arXiv subjects

Leying Guan

Publications and source records attributed to Leying Guan.

15 recordsLinked to original sources

arXiv2026

Gradient flows for empirical Bayes in high-dimensional linear models

Empirical Bayes provides a powerful framework for learning and adapting to latent structure in data. In sequence models where an independent observation is associated to each latent parameter, theory and methods around empirical Bayes are well-developed. However, in models where latent parameters and observed data interact through more complex designs, many statistical and algorithmic questions remain unanswered. In this work, we study a canonical setting of empirical Bayes estimation for the distribution of regression coefficients in a high-dimensional Bayesian or random effects linear model. Computationally, we propose a new system of gradient flow equations for computing a nonparametric maximum likelihood estimator (NPMLE), which jointly optimizes over the prior and posterior distributions of the regression coefficients in a Gibbs variational representation of the marginal log-likelihood. A diffusion-based implementation yields an adaptive Langevin dynamics algorithm in which the prior evolves continuously to optimize a sequence model log-likelihood defined by the coordinates of the Langevin sample. Theoretically, we show polynomial-time convergence of the proposed gradient flow to a near-NPMLE from any initialization within a convex sub-level set of the marginal log-likelihood, by developing a high-temperature log-Sobolev inequality for the posterior law. We establish the statistical consistency of any near-NPMLE under deterministic conditions for the regression design as $n,p\rightarrow\infty$.

math.ST↗

arXiv2025

FairICP: Encouraging Equalized Odds via Inverse Conditional Permutation

$\textit{Equalized odds}$, an important notion of algorithmic fairness, aims to ensure that sensitive variables, such as race and gender, do not unfairly influence the algorithm's prediction when conditioning on the true outcome. Despite rapid advancements, current research primarily focuses on equalized odds violations caused by a single sensitive attribute, leaving the challenge of simultaneously accounting for multiple attributes under-addressed. We bridge this gap by introducing an in-processing fairness-aware learning approach, FairICP, which integrates adversarial learning with a novel inverse conditional permutation scheme. FairICP offers a flexible and efficient scheme to promote equalized odds under fairness conditions described by complex and multi-dimensional sensitive attributes. The efficacy and adaptability of our method are demonstrated through both simulation studies and empirical analyses of real-world datasets.

stat.ML↗

arXiv2024

Conformalized Semi-supervised Random Forest for Classification and Abnormality Detection

The Random Forests classifier, a widely utilized off-the-shelf classification tool, assumes training and test samples come from the same distribution as other standard classifiers. However, in safety-critical scenarios like medical diagnosis and network attack detection, discrepancies between the training and test sets, including the potential presence of novel outlier samples not appearing during training, can pose significant challenges. To address this problem, we introduce the Conformalized Semi-Supervised Random Forest (CSForest), which couples the conformalization technique Jackknife+aB with semi-supervised tree ensembles to construct a set-valued prediction $C(x)$. Instead of optimizing over the training distribution, CSForest employs unlabeled test samples to enhance accuracy and flag unseen outliers by generating an empty set. Theoretically, we establish CSForest to cover true labels for previously observed inlier classes under arbitrarily label-shift in the test data. We compare CSForest with state-of-the-art methods using synthetic examples and various real-world datasets, under different types of distribution changes in the test domain. Our results highlight CSForest's effective prediction of inliers and its ability to detect outlier samples unique to the test data. In addition, CSForest shows persistently good performance as the sizes of the training and test sets vary. Codes of CSForest are available at https://github.com/yujinhan98/CSForest.

cs.LG↗

arXiv2023

A conformal test of linear models via permutation-augmented regressions

Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2α$, given any targeted level $α$, for arbitrary fixed designs and error distributions. We have confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT) and residual permutation test (RPT), which also offer theoretical guarantees, PALMRT does not compromise as much on power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate the differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test after multiple corrections, while both CPT and RPT suffered from a drastic loss of power and failed to identify any discoveries. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity. An R package for PALMRT is available at \url{https://github.com/LeyingGuan/PairedRegression}.

stat.ME↗

arXiv2023

GAN-based Vertical Federated Learning for Label Protection in Binary Classification

Split learning (splitNN) has emerged as a popular strategy for addressing the high computational costs and low modeling efficiency in Vertical Federated Learning (VFL). However, despite its popularity, vanilla splitNN lacks encryption protection, leaving it vulnerable to privacy leakage issues, especially Label Leakage from Gradients (LLG). Motivated by the LLG issue resulting from the use of labels during training, we propose the Generative Adversarial Federated Model (GAFM), a novel method designed specifically to enhance label privacy protection by integrating splitNN with Generative Adversarial Networks (GANs). GAFM leverages GANs to indirectly utilize label information by learning the label distribution rather than relying on explicit labels, thereby mitigating LLG. GAFM also employs an additional cross-entropy loss based on the noisy labels to further improve the prediction accuracy. Our ablation experiment demonstrates that the combination of GAN and the cross-entropy loss component is necessary to enable GAFM to mitigate LLG without significantly compromising the model utility. Empirical results on various datasets show that GAFM achieves a better and more robust trade-off between model utility and privacy compared to all baselines across multiple random runs. In addition, we provide experimental justification to substantiate GAFM's superiority over splitNN, demonstrating that it offers enhanced label protection through gradient perturbation relative to splitNN.

cs.LG↗

arXiv2022

Smooth and probabilistic PARAFAC model with auxiliary covariates

In immunological and clinical studies, matrix-valued time-series data clustering is increasingly popular. Researchers are interested in finding low-dimensional embedding of subjects based on potentially high-dimensional longitudinal features and investigating relationships between static clinical covariates and the embedding. These studies are often challenging due to high dimensionality, as well as the sparse and irregular nature of sample collection along the time dimension. We propose a smoothed probabilistic PARAFAC model with covariates (SPACO) to tackle these two problems while utilizing auxiliary covariates of interest. We provide intensive simulations to test different aspects of SPACO and demonstrate its use on an immunological data set from patients with SARs-CoV-2 infection.

stat.ME↗

arXiv2022

Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction

We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample, and can be combined with different conformal score constructions. The proposed framework enjoys an assumption-free finite sample marginal coverage guarantee, and it also offers additional local coverage guarantees under suitable assumptions. We demonstrate how to change from conformal prediction to localized conformal prediction using several conformal scores, and we illustrate a potential gain via numerical examples.

math.ST↗

arXiv2022

$\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent

Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient descent algorithm with $\ell_1$ constraint for high dimensional data. In particular, we use a decaying sequence of constraints over proximal iterations, and show that the resulting estimate is rate-optimal under suitable assumptions. Although several previous works have demonstrated such optimality for the $\ell_0$ constrained problem using iterative approaches, the same level of theoretical understanding for the $\ell_1$ constrained formulation is still lacking. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially. We compare our proposals to several existing methods whose implementations are available on R CRAN, and the proposed methods show competitive performances in both simulations and a real data example.

stat.ME↗

arXiv2020

Conformal prediction with localization

We propose a new method called localized conformal prediction, where we can perform conformal inference using only a local region around a new test sample to construct its confidence interval. Localized conformal inference is a natural extension to conformal inference. It generalizes the method of conformal prediction to the case where we can break the data exchangeability, so as to give the test sample a special role. To our knowledge, this is the first work that introduces such a localization to the framework of conformal prediction. We prove that our proposal can also have assumption-free and finite sample coverage guarantees, and we compare the behaviors of localized conformal prediction and conformal prediction in simulations.

math.ST↗

arXiv2019

Prediction and outlier detection in classification problems

We consider the multi-class classification problem when the training data and the out-of-sample test data may have different distributions and propose a method called BCOPS (balanced and conformal optimized prediction sets). BCOPS constructs a prediction set $C(x)$ as a subset of class labels, possibly empty. It tries to optimize the out-of-sample performance, aiming to include the correct class as often as possible, but also detecting outliers $x$, for which the method returns no prediction (corresponding to $C(x)$ equal to the empty set). The proposed method combines supervised-learning algorithms with the method of conformal prediction to minimize a misclassification loss averaged over the out-of-sample distribution. The constructed prediction sets have a finite-sample coverage guarantee without distributional assumptions. We also propose a method to estimate the outlier detection rate of a given method. We prove asymptotic consistency and optimality of our proposals under suitable assumptions and illustrate our methods on real data examples.

stat.ME↗

arXiv2018

Detecting strong signals in gene perturbation experiments: An adaptive approach with power guarantee and FDR control

The perturbation of a transcription factor should affect the expression levels of its direct targets. However, not all genes showing changes in expression are direct targets. To increase the chance of detecting direct targets, we propose a modified two-group model where the null group corresponds to genes which are not direct targets, but can have small non-zero effects. We model the behaviour of genes from the null set by a Gaussian distribution with unknown variance $τ^2$, and we discuss and compare three methods which adaptively estimate $τ^2$ from the data: the iterated empirical Bayes estimator, the truncated MLE and the central moment matching estimator. We conduct a detailed analysis of the properties of the iterated EB estimate which has the best performance in the simulations. In particular, we provide theoretical guarantee of its good performance under mild conditions. We provide simulations comparing the new modeling approach with existing methods, and the new approach shows more stable and better performance under different situations. We also apply it to a real data set from gene knock-down experiments and obtained better results compared with the original two-group model testing for non-zero effects.

stat.ME↗

arXiv2018

Post model-fitting exploration via a "Next-Door" analysis

We propose a simple method for evaluating the model that has been chosen by an adaptive regression procedure, our main focus being the lasso. This procedure deletes each chosen predictor and refits the lasso to get a set of models that are "close" to the one chosen, referred to as "base model". If the deletion of a predictor leads to significant deterioration in the model's predictive power, the predictor is called indispensable; otherwise, the nearby model is called acceptable and can serve as a good alternative to the base model. This provides both an assessment of the predictive contribution of each variable and a set of alternative models that may be used in place of the chosen model. In this paper, we will focus on the cross-validation (CV) setting and a model's predictive power is measured by its CV error, with base model tuned by cross-validation. We propose a method for comparing the error rates of the base model with that of nearby models, and a p-value for testing whether a predictor is dispensable. We also propose a new quantity called model score which works similarly as the p-value for the control of type I error. Our proposal is closely related to the LOCO (leave-one-covarate-out) methods of ([Rinaldo 2016 Bootstrapping]) and less so, to Stability Selection ([Meinshausen 2010 stability]). We call this procedure "Next-Door analysis" since it examines models close to the base model. It can be applied to Gaussian regression data, generalized linear models, and other supervised learning problems with $\ell_1$ penalization. It could also be applied to best subset and stepwise regression procedures. We have implemented it in the R language as a library to accompany the well-known {\tt glmnet} library.

stat.ME↗

arXiv2018

Test Error Estimation after Model Selection Using Validation Error

When performing supervised learning with the model selected using validation error from sample splitting and cross validation, the minimum value of the validation error can be biased downward. We propose two simple methods that use the errors produced in the validating step to estimate the test error after model selection, and we focus on the situations where we select the model by minimizing the validation error and the randomized validation error. Our methods do not require model refitting, and the additional computational cost is negligible. In the setting of sample splitting, we show that, the proposed test error estimates have biases of size $o(1/\sqrt{n})$ under suitable assumptions. We also propose to use the bootstrap to construct confidence intervals for the test error based on this result. We apply our proposed methods to a number of simulations and examine their performance.

stat.ME↗

arXiv2017

Approximate $l_0$-penalized estimation of piecewise-constant signals on graphs

We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_0$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical risk guarantees are achieved by the $α$-expansion algorithm which computes an approximate minimizer in polynomial time. We establish that for graphs with small average vertex degree, these guarantees are minimax rate-optimal over classes of edge-sparse signals. For spatially inhomogeneous graphs, we propose minimization of an edge-weighted objective where each edge is weighted by its effective resistance or another measure of its contribution to the graph's connectivity. We establish minimax optimality of the resulting estimators over corresponding edge-weighted sparsity classes. We show theoretically that these risk guarantees are not always achieved by the estimator minimizing the $l_1$/total-variation relaxation, and empirically that the $l_0$-based estimates are more accurate in high signal-to-noise settings.

stat.ME↗

arXiv2016

Regularization for supervised learning via the "hubNet" procedure

We propose a new method for supervised learning. The hubNet procedure fits a hub-based graphical model to the predictors, to estimate the amount of "connection" that each predictor has with other predictors. This yields a set of predictor weights that are then used in a regularized regression such as the lasso or elastic net. The resulting procedure is easy to implement, can sometimes yields higher prediction accuracy that the lasso, and can give insights into the underlying structure of the predictors. HubNet can also be generalized seamlessly to other supervised problems such as regularized logistic regression (and other GLMs), Cox's proportional hazards model, and nonlinear procedures such as random forests and boosting. We prove some recovery results under a specialized model and illustrate the method on real and simulated data.

stat.ME↗