Comparability of a linear encoder under the same outcome-guided loss

Determine whether a linear encoder trained with the same composite outcome-guided loss as the proposed nonlinear autoencoder can achieve comparable results in retaining held-out prognostic information and structuring the latent representation.

Background

The paper uses a nonlinear autoencoder whose composite objective combines predictor reconstruction with local prognostic and native-site losses. Conditional on the fixed upstream preprocessing, this representation retained more held-out prognostic information than PCA and a reconstruction-only autoencoder, although its performance remained within the range of raw-feature linear models. The authors identify whether comparable performance could be obtained with a linear encoder under the same outcome-guided objective as an unresolved methodological question.

References

This supports the outcome-guided objective, but leaves open whether a linear encoder with the same loss could achieve comparable results.

— Distinguishing case-mix from context heterogeneity in prognostic regression model synthesis settings  (2608.12885 - Behrens et al., 13 Aug 2026) in Section Discussion, paragraph beginning “The representation itself also warrants further evaluation.”