Knowledge-Embedded Latent Projection for Robust Representation Learning

TL;DR

This paper introduces a knowledge-embedded latent projection model that leverages semantic embeddings to improve representation learning in high-dimensional, imbalanced EHR data matrices, with theoretical guarantees and practical validation.

Contribution

It proposes a novel method combining semantic embeddings with kernel PCA and scalable optimization, providing estimation error bounds and convergence guarantees.

Findings

Effective in handling imbalanced high-dimensional data

Improves representation quality with semantic side information

Validated through simulations and real EHR data

Abstract

Latent space models are widely used for analyzing high-dimensional discrete data matrices, such as patient-feature matrices in electronic health records (EHRs), by capturing complex dependence structures through low-dimensional embeddings. However, estimation becomes challenging in the imbalanced regime, where one matrix dimension is much larger than the other. In EHR applications, cohort sizes are often limited by disease prevalence or data availability, whereas the feature space remains extremely large due to the breadth of medical coding system. Motivated by the increasing availability of external semantic embeddings, such as pre-trained embeddings of clinical concepts in EHRs, we propose a knowledge-embedded latent projection model that leverages semantic side information to regularize representation learning. Specifically, we model column embeddings as smooth functions of semantic embeddings via a mapping in a reproducing kernel Hilbert space. We develop a computationally efficient two-step estimation procedure that combines semantically guided subspace construction via kernel principal component analysis with scalable projected gradient descent. We establish estimation error bounds that characterize the trade-off between statistical error and approximation error induced by the kernel projection. Furthermore, we provide local convergence guarantees for our non-convex optimization procedure. Extensive simulation studies and a real-world EHR application demonstrate the effectiveness of the proposed method.