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).
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")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.
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] 1Next, 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$learner_estimate[1:5, 1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.1468889 -1.63414688 1.1857308 0.008093962 0.2196070
#> [2,] 0.1087766 -0.24392770 -1.0061737 -0.058119721 -0.4012974
#> [3,] -0.6213028 1.04206753 -0.6907776 0.905709331 -0.5324437
#> [4,] 1.5811588 -3.00001490 0.3978080 -2.124285120 0.6909386
#> [5,] 0.5046133 0.01845138 -1.4798209 -0.765601712 -0.2230227We can check the convergence of the numerical optimization algorithm by plotting the values of the objective function at each iteration:
plot(res_learner$objective_values,
xlab = 'Iteration', ylab = 'Objective function',
type = 'l', col = 'blue', lwd = 2)
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