Knowledge-Embedded Latent Projection for Robust Representation Learning

"The paper presents a novel approach to analyzing high-dimensional discrete data matrices, particularly in the context of electronic health records (EHRs). The authors highlight the challenges posed by imbalanced data regimes, where one dimension of the data matrix (e.g., the number of patients) is significantly smaller than the other (e.g., the number of features or medical codes). This imbalance is a common issue in EHR applications due to the limited cohort sizes resulting from disease prevalence and data availability, juxtaposed with the vast feature space that medical coding entails. To address these challenges, the authors propose a knowledge-embedded latent projection model that integrates external semantic embeddings, which are pre-trained representations of clinical concepts, to enhance the representation learning process. The methodology involves modeling the column embeddings of the data matrix as smooth functions of the semantic embeddings, utilizing a mapping within a reproducing kernel Hilbert space. This approach allows for the incorporation of semantic information into the latent space, thereby regularizing the learning process and potentially improving the quality of the embeddings derived from the data. The authors develop a two-step estimation procedure that is computationally efficient. The first step involves constructing a semantically guided subspace through kernel principal component analysis (KPCA), which reduces the dimensionality of the feature space while preserving the essential semantic structure. The second step employs scalable projected gradient descent to optimize the latent representations. The theoretical contributions of the paper include the establishment of estimation error bounds that delineate the trade-off between statistical error and approximation error introduced by the kernel projection. This is crucial for understanding the performance of the proposed model in practical applications. Additionally, the authors provide local convergence guarantees for their non-convex optimization procedure, which is essential for ensuring the reliability of the estimation process in real-world scenarios. To validate their approach, the authors conduct extensive simulation studies alongside a real-world application using EHR data. The results demonstrate the effectiveness of the knowledge-embedded latent projection model in capturing complex dependence structures within the data, ultimately leading to improved predictive performance and insights into patient features. This research contributes significantly to the field of data analysis in healthcare, offering a robust framework for leveraging semantic information to enhance the understanding of high-dimensional data matrices in EHRs."