arXiv subjects

Zhi-Yu Jou

Publications and source records attributed to Zhi-Yu Jou.

5 recordsLinked to original sources

arXiv2026

Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations

The inference of conditional distributions is a fundamental problem in statistics, essential for prediction, uncertainty quantification, and probabilistic modeling. A wide range of methodologies have been developed for this task. This article reviews and compares several representative approaches spanning classical nonparametric methods and modern generative models. We begin with the single-index method of Hall and Yao (2005), which estimates the conditional distribution through a dimension-reducing index and nonparametric smoothing of the resulting one-dimensional cumulative conditional distribution function. We then examine the basis-expansion approaches, including FlexCode (Izbicki and Lee, 2017) and DeepCDE (Dalmasso et al., 2020), which convert conditional density estimation into a set of nonparametric regression problems. In addition, we discuss two recent generative simulation-based methods that leverage modern deep generative architectures: the generative conditional distribution sampler (Zhou et al., 2023) and the conditional denoising diffusion probabilistic model (Fu et al., 2024; Yang et al., 2025). A systematic numerical comparison of these approaches is provided using a unified evaluation framework that ensures fairness and reproducibility. The performance metrics used for the estimated conditional distribution include the mean-squared errors of conditional mean and standard deviation, as well as the Wasserstein distance. We also discuss their flexibility and computational costs, highlighting the distinct advantages and limitations of each approach.

stat.ML↗

arXiv2025

The $ϕ$-PCA Framework: A Unified and Efficiency-Preserving Approach with Robust Variants

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these challenges, we introduce the $ϕ$-PCA framework which provides a unified formulation of robust and distributed PCA. The class of $ϕ$-PCA methods retains the asymptotic efficiency of standard PCA, while aggregating multiple local estimates using a proper $ϕ$ function enhances ordering-robustness, leading to more accurate eigensubspace estimation under contamination. Notably, the harmonic mean PCA (HM-PCA), corresponding to the choice $ϕ(u)=u^{-1}$, achieves optimal ordering-robustness and is recommended for practical use. Theoretical results further show that robustness increases with the number of partitions, a phenomenon seldom explored in the literature on robust or distributed PCA. Altogether, the partition-aggregation principle underlying $ϕ$-PCA offers a general strategy for developing robust and efficiency-preserving methodologies applicable to both robust and distributed data analysis.

stat.ME↗

arXiv2024

A Generalized Mean Approach for Distributed-PCA

Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating results across multiple machines or computing nodes due to computational overhead. Fan et al. (2019) introduced a pioneering DPCA method to estimate the leading rank-$r$ eigenspace, aggregating local rank-$r$ projection matrices by averaging. However, their method does not utilize eigenvalue information. In this article, we propose a novel DPCA method that incorporates eigenvalue information to aggregate local results via the matrix $β$-mean, which we call $β$-DPCA. The matrix $β$-mean offers a flexible and robust aggregation method through the adjustable choice of $β$ values. Notably, for $β=1$, it corresponds to the arithmetic mean; for $β=-1$, the harmonic mean; and as $β\to 0$, the geometric mean. Moreover, the matrix $β$-mean is shown to associate with the matrix $β$-divergence, a subclass of the Bregman matrix divergence, to support the robustness of $β$-DPCA. We also study the stability of eigenvector ordering under eigenvalue perturbation for $β$-DPCA. The performance of our proposal is evaluated through numerical studies.

stat.ML↗

arXiv2017

Robust mislabel logistic regression without modeling mislabel probabilities

Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M-estimation by down-weighting suspected instances. In this work, we propose a new robust mislabel logistic regression based on gamma-divergence. Our proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum gamma-divergence estimation leads to a weighted estimating equation without the need to subtract any bias correction term, i.e., it is automatically bias corrected. These properties make the proposed gamma-logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. Our method is also easy to implement, and two types of algorithms are included. Simulation and real data application results are presented to demonstrate the performance of gamma-logistic.

stat.AP↗

arXiv2016

A low-rank based estimation-testing procedure for matrix-covariate regression

Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy, however, results in a large number of parameters, while the available sample size is relatively too small to have reliable analysis results. To overcome the problem of high-dimensionality in hypothesis testing, variance component test has been proposed with promise detection power, but is not straightforward to provide estimates of effect size. In this work, we overcome the problem of high-dimensionality by utilizing the inherent structure of the matrix-covariate. The advantage is that estimation and hypothesis testing can be conducted simultaneously as in the conventional case, while the estimation efficiency and detection power can be largely improved, due to a parsimonious parameterization for the coefficients of matrix-covariate. Our method is applied to test the significance of gene-gene interactions in the PSQI data, and is applied to test if electroencephalography is associated with the alcoholic status in the EEG data, wherein sparse effects and low-rank effects of matrix-covariates are identified, respectively.

stat.AP↗