psvmSDR (version 3.0.1)

rtpsdr: Real time sufficient dimension reduction through principal least squares SVM

Description

This function implements a real-time version of principal SDR based on least squares SVM loss. It is intended for streaming or sequential data settings where new observations arrive continuously and re-fitting the full SDR model would be computationally expensive.

After an initial psdr or rtpsdr fit is obtained, this function updates the working matrix M, slice statistics, and eigen-decomposition efficiently using only the new batch of data. The method supports both regression and binary classification, automatically choosing the appropriate LS-SVM variant.

The returned object includes cumulative sample size, updated mean vector, slice coefficients, intermediate matrices required for updates, and the resulting central subspace basis.

Usage

rtpsdr(x, y, obj = NULL, h = 10, lambda = 1)

Value

An object of class c("rtpsdr","psdr") containing:

• x, y: latest batch data

• M: working matrix

• evalues, evectors: eigen-decomposition of M (central subspace basis)

• N: cumulative sample size

• Xbar: cumulative mean vector

• r: slice-specific coefficient matrix

• A: new A part for update. See Artemiou et. al., (2021)

• loss: "lssvm" (continuous) or "wlssvm" (binary)

• fit: metadata (mode="realtime", H, cutpoints, weight_cutpoints, lambda, etc.)

Arguments

x

x in new data

y

y in new data, y is continuous

obj

the latest output object from the rtpsdr

h

unified control for slicing or weighting; accepts either an integer or a numeric vector.

lambda

hyperparameter for the loss function. default is set to 1.

Author

Jungmin Shin, , Seung Jun Shin, , Andreas Artemiou

References

Artemiou, A. and Dong, Y. (2016) Sufficient dimension reduction via principal lq support vector machine, Electronic Journal of Statistics 10: 783–805.
Artemiou, A., Dong, Y. and Shin, S. J. (2021) Real-time sufficient dimension reduction through principal least squares support vector machines, Pattern Recognition 112: 107768.
Kim, B. and Shin, S. J. (2019) Principal weighted logistic regression for sufficient dimension reduction in binary classification, Journal of the Korean Statistical Society 48(2): 194–206.
Li, B., Artemiou, A. and Li, L. (2011) Principal support vector machines for linear and nonlinear sufficient dimension reduction, Annals of Statistics 39(6): 3182–3210.
Soale, A.-N. and Dong, Y. (2022) On sufficient dimension reduction via principal asymmetric least squares, Journal of Nonparametric Statistics 34(1): 77–94.
Wang, C., Shin, S. J. and Wu, Y. (2018) Principal quantile regression for sufficient dimension reduction with heteroscedasticity, Electronic Journal of Statistics 12(2): 2114–2140.
Shin, S. J., Wu, Y., Zhang, H. H. and Liu, Y. (2017) Principal weighted support vector machines for sufficient dimension reduction in binary classification, Biometrika 104(1): 67–81.
Li, L. (2007) Sparse sufficient dimension reduction, Biometrika 94(3): 603–613.

See Also

psdr, npsdr

Examples

# \donttest{
set.seed(1)
p <- 5; m <- 300; B <- 3
obj <- NULL
for (b in 1:B) {
  x <- matrix(rnorm(m*p), m, p)
  y <- x[,1]/(0.5+(x[,2]+1)^2) + 0.2*rnorm(m)
  obj <- rtpsdr(x, y, obj=obj, h=8, lambda=1)
}
print(obj)
summary(obj)
# }