trans.smap {matrans}

Parameter-transfer learning for partially linear models based on semiparametric model averaging.

Description

Obtain optimal weights and estimated coefficients based on Trans-SMAP.

Usage

trans.smap(train.data, nfold = NULL, bs.para, lm.set = NULL)

Arguments

train.data

a list containing the observations of predictors and response for fitting models. Should be a list with elements "data.y", "data.x" and "data.z", where "data.y" indicates a response list for all data sources, "data.x" indicates a parametric predictor list for all data sources, and "data.z" indicates a nonparametric predictor list for all data sources. Each element in "data.x" and "data.z" is a matrix with each row as an observation and each column as a variable. By default, the first element in "data.y", "data.x" and "data.z" is target data, and others are source data.

nfold

the number of folds for the cross-validation weight criterion. Default is NULL (leave-one-out).

bs.para

a list containing the parameters for B-spline construction in function bs. Should be a list with elements "bs.df" and "bs.degree", each component of which is a vector with the same length as the number of nonparametric variables. For example, bs.para = list(bs.df=c(3,3,3), bs.degree=c(3,3,3)).

• "bs.df": degrees of freedom for each nonparametric component; The details can be referred to the arguments in function bs.

• "bs.degree": degree of the piecewise polynomial for each nonparametric component; The default is 3 for cubic splines.

lm.set

the vector of indices for the linear regression models, which means the corresponding models are constructed by ordinary linear models instead of partially linear models. Default is NULL.

Value

a result list containing the estimated weight vector, the execution time of solving the optimal weights and the summarized results of fitting models.

References

Hu, X., & Zhang, X. (2023). Optimal Parameter-Transfer Learning by Semiparametric Model Averaging. Journal of Machine Learning Research, 24(358), 1-53.

Examples

## correct target model setting

# generate simulation dataset
coeff0 <- cbind(
  as.matrix(c(1.4, -1.2, 1, -0.8, 0.65, 0.3)),
  as.matrix(c(1.4, -1.2, 1, -0.8, 0.65, 0.3) + 0.02),
  as.matrix(c(1.4, -1.2, 1, -0.8, 0.65, 0.3) + 0.3),
  as.matrix(c(1.4, -1.2, 1, -0.8, 0.65, 0.3))
)
whole.data <- simdata.gen(
  px = 6, num.source = 4, size = c(150, 200, 200, 150), coeff0 = coeff0,
  coeff.mis = as.matrix(c(coeff0[, 2], 1.8)), err.sigma = 0.5, rho = 0.5, size.test = 500,
  sim.set = "homo", tar.spec = "cor", if.heter = FALSE
)
data.train <- whole.data$data.train
data.test <- whole.data$data.test

# running Trans-SMAP and obtain the optimal weight vector
data.train$data.x[[2]] <- data.train$data.x[[2]][, -7]
fit.transsmap <- trans.smap(
  train.data = data.train, nfold = 5,
  bs.para = list(bs.df = rep(3, 3), bs.degree = rep(3, 3))
)
ma.weights <- fit.transsmap$weight.est


## misspecified target model setting

# generate simulation dataset
coeff.mis <- matrix(c(c(coeff0[, 1], 0.1), c(coeff0[, 2], 1.8)), ncol = 2)
whole.data <- simdata.gen(
  px = 6, num.source = 4, size = c(150, 200, 200, 150), coeff0 = coeff0,
  coeff.mis = coeff.mis, err.sigma = 0.5, rho = 0.5, size.test = 500,
  sim.set = "homo", tar.spec = "mis", if.heter = FALSE
)
data.train <- whole.data$data.train
data.test <- whole.data$data.test

# running Trans-SMAP and obtain the optimal weight vector
data.train$data.x[[1]] <- data.train$data.x[[1]][, -7]
data.train$data.x[[2]] <- data.train$data.x[[2]][, -7]
fit.transsmap <- trans.smap(
  train.data = data.train, nfold = 5,
  bs.para = list(bs.df = rep(3, 3), bs.degree = rep(3, 3))
)
ma.weights <- fit.transsmap$weight.est