arXiv subjects

Cheolwoo Park

Publications and source records attributed to Cheolwoo Park.

6 recordsLinked to original sources

arXiv2025

GoMS: Graph of Molecule Substructure Network for Molecule Property Prediction

While graph neural networks have shown remarkable success in molecular property prediction, current approaches like the Equivariant Subgraph Aggregation Networks (ESAN) treat molecules as bags of independent substructures, overlooking crucial relationships between these components. We present Graph of Molecule Substructures (GoMS), a novel architecture that explicitly models the interactions and spatial arrangements between molecular substructures. Unlike ESAN's bag-based representation, GoMS constructs a graph where nodes represent subgraphs and edges capture their structural relationships, preserving critical topological information about how substructures are connected and overlap within the molecule. Through extensive experiments on public molecular datasets, we demonstrate that GoMS outperforms ESAN and other baseline methods, with particularly improvements for large molecules containing more than 100 atoms. The performance gap widens as molecular size increases, demonstrating GoMS's effectiveness for modeling industrial-scale molecules. Our theoretical analysis demonstrates that GoMS can distinguish molecules with identical subgraph compositions but different spatial arrangements. Our approach shows particular promise for materials science applications involving complex molecules where properties emerge from the interplay between multiple functional units. By capturing substructure relationships that are lost in bag-based approaches, GoMS represents a significant advance toward scalable and interpretable molecular property prediction for real-world applications.

cs.LG↗

arXiv2025

Limit Theorems for Verbose Persistence Diagrams

The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the persistence diagram. Whereas the persistence diagram is a complete invariant of persistent homology, the verbose persistence diagram is a complete invariant of the one-level higher object -- a filtered chain complex. It therefore strictly contains the persistence diagram, both in form and in the amount of information it encodes. Concretely, the verbose diagram incorporates ephemeral features that arise in a filtered topological space, representing them as additional points along the diagonal. In this work, we initiate the study of random verbose diagrams. We establish a strong law of large numbers for verbose diagrams as a random point cloud grows in size -- that is, we prove the existence of a limiting verbose diagram, viewed as a measure on the half-plane on and above the diagonal. Also, we characterize its support and compute its total mass. Along the way, we extend the notion of the persistent Betti number, reveal the relation between this extended notion and the verbose diagram (which is an extension of the fundamental lemma of persistent homology), and establish results on the asymptotic behavior of the extended persistent Betti numbers. This work extends the main results of the work by Hiraoka, Shirai, and Trinh and its sequel by Shirai and Suzaki to the setting of verbose diagrams.

math.AT↗

arXiv2025

Geometry-preserving and interpretable dimension reduction for compositional data

High-dimensional compositional data pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data, conventional approaches often rely on log-ratio transformations that compromise interpretability and distort the data through ad hoc zero replacements. To address these issues, we introduce a geometry-preserving framework for dimension reduction of compositional data, mapping high-dimensional compositions directly to a lower-dimensional simplex. This framework is interpretable as a softened amalgamation of compositions and enables dual visualization -- showing both projected data and how variables contribute to reduced components -- for at-a-glance interpretation. Within this geometry, we define a new sufficient dimension reduction (SDR) approach for compositional predictors, whose identifiable object, termed the central compositional subspace, differs from the classical central subspace in Euclidean SDR. For estimation, we propose a kernel-based method that yields sparse solutions and comes with an intrinsic predictive model for direct downstream analyses. We prove consistency through a new subspace-comparison argument that allows the estimated and target subspaces to have different dimensions. Applications to real microbiome datasets demonstrate that our approach provides a powerful graphical exploration tool for uncovering meaningful biological patterns in high-dimensional compositional data.

stat.ME↗

arXiv2025

Optimal differentially private kernel learning with random projection

Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We propose a novel differentially private kernel ERM algorithm based on random projection in the reproducing kernel Hilbert space using Gaussian processes. Our method achieves minimax-optimal excess risk rates for both the squared loss and Lipschitz-smooth convex loss functions under a local strong convexity condition. We further show that existing approaches based on alternative dimension reduction techniques, such as random Fourier feature mappings or $\ell_2$ regularization, yield suboptimal excess risk bounds. Our key theoretical contribution also includes the derivation of dimension-free excess risk bounds for objective perturbation-based private linear ERM, marking the first such result that does not rely on noisy gradient-based mechanisms. Additionally, we obtain sharper excess risk bounds for existing differentially private kernel ERM algorithms. Empirical evaluations support our theoretical claims, demonstrating that random projection enables statistically efficient and optimally private kernel learning. These findings provide new insights into the design of differentially private algorithms and highlight the central role of dimension reduction in balancing privacy and utility.

stat.ML↗

arXiv2010

Analysis of dependence among size, rate and duration in internet flows

In this paper we examine rigorously the evidence for dependence among data size, transfer rate and duration in Internet flows. We emphasize two statistical approaches for studying dependence, including Pearson's correlation coefficient and the extremal dependence analysis method. We apply these methods to large data sets of packet traces from three networks. Our major results show that Pearson's correlation coefficients between size and duration are much smaller than one might expect. We also find that correlation coefficients between size and rate are generally small and can be strongly affected by applying thresholds to size or duration. Based on Transmission Control Protocol connection startup mechanisms, we argue that thresholds on size should be more useful than thresholds on duration in the analysis of correlations. Using extremal dependence analysis, we draw a similar conclusion, finding remarkable independence for extremal values of size and rate.

stat.AP↗

arXiv2007

SiZer for time series: A new approach to the analysis of trends

Smoothing methods and SiZer are a useful statistical tool for discovering statistically significant structure in data. Based on scale space ideas originally developed in the computer vision literature, SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical device to assess which observed features are `really there' and which are just spurious sampling artifacts. In this paper, we develop SiZer like ideas in time series analysis to address the important issue of significance of trends. This is not a straightforward extension, since one data set does not contain the information needed to distinguish `trend' from `dependence'. A new visualization is proposed, which shows the statistician the range of trade-offs that are available. Simulation and real data results illustrate the effectiveness of the method.

stat.ME↗