Jun-Young Park

Junyoung Park, Irina Gaynanova

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which additionally encode dependence across univariate marginals, have received less attention and pose computational and statistical challenges. In this work, we address these challenges with a new regression approach for multivariate distributional responses, in which distributions are modeled within the semiparametric nonparanormal family. By incorporating the nonparanormal transport (NPT) metric -- an efficient closed-form surrogate for the Wasserstein distance -- into the Fréchet regression framework, our approach decomposes the problem into separate regressions of marginal distributions and their dependence structure, facilitating both efficient estimation and granular interpretation of predictor effects. We provide theoretical justification for NPT, establishing its topological equivalence to the Wasserstein distance and proving that it mitigates the curse of dimensionality. We further prove uniform convergence guarantees for regression estimators, both when distributional responses are fully observed and when they are estimated from empirical samples, attaining fast convergence rates comparable to the univariate case. The utility of our method is demonstrated via simulations and an application to continuous glucose monitoring data.

Yeseul Kim, Kyung Hwan Kim, Junyoung Park et al.

We propose predictive models that estimate GBM patients' health status of one-year after treatments (Classification task), predict the long-term prognosis of GBM patients at an individual level (Survival task). We used total of 467 GBM patients' clinical profile consists of 13 features and two follow-up dates. For baseline models of random forest classifier(RFC) and random survival forest model (RSF), we introduced generalized linear model (GLM), support vector machine (SVM) and Cox proportional hazardous model (COX), accelerated failure time model (AFT) respectively. After preprocessing and prefixing stratified 5-fold data set, we generated best performing models for model types using recursive feature elimination process. Total 10, 4, and 13 features were extracted for best performing one-year survival/progression status RFC models and RSF model via the recursive feature elimination process. In classification task, AUROC of best performing RFC recorded 0.6990 (for one-year survival status classification) and 0.7076 (for one-year progression classification) while that of second best baseline models (GLM in both cases) recorded 0.6691 and 0.6997 respectively. About survival task, the highest C-index of 0.7157 and the lowest IBS of 0.1038 came from the best performing RSF model while that of second best baseline models were 0.6556 and 0.1139 respectively. A simplified linear correlation (extracted from LIME and virtual patient group analysis) between each feature and prognosis of GBM patient were consistent with proven medical knowledge. Our machine learning models suggest that the top three prognostic factors for GBM patient survival were MGMT gene promoter, the extent of resection, and age. To the best of our knowledge, this study is the very first study introducing a interpretable and medical knowledge consistent GBM prognosis predictive models.