gamma_smote {npcs}

Gamma-synthetic minority over-sampling technique (gamma-SMOTE).

Description

gamma-SMOTE with some gamma in [0,1], which is a variant of the original SMOTE proposed by Chawla, N. V. et. al (2002). This can be combined with the NPMC methods proposed in Tian, Y., & Feng, Y. (2021). See Section 5.2.3 in Tian, Y., & Feng, Y. (2021) for more details.

Usage

gamma_smote(x, y, dup_rate = 1, gamma = 0.5, k = 5)

Arguments

x

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

y

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

dup_rate

duplicate rate of original data. Default = 1, which finally leads to a new data set with twice sample size.

gamma

the upper bound of uniform distribution used when generating synthetic data points in SMOTE. Can be any number between 0 and 1. Default = 0.5. When it equals to 1, gamma-SMOTE is equivalent to the original SMOTE (Chawla, N. V. et. al (2002)).

k

the number of nearest neighbors during sampling process in SMOTE. Default = 5.

Value

A list consisting of merged original and synthetic data, with two components x and y. x is the predictor matrix and y is the label vector.

References

Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). SMOTE: synthetic minority over-sampling technique. Journal of artificial intelligence research, 16, 321-357.

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

See Also

npcs, predict.npcs, error_rate, and generate_data.

Examples

## Not run: 
set.seed(123, kind = "L'Ecuyer-CMRG")
train.set <- generate_data(n = 200, 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 based on multinomial logistic regression, and vanilla multinomial
## logistic regression without SMOTE. NPMC-ER outputs the infeasibility error information.
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))
fit.vanilla <- nnet::multinom(y~., data = data.frame(x = x, y = factor(y)), trace = FALSE)

# test error of NPMC-CX based on multinomial logistic regression without SMOTE
y.pred.CX <- predict(fit.npmc.CX, x.test)
error_rate(y.pred.CX, y.test)

# test error of vanilla multinomial logistic regression without SMOTE
y.pred.vanilla <- predict(fit.vanilla, newdata = data.frame(x = x.test))
error_rate(y.pred.vanilla, y.test)


## create synthetic data by 0.5-SMOTE
D.syn <- gamma_smote(x, y, dup_rate = 1, gamma = 0.5, k = 5)
x <- D.syn$x
y <- D.syn$y

## try NPMC-CX, NPMC-ER based on multinomial logistic regression, and vanilla multinomial logistic
## regression with SMOTE. NPMC-ER can successfully find a solution after SMOTE.
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))
fit.vanilla <- nnet::multinom(y~., data = data.frame(x = x, y = factor(y)), trace = FALSE)

# test error of NPMC-CX based on multinomial logistic regression with SMOTE
y.pred.CX <- predict(fit.npmc.CX, x.test)
error_rate(y.pred.CX, y.test)

# test error of NPMC-ER based on multinomial logistic regression with SMOTE
y.pred.ER <- predict(fit.npmc.ER, x.test)
error_rate(y.pred.ER, y.test)

# test error of vanilla multinomial logistic regression wit SMOTE
y.pred.vanilla <- predict(fit.vanilla, newdata = data.frame(x = x.test))
error_rate(y.pred.vanilla, y.test)

## End(Not run)