arXiv subjects

Yuexiao Dong

Publications and source records attributed to Yuexiao Dong.

18 recordsLinked to original sources

arXiv2026

Robust Diffusion Models via Divergence-Induced Weighted Denoising

We show that replacing the standard MSE denoising loss in diffusion models with a nonlinear transformation induced by an f-divergence yields a simple robust training surrogate that empirically improves performance under data contamination, with small additional computational overhead. The theoretical foundation rests on a local divergence construction: under the Gaussian reverse-kernel structure of DDPM, each per-step likelihood ratio follows a lognormal distribution parameterized by a scalar mismatch, so the conditional f-divergence at each step reduces to a one-dimensional function of the denoising error. Summing these local divergences yields a training objective that unifies diffusion training as divergence induced weighted denoising, where the derivative of the induced divergence acts as a residual-space influence weight that controls the contribution of each sample. Bounded-influence divergences (Hellinger, negative exponential) suppress large error samples, with Hellinger yielding an explicit exponential weight, connecting the framework to robust M-estimation. Empirically, on CIFAR-10 under 30% contamination, NED reduces FID from 93.0 (KL) to 77.5, while also outperforming standard robust losses such as Huber and clipped MSE.

stat.ML↗

arXiv2026

Probabilistic Win Ratio Method For Hierarchical Composite Endpoints With Coarsened Outcomes

The win ratio is increasingly used to analyze prioritized composite endpoints in clinical trials, but standard implementations rely on deterministic pairwise comparisons and can perform poorly in the presence of censoring and endpoint-specific missingness. In such settings, unresolved comparisons are often treated as ties, leading to loss of efficiency and potentially biased inference, particularly when lower-priority outcomes are incompletely observed. We propose the probabilistic win ratio (PWR), a framework for estimating the classical win ratio under coarsened observation. The PWR replaces deterministic pairwise decisions with conditional probabilities of win, loss, or tie given the observed data, allowing partially observed comparisons to contribute fractionally while being explicitly penalized according to their uncertainty. Comparisons with greater coarsening receive smaller effective weight, whereas fully observed comparisons contribute as in the classical analysis, preserving the clinical priority structure. When outcomes are fully observed, the PWR reduces exactly to the standard win ratio estimator. Simulation studies show that the PWR maintains low bias and mean squared error across a range of censoring and missingness scenarios. Two clinical trial case studies illustrate complementary data regimes, demonstrating calibration in near-complete data and stability under substantial right censoring.

stat.ME↗

arXiv2026

FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows

Sufficient dimension reduction (SDR) seeks a low-dimensional linear projection of predictors that preserves the conditional distribution of the response. Existing methods target this conditional distribution indirectly, via inverse moments, local forward regression, or neural ensemble regression. We propose FlowSDR, a likelihood-based framework that jointly learns the projection and the conditional density by maximizing a conditional log-likelihood, with the density parameterized by monotone rational-quadratic spline flows. The estimator is Fisher consistent under the SDR model, and its sample objective admits a population interpretation in terms of mutual information. As a complementary model within the same likelihood framework, we introduce the neural Gaussian SDR, a heteroscedastic conditional Gaussian model whose mean and variance are parameterized by shared neural-network functions of the projected predictors. In simulations spanning Gaussian errors, heavy-tailed distributions, two-component mixtures, and settings with tail behavior not captured by mean-variance structure, FlowSDR recovers the central subspace more accurately than existing SDR methods and the neural Gaussian SDR baseline. We further validate these advantages on a face-age prediction task using the UTKFace dataset.

stat.ME↗

arXiv2026

Linear Discriminant Analysis with Gradient Optimization

Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be reliably estimated. We propose LDA with gradient optimization (LDA-GO), which learns a low-rank precision matrix via scalable gradient-based optimization. The method automatically selects between a Gaussian likelihood and a cross-entropy loss using data-driven structural diagnostics, adapting to the signal structure without user tuning. The gradient computation avoids any quadratic-sized intermediate matrix, keeping the per-iteration cost linear in the number of dimensions. Theoretically, we prove several properties of the method, including the convexity of the objective functions, Bayes-optimality of the method, and a finite-sample bound of the excess error. Numerically, we conducted a variety of simulations and real data experiments to show that LDA-GO wins a majority of settings among other LDA variants, particularly in sparse-signal high-dimensional regimes.

stat.CO↗

arXiv2025

Decision Tree Embedding by Leaf-Means

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high estimation variance, while large ensembles reduce this variance at the cost of substantial computational overhead and diminished interpretability. In this paper, we propose Decision Tree Embedding (DTE), a fast and effective method that leverages the leaf partitions of a trained classification tree to construct an interpretable feature representation. By using the sample means within each leaf region as anchor points, DTE maps inputs into an embedding space defined by the tree's partition structure, effectively circumventing the high variance inherent in decision-tree splitting rules. We further introduce an ensemble extension based on additional bootstrap trees, and pair the resulting embedding with linear discriminant analysis for classification. We establish several population-level theoretical properties of DTE, including its preservation of conditional density under mild conditions and a characterization of the resulting classification error. Empirical studies on synthetic and real datasets demonstrate that DTE strikes a strong balance between accuracy and computational efficiency, outperforming or matching random forest and shallow neural networks while requiring only a fraction of their training time in most cases. Overall, the proposed DTE method can be viewed either as a scalable decision tree classifier that improves upon standard split rules, or as a neural network model whose weights are learned from tree-derived anchor points, achieving an intriguing integration of both paradigms.

stat.ML↗

arXiv2025

A Graph Sufficiency Perspective for Neural Networks

This paper analyzes neural networks through graph variables and statistical sufficiency. We interpret neural network layers as graph-based transformations, where neurons act as pairwise functions between inputs and learned anchor points. Within this formulation, we establish conditions under which layer outputs are sufficient for the layer inputs, that is, each layer preserves the conditional distribution of the target variable given the input variable. We explore two theoretical paths under this graph-based view. The first path assumes dense anchor points and shows that asymptotic sufficiency holds in the infinite-width limit and is preserved throughout training. The second path, more aligned with practical architectures, proves exact or approximate sufficiency in finite-width networks by assuming region-separated input distributions and constructing appropriate anchor points. This path can ensure the sufficiency property for an infinite number of layers, and provide error bounds on the optimal loss for both regression and classification tasks using standard neural networks. Our framework covers fully connected layers, general pairwise functions, ReLU and sigmoid activations, and convolutional neural networks. Overall, this work bridges statistical sufficiency, graph-theoretic representations, and deep learning, providing a new statistical understanding of neural networks.

cs.LG↗

arXiv2025

Principal Graph Encoder Embedding and Principal Community Detection

In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.

cs.SI↗

arXiv2025

High-Dimensional Independence Testing via Maximum and Average Distance Correlations

This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally dependent dimensions, compare the advantages of each test statistic, examine their respective null distributions, and present a fast chi-square-based testing procedure. The resulting tests are non-parametric and applicable to both Euclidean distance and the Gaussian kernel as the underlying metric. To better understand the practical use cases of the proposed tests, we evaluate the empirical performance of the maximum distance correlation, average distance correlation, and the original distance correlation across various multivariate dependence scenarios, as well as conduct a real data experiment to test the presence of various cancer types and peptide levels in human plasma.

stat.ML↗

arXiv2024

A Cepstral Model for Efficient Spectral Analysis of Covariate-dependent Time Series

This article introduces a novel and computationally fast model to study the association between covariates and power spectra of replicated time series. A random covariate-dependent Cramér spectral representation and a semiparametric log-spectral model are used to quantify the association between the log-spectra and covariates. Each replicate-specific log-spectrum is represented by the cepstrum, inducing a cepstral-based multivariate linear model with the cepstral coefficients as the responses. By using only a small number of cepstral coefficients, the model parsimoniously captures frequency patterns of time series and saves a significant amount of computational time compared to existing methods. A two-stage estimation procedure is proposed. In the first stage, a Whittle likelihood-based approach is used to estimate the truncated replicate-specific cepstral coefficients. In the second stage, parameters of the cepstral-based multivariate linear model, and consequently the effect functions of covariates, are estimated. The model is flexible in the sense that it can accommodate various estimation methods for the multivariate linear model, depending on the application, domain knowledge, or characteristics of the covariates. Numerical studies confirm that the proposed method outperforms some existing methods despite its simplicity and shorter computational time. Supplementary materials for this article are available online.

stat.ME↗

arXiv2024

Sufficient dimension reduction for regression with metric space-valued responses

Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fréchét dimension reduction methods require that the response metric space be continuously embeddable into a Hilbert space, which imposes restriction on the type of metric and kernel choice. We relax this assumption by proposing a Euclidean embedding technique which avoids the use of kernels. Under this framework, classical dimension reduction methods such as ordinary least squares and sliced inverse regression are extended. An extensive simulation experiment demonstrates the superior performance of the proposed method on synthetic data compared to existing methods where applicable. The real data analysis of factors influencing the distribution of COVID-19 transmission in the U.S. and the association between BMI and structural brain connectivity of healthy individuals are also investigated.

stat.ME↗

arXiv2022

A selective review of sufficient dimension reduction for multivariate response regression

We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse regression family include pooled marginal estimators, projective resampling estimators, and distance-based estimators. Ordinary least squares, partial least squares, and semiparametric SDR estimators, on the other hand, are discussed as estimators from the forward regression family.

stat.ME↗

arXiv2020

On expectile-assisted inverse regression estimation for sufficient dimension reduction

Moment-based sufficient dimension reduction methods such as sliced inverse regression may not work well in the presence of heteroscedasticity. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data.

stat.CO↗

arXiv2020

On sufficient dimension reduction via principal asymmetric least squares

In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) may not perform well in the presence of heteroscedasticity, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function.

math.ST↗

arXiv2020

Sparse Representation Classification Beyond L1 Minimization and the Subspace Assumption

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency under a latent subspace model and contamination. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance and significantly faster.

stat.ML↗

arXiv2019

High-dimensional Interactions Detection with Sparse Principal Hessian Matrix

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interaction effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.

stat.ME↗

arXiv2019

Sparse Representation Classification via Screening for Graphs

The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency for random graphs drawn from stochastic blockmodels. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance but significantly faster.

cs.LG↗

arXiv2014

Trace Pursuit: A General Framework for Model-Free Variable Selection

We propose trace pursuit for model-free variable selection under the sufficient dimension reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection consistency with fixed p, and is readily applicable in the challenging setting with p>n. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality. The screening consistency property of forward trace pursuit based on sliced inverse regression is established. Finite sample performances of trace pursuit and other model-free variable selection methods are compared through numerical studies.

stat.ME↗

arXiv2009

Dimension reduction for nonelliptically distributed predictors

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately. For example, a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution. In this paper, we reformulate the commonly used dimension reduction methods, via the notion of "central solution space," so as to circumvent the requirements of such strong assumptions, while at the same time preserve the desirable properties of the classical methods, such as $\sqrt{n}$-consistency and asymptotic normality. Imposing elliptical distributions or even stronger assumptions on predictors is often considered as the necessary tradeoff for overcoming the "curse of dimensionality," but the development of this paper shows that this need not be the case. The new methods will be compared with existing methods by simulation and applied to a data set.

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