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)


[Package learner version 1.0.0 Index]