Latent Space-Based Transfer Learning.
learner
The learner package implements transfer learning methods for low-rank matrix estimation. These methods leverage similarity in the latent row and column spaces between the source and target populations to improve estimation in the target population. The methods include the LatEnt spAce-based tRaNsfer lEaRning (LEARNER) method and the direct projection LEARNER (D-LEARNER) method described by McGrath et al. (2024).
Installation
You can install the released version of learner from CRAN with:
install.packages("learner")
You can install the development version of learner from GitHub with:
# install.packages("devtools")
devtools::install_github("stmcg/learner")
Example
We illustrate an example of how learner can be used. We first load the package.
library(learner)
In this illustration, we will use one of the toy data sets in the package (dat_highsim) that has a high degree of similarity between the latent spaces of the source and target populations. The object dat_highsim is a list which contains the observed source population data matrix Y_source and the target population data matrix Y_target. Since the data was simulated, the true values of the matrices are included in dat_highsim as Theta_source and Theta_target.
LEARNER Method
We can apply the LEARNER method via the learner function.
This method allows for flexible patterns of heterogeneity across the source and target populations. It consequently requires specifying the tuning parameters lambda_1 and lambda_2 which control the degree of transfer learning between the populations. These values can be selected based on cross-validation via the cv.learner function. For example, we can specify candidate values of 1, 10, and 100 for lambda_1 and lambda_2 and select the optimal values based on cross-validation as follows:
res_cv.learner <- cv.learner(Y_source = dat_highsim$Y_source,
Y_target = dat_highsim$Y_target,
lambda_1_all = c(1, 10, 100),
lambda_2_all = c(1, 10, 100),
step_size = 0.003)
res_cv.learner$lambda_1_min
#> [1] 100
res_cv.learner$lambda_2_min
#> [1] 1
Next, we apply the learner function with these values of lambda_1 and lambda_2:
res_learner <- learner(Y_source = dat_highsim$Y_source,
Y_target = dat_highsim$Y_target,
lambda_1 = 100, lambda_2 = 1,
step_size = 0.003)
The LEARNER estimate is given by the learner_estimate component in the output of the learner function, e.g.,
res_learner$learner_estimate[1:5, 1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.1468889 -1.63414688 1.1857308 0.008093962 0.2196070
#> [2,] 0.1087766 -0.24392770 -1.0061737 -0.058119721 -0.4012974
#> [3,] -0.6213028 1.04206753 -0.6907776 0.905709331 -0.5324437
#> [4,] 1.5811588 -3.00001490 0.3978080 -2.124285120 0.6909386
#> [5,] 0.5046133 0.01845138 -1.4798209 -0.765601712 -0.2230227
We can check the convergence of the numerical optimization algorithm by plotting the values of the objective function at each iteration:
plot(res_learner$objective_values,
xlab = 'Iteration', ylab = 'Objective function',
type = 'l', col = 'blue', lwd = 2)
D-LEARNER Method
We can apply the D-LEARNER method via the dlearner function. This method makes stronger assumptions on the heterogeneity across the source and target populations. It consequently does not rely on choosing tuning parameters. The dlearner function can be applied as follows:
res_dlearner <- dlearner(Y_source = dat_highsim$Y_source,
Y_target = dat_highsim$Y_target)
res_dlearner$dlearner_estimate[1:5, 1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0959171 -1.72143637 1.15500149 0.005478273 0.3258085
#> [2,] 0.1077137 -0.32243480 -1.03557177 -0.108195636 -0.4093049
#> [3,] -0.7237275 0.86634922 -0.43528206 1.105802194 -0.5961351
#> [4,] 1.6347696 -2.91985925 0.04876288 -2.357504089 0.8127403
#> [5,] 0.4757450 0.05665543 -1.50373470 -0.744076401 -0.2876033