dlearner {learner} | R Documentation |
Latent space-based transfer learning
Description
This function applies the Direct project LatEnt spAce-based tRaNsfer lEaRning (D-LEARNER) method (McGrath et al. 2024) to leverage data from a source population to improve estimation of a low rank matrix in an underrepresented target population.
Usage
dlearner(Y_source, Y_target, r)
Arguments
Y_source |
matrix containing the source population data |
Y_target |
matrix containing the target population data |
r |
(optional) integer specifying the rank of the knowledge graphs. By default, ScreeNOT (Donoho et al. 2023) is applied to the source population knowledge graph to select the rank. |
Details
Data and notation:
The data consists of a matrix in the target population Y_0 \in \mathbb{R}^{p \times q}
and the source population Y_1 \in \mathbb{R}^{p \times q}
.
Let \hat{U}_{k} \hat{\Lambda}_{k} \hat{V}_{k}^{\top}
denote the truncated singular value decomposition (SVD) of Y_k
, k = 0, 1
.
For k = 0, 1
, one can view Y_k
as a noisy version of \Theta_k
, referred to as the knowledge graph. The target of inference is the target population knowledge graph, \Theta_0
.
Estimation:
This method estimates \Theta_0
by \hat{U}_{1}^{\top}\hat{U}_{1} Y_0 \hat{V}_{1}^{\top}\hat{V}_{1}
.
Value
A list with the following components:
dlearner_estimate |
matrix containing the D-LEARNER estimate of the target population knowledge graph. |
r |
rank value used. |
References
Donoho, D., Gavish, M. and Romanov, E. (2023). ScreeNOT: Exact MSE-optimal singular value thresholding in correlated noise. The Annals of Statistics, 51(1), pp.122-148.
Examples
res <- dlearner(Y_source = dat_highsim$Y_source,
Y_target = dat_highsim$Y_target)