Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1606.05988

Continuum directions for supervised dimension reduction

Sungkyu Jung
View original source ↗Read source document ↗Export metadata ↓

Abstract

Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and the resulting basis is called continuum directions. With a presence of binary supervision data, these directions continuously bridge the principal component, mean difference and linear discriminant directions, thus ranging from unsupervised to fully supervised dimension reduction. High-dimensional asymptotic studies of continuum directions for binary supervision reveal several interesting facts. The conditions under which the sample continuum directions are inconsistent, but their classification performance is good, are specified. While the proposed method can be directly used for binary and multi-category classification, its generalizations to incorporate any form of auxiliary data are also presented. The proposed method enjoys fast computation, and the performance is better or on par with more computer-intensive alternatives.

Explore related subjects

stat.MEcs.LGstat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sungkyu Jung. 2018-03-21. Continuum directions for supervised dimension reduction. https://doi.org/10.1016/j.csda.2018.03.015

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Efficient and scalable clustering of survival curves

Survival analysis encompasses a broad range of methods for analyzing time-to-event data, with one key objective being the comparison of survival curves across groups. Traditional approaches for identifying clusters of survival curves often rely on computationally intensive bootstrap techniques to approximate the null hypothesis distribution. While effective, these methods impose significant computational burdens. In this work, we propose a novel approach that leverages the k-means and log-rank test to efficiently identify and cluster survival curves. Our method eliminates the need for computationally expensive resampling, significantly reducing processing time while maintaining statistical reliability. By systematically evaluating survival curves and determining optimal clusters, the proposed method ensures a practical and scalable alternative for large-scale survival data analysis. Through simulation studies, we demonstrate that our approach achieves results comparable to existing bootstrap-based clustering methods while dramatically improving computational efficiency. These findings suggest that the log-rank-based clustering procedure offers a viable and time-efficient solution for researchers working with multiple survival curves in medical and epidemiological studies.

stat.ME↗
arXiv2026

Bayesian Modular Inference for Copula Models with Potentially Misspecified Marginals

Copula models of multivariate data are popular because they allow separate specification of marginal distributions and the copula function. These components can be treated as inter-related modules in a modified Bayesian inference approach called ''cutting feedback'' that is robust to their misspecification. Recent work uses a two module approach, where all $d$ marginals form a single module, to robustify inference for the marginals against copula function misspecification, or vice versa. However, marginals can exhibit differing levels of misspecification, making it attractive to assign each its own module with an individual influence parameter controlling its contribution to a joint semi-modular inference (SMI) posterior. This generalizes existing two module SMI methods, which interpolate between cut and conventional posteriors using a single influence parameter. We develop a novel copula SMI method and select the influence parameters using Bayesian optimization. It provides an efficient continuous relaxation of the discrete optimization problem over $2^d$ cut/uncut configurations. We establish theoretical properties of the resulting semi-modular posterior and demonstrate the approach on simulated and real data. The real data application uses a skew-normal copula model of asymmetric dependence between equity volatility and bond yields, where robustifying copula estimation against marginal misspecification is strongly motivated.

stat.ME↗
arXiv2026

On Asymptotic Outlier Rejection in Bayesian Mixed Poisson Regression Models Under Extreme Target and Covariate Values

Bayesian models are defined to be fully robust against outliers if observations infinitely far from the other data do not influence the posterior. In regression models, this entails a need to consider outliers in both target and covariate values. While in linear regression these cases are interchangeable, as both lead to anomalously large residuals, this symmetry does not apply to generalized linear models. Importantly, Hamura et al. (2025, arXiv:2106.10503) presented sufficient conditions for mixed Poisson count regression models to be robust against infinitely large target values and proposed a mixed Poisson-Rescaled Beta model fulfilling these conditions. We continue from their work and study the robustness properties of mixed Poisson regression models with Gaussian latent variables in the presence of outliers in covariates. We show that in count regression the symmetry between covariate and target outliers breaks: mixed Poisson models are not robust to outlier covariates even if they were robust to target outliers. Furthermore, we show that, as a covariate gets infinitely large, the corresponding regression coefficient posterior collapses to a point-mass distribution concentrated around zero. We hence introduce a novel robustified mixed Poisson model which we denote as $x$-outlier rejective ($x$-OR) mixed Poisson, and demonstrate its theoretical and practical ability to accommodate outliers in the covariates. We investigate robustness properties of alternative ($x$-OR) mixed Poisson models in the presence of moderate outliers with simulations and a real world case study and show that the $x$-OR log-$t$ and Rescaled Beta mixed Poisson models reject both types of outliers, leading to improved inference.

stat.ME↗