", which implements NPMC-CX or NPMC-ER in Tian, Y. & Feng, Y. (2021).

classifier

which model to use for estimating the posterior distribution P(Y|X = x). String only.

seed

random seed

w

the weights in objective function. Should be a vector of length K, where K is the number of classes.

alpha

the levels we want to control for error rates of each class. Should be a vector of length K, where K is the number of classes. Use NA if if no error control is imposed for specific classes.

trControl

list; resampling method

tuneGrid

list; for hyperparameters tuning or setting

split.ratio

the proportion of data to be used in searching lambda (cost parameters). Should be between 0 and 1. Default = 0.5. Only useful when algorithm = "ER".

split.mode

two different modes to split the data for NPMC-ER. String only. Can be either "per-class" or "merged". Default = "per-class". Only useful when algorithm = "ER".

• per-class: split the data by class.

• merged: split the data as a whole.

tol

the convergence tolerance. Default = 1e-06. Used in the lambda-searching step. The optimization is terminated when the step length of the main loop becomes smaller than tol. See pages of hjkb and nmkb for more details.

refit

whether to refit the classifier using all data after finding lambda or not. Boolean value. Default = TRUE. Only useful when algorithm = "ER".

protect

whether to threshold the close-zero lambda or not. Boolean value. Default = TRUE. This parameter is set to avoid extreme cases that some lambdas are set equal to zero due to computation accuracy limit. When protect = TRUE, all lambdas smaller than 1e-03 will be set equal to 1e-03.

opt.alg

optimization method to use when searching lambdas. String only. Can be either "Hooke-Jeeves" or "Nelder-Mead". Default = "Hooke-Jeeves".

Value

An object with S3 class "npcs".

lambda

the estimated lambda vector, which consists of Lagrangian multipliers. It is related to the cost. See Section 2 of Tian, Y. & Feng, Y. (2021) for details.

fit

the fitted classifier.

classifier

which classifier to use for estimating the posterior distribution P(Y|X = x).

algorithm

the NPMC algorithm to use.

alpha

the levels we want to control for error rates of each class.

w

the weights in objective function.

pik

the estimated marginal probability for each class.

References

Tian, Y., & Feng, Y. (2021). Neyman-Pearson Multi-class Classification via Cost-sensitive Learning. Submitted. Available soon on arXiv.

See Also

predict.npcs, error_rate, generate_data, gamma_smote.

Examples

# data generation: case 1 in Tian, Y., & Feng, Y. (2021) with n = 1000
set.seed(123, kind = "L'Ecuyer-CMRG")
train.set <- generate_data(n = 1000, model.no = 1)
x <- train.set$x
y <- train.set$y

test.set <- generate_data(n = 1000, model.no = 1)
x.test <- test.set$x
y.test <- test.set$y

# contruct the multi-class NP problem: case 1 in Tian, Y., & Feng, Y. (2021)
alpha <- c(0.05, NA, 0.01)
w <- c(0, 1, 0)

# try NPMC-CX, NPMC-ER, and vanilla multinomial logistic regression
fit.vanilla <- nnet::multinom(y~., data = data.frame(x = x, y = factor(y)), trace = FALSE)
fit.npmc.CX <- try(npcs(x, y, algorithm = "CX", classifier = "multinom", 
w = w, alpha = alpha))
fit.npmc.ER <- try(npcs(x, y, algorithm = "ER", classifier = "multinom", 
w = w, alpha = alpha, refit = TRUE))
# test error of vanilla multinomial logistic regression
y.pred.vanilla <- predict(fit.vanilla, newdata = data.frame(x = x.test))
error_rate(y.pred.vanilla, y.test)
# test error of NPMC-CX
y.pred.CX <- predict(fit.npmc.CX, x.test)
error_rate(y.pred.CX, y.test)
# test error of NPMC-ER
y.pred.ER <- predict(fit.npmc.ER, x.test)
error_rate(y.pred.ER, y.test)