arXiv subjects

Eunho Koo

Publications and source records attributed to Eunho Koo.

4 recordsLinked to original sources

arXiv2026

Statistical Matching via Schr\"odinger Bridge beyond Conditional Independence

Statistical matching combines partially overlapping datasets that share covariates $X$ but observe the target $Y$ and auxiliary variables $Z$ separately. Classical approaches typically invoke the conditional independence assumption (CIA), which makes the problem identifiable but fundamentally implies that the imported auxiliary variable provides no additional predictive power for $Y$ once $X$ is known. To capture this latent $Y$--$Z$ dependence, we propose a novel dependency-aware Schr\"odinger bridge for predictive statistical matching. Our approach couples the two separated databases by tilting the conservative CIA baseline with a transportation-based compatibility cost, recovering an informative joint distribution. The resulting statistical learning framework yields full probabilistic posterior rules for bidirectional imputation. Theoretically, we establish a sufficient condition under which the learned bridge strictly improves over the CIA baseline, alongside an exact joint recovery guarantee in the Gaussian setting under an appropriate cost. Across synthetic benchmarks and real-world datasets (CelebA and Adult), we demonstrate that our dependency-aware completion consistently improves downstream predictive utility, proving especially beneficial in settings like data recoding where the underlying population exhibits strong $Y$--$Z$ dependence.

cs.LG↗

arXiv2025

Node Classification via Simplicial Interaction with Augmented Maximal Clique Selection

Considering higher-order interactions allows for a more comprehensive understanding of network structures beyond simple pairwise connections. While leveraging all cliques in a network to handle higher-order interactions is intuitive, it often leads to computational inefficiencies due to overlapping information between higher-order and lower-order cliques. To address this issue, we propose an augmented maximal clique strategy. Although using only maximal cliques can reduce unnecessary overlap and provide a concise representation of the network, certain nodes may still appear in multiple maximal cliques, resulting in imbalanced training data. Therefore, our augmented maximal clique approach selectively includes some non-maximal cliques to mitigate the overrepresentation of specific nodes and promote more balanced learning across the network. Comparative analyses on synthetic networks and real-world citation datasets demonstrate that our method outperforms approaches based on pairwise interactions, all cliques, or only maximal cliques. Finally, by integrating this strategy into GNN-based semi-supervised learning, we establish a link between maximal clique-based methods and GNNs, showing that incorporating higher-order structures improves predictive accuracy. As a result, the augmented maximal clique strategy offers a computationally efficient and effective solution for higher-order network learning.

cs.SI↗

arXiv2024

Node classification in networks via simplicial interactions

In the node classification task, it is natural to presume that densely connected nodes tend to exhibit similar attributes. Given this, it is crucial to first define what constitutes a dense connection and to develop a reliable mathematical tool for assessing node cohesiveness. In this paper, we propose a probability-based objective function for semi-supervised node classification that takes advantage of higher-order networks' capabilities. The proposed function reflects the philosophy aligned with the intuition behind classifying within higher order networks, as it is designed to reduce the likelihood of nodes interconnected through higher-order networks bearing different labels. Additionally, we propose the Stochastic Block Tensor Model (SBTM) as a graph generation model designed specifically to address a significant limitation of the traditional stochastic block model, which does not adequately represent the distribution of higher-order structures in real networks. We evaluate the objective function using networks generated by the SBTM, which include both balanced and imbalanced scenarios. Furthermore, we present an approach that integrates the objective function with graph neural network (GNN)-based semi-supervised node classification methodologies, aiming for additional performance gains. Our results demonstrate that in challenging classification scenarios--characterized by a low probability of homo-connections, a high probability of hetero-connections, and limited prior node information--models based on the higher-order network outperform pairwise interaction-based models. Furthermore, experimental results suggest that integrating our proposed objective function with existing GNN-based node classification approaches enhances classification performance by efficiently learning higher-order structures distributed in the network.

cs.SI↗

arXiv2020

Empirical Strategy for Stretching Probability Distribution in Neural-network-based Regression

In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient descent procedure under a given loss function, the loss function structure can affect the performance significantly. In this study, we considered the distribution error, i.e., the inconsistency of two distributions (those of the predicted values and label), as the prediction error, and proposed weighted empirical stretching (WES) as a novel loss function to increase the overlap area of the two distributions. The function depends on the distribution of a given label, thus, it is applicable to any distribution shape. Moreover, it contains a scaling hyperparameter such that the appropriate parameter value maximizes the common section of the two distributions. To test the function capability, we generated ideal distributed curves (unimodal, skewed unimodal, bimodal, and skewed bimodal) as the labels, and used the Fourier-extracted input data from the curves under a feedforward neural network. In general, WES outperformed loss functions in wide use, and the performance was robust to the various noise levels. The improved results in RMSE for the extreme domain (i.e., both tail regions of the distribution) are expected to be utilized for prediction of abnormal events in non-linear complex systems such as natural disaster and financial crisis.

cs.LG↗