Chan‐Woo Lee

Chanwoo Lee

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and column-wise interpretations and contain structural information that can be lost with naive vectorization approaches. To address this, we propose a method called principal support matrix machine (PSMM) for the matrix sufficient dimension reduction. The PSMM converts the sufficient dimension reduction problem into a series of classification problems by dividing the response variables into slices. It effectively utilizes the matrix structure by finding hyperplanes with rank-1 normal matrix that optimally separate the sliced responses. Additionally, we extend our approach to the higher-order tensor case. Our numerical analysis demonstrates that the PSMM outperforms existing methods and has strong interpretability in real data applications.

Junhyeong Lee, Jong Min Yuk, Chan-Woo Lee

The construction of experimental datasets is essential for expanding the scope of data-driven scientific discovery. Recent advances in natural language processing (NLP) have facilitated automatic extraction of structured data from unstructured scientific literature. While existing approaches-multi-step and direct methods-offer valuable capabilities, they also come with limitations when applied independently. Here, we propose a novel hybrid text-mining framework that integrates the advantages of both methods to convert unstructured scientific text into structured data. Our approach first transforms raw text into entity-recognized text, and subsequently into structured form. Furthermore, beyond the overall data structuring framework, we also enhance entity recognition performance by introducing an entity marker-a simple yet effective technique that uses symbolic annotations to highlight target entities. Specifically, our entity marker-based hybrid approach not only consistently outperforms previous entity recognition approaches across three benchmark datasets (MatScholar, SOFC, and SOFC slot NER) but also improve the quality of final structured data-yielding up to a 58% improvement in entity-level F1 score and up to 83% improvement in relation-level F1 score compared to direct approach.

Chanwoo Lee, Miaoyan Wang

We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we develop a general family of smooth tensor models up to arbitrary index permutations; the model incorporates the popular tensor block models and Lipschitz hypergraphon models as special cases. We show that a constrained least-squares estimator in the block-wise polynomial family achieves the minimax error bound. A phase transition phenomenon is revealed with respect to the smoothness threshold needed for optimal recovery. In particular, we find that a polynomial of degree up to $(m-2)(m+1)/2$ is sufficient for accurate recovery of order-$m$ tensors, whereas higher degree exhibits no further benefits. This phenomenon reveals the intrinsic distinction for smooth tensor estimation problems with and without unknown permutations. Furthermore, we provide an efficient polynomial-time Borda count algorithm that provably achieves optimal rate under monotonicity assumptions. The efficacy of our procedure is demonstrated through both simulations and Chicago crime data analysis.

Chanwoo Lee, Miaoyan Wang

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete, ordinal-valued observations. Two related problems are studied, one on tensor denoising and the other on tensor completion. We propose a multi-linear cumulative link model, develop a rank-constrained M-estimator, and obtain theoretical accuracy guarantees. Our mean squared error bound enjoys a faster convergence rate than previous results, and we show that the proposed estimator is minimax optimal under the class of low-rank models. Furthermore, the procedure developed serves as an efficient completion method which guarantees consistent recovery of an order-$K$ $(d,\ldots,d)$-dimensional low-rank tensor using only $\tilde{\mathcal{O}}(Kd)$ noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.