Low-Rank Plus Sparse Matrix Transfer Learning under Growing Representations and Ambient Dimensions

Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation under simultaneous growth of the ambient dimension and the intrinsic representation, where a well-estimated source task is embedded as a subspace of a higher-dimensional target task. We propose a general transfer framework in which the target parameter decomposes into an embedded source component, low-dimensional low-rank innovations, and sparse edits, and develop an anchored alternating projection estimator that preserves transferred subspaces while estimating only low-dimensional innovations and sparse modifications. We establish deterministic error bounds that separate target noise, representation growth, and source estimation error, yielding strictly improved rates when rank and sparsity increments are small. We demonstrate the generality of the framework by applying it to two canonical problems. For Markov transition matrix estimation from a single trajectory, we derive end-to-end theoretical guarantees under dependent noise. For structured covariance estimation under enlarged dimensions, we provide complementary theoretical analysis in the appendix and empirically validate consistent transfer gains.

Exploring Consistency in Graph Representations:from Graph Kernels to Graph Neural Networks

Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman subtree (WL-subtree) and Weisfeiler-Lehman optimal assignment (WLOA) kernels are effective in capturing similarity relationships, they rely heavily on predefined kernels and lack sufficient non-linearity for more complex data patterns. Our work aims to bridge the gap between neural network methods and kernel approaches by enabling GNNs to consistently capture relational structures in their learned representations. Given the analogy between the message-passing process of GNNs and WL algorithms, we thoroughly compare and analyze the properties of WL-subtree and WLOA kernels. We find that the similarities captured by WLOA at different iterations are asymptotically consistent, ensuring that similar graphs remain similar in subsequent iterations, thereby leading to superior performance over the WL-subtree kernel. Inspired by these findings, we conjecture that the consistency in the similarities of graph representations across GNN layers is crucial in capturing relational structures and enhancing graph classification performance. Thus, we propose a loss to enforce the similarity of graph representations to be consistent across different layers. Our empirical analysis verifies our conjecture and shows that our proposed consistency loss can significantly enhance graph classification performance across several GNN backbones on various datasets.

TreeMAN: Tree-enhanced Multimodal Attention Network for ICD Coding

ICD coding is designed to assign the disease codes to electronic health records (EHRs) upon discharge, which is crucial for billing and clinical statistics. In an attempt to improve the effectiveness and efficiency of manual coding, many methods have been proposed to automatically predict ICD codes from clinical notes. However, most previous works ignore the decisive information contained in structured medical data in EHRs, which is hard to be captured from the noisy clinical notes. In this paper, we propose a Tree-enhanced Multimodal Attention Network (TreeMAN) to fuse tabular features and textual features into multimodal representations by enhancing the text representations with tree-based features via the attention mechanism. Tree-based features are constructed according to decision trees learned from structured multimodal medical data, which capture the decisive information about ICD coding. We can apply the same multi-label classifier from previous text models to the multimodal representations to predict ICD codes. Experiments on two MIMIC datasets show that our method outperforms prior state-of-the-art ICD coding approaches. The code is available at https://github.com/liu-zichen/TreeMAN.