arXiv subjects

Yao Xie

Publications and source records attributed to Yao Xie.

At least 55 records · Page 3Linked to original sources

arXiv2025

Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with low-dimensional structures. The kernel max-sliced (KMS) Wasserstein distance is developed for this purpose by finding an optimal nonlinear mapping that reduces data into $1$ dimension before computing the Wasserstein distance. However, its theoretical properties have not yet been fully developed. In this paper, we provide sharp finite-sample guarantees under milder technical assumptions compared with state-of-the-art for the KMS $p$-Wasserstein distance between two empirical distributions with $n$ samples for general $p\in[1,\infty)$. Algorithm-wise, we show that computing the KMS $2$-Wasserstein distance is NP-hard, and then we further propose a semidefinite relaxation (SDR) formulation (which can be solved efficiently in polynomial time) and provide a relaxation gap for the obtained solution. We provide numerical examples to demonstrate the good performance of our scheme for high-dimensional two-sample testing.

stat.ML↗

arXiv2025

Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributions

Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method built on Continuous Normalizing Flow (CNF) for sampling from high-dimensional and multi-modal distributions. AF is trained with a dynamic Optimal Transport (OT) objective incorporating Wasserstein regularization, and guided by annealing procedures, facilitating effective exploration of modes in high-dimensional spaces. Compared to recent NF methods, AF greatly improves training efficiency and stability, with minimal reliance on MC assistance. We demonstrate the superior performance of AF compared to state-of-the-art methods through experiments on various challenging distributions and real-world datasets, particularly in high-dimensional and multi-modal settings. We also highlight AF potential for sampling the least favorable distributions.

stat.ML↗

arXiv2025

Survival Analysis with Graph-Based Regularization for Predictors

We study the variable selection problem in survival analysis to identify the most important factors affecting survival time. Our method incorporates prior knowledge of mutual correlations among variables, represented through a graph. We utilize the Cox proportional hazard model with a graph-based regularizer for variable selection. We present a computationally efficient algorithm developed to solve the graph regularized maximum likelihood problem by establishing connections with the group lasso, and provide theoretical guarantees about the recovery error and asymptotic distribution of the proposed estimators. The improved performance of the proposed approach compared with existing methods are demonstrated in both synthetic and real organ transplantation datasets.

math.ST↗

arXiv2025

Higher-criticism for sparse multi-stream change-point detection

We study a statistical procedure based on higher criticism (HC) to address the sparse multi-stream quickest change-point detection problem. Namely, we aim to detect a potential change in the distribution of multiple data streams at some unknown time. If a change occurs, only a few streams are affected, whereas the identity of the affected streams is unknown. The HC-based procedure involves testing for a change point in individual streams and combining multiple tests using higher criticism. Relying on HC thresholding, the procedure also indicates a set of streams suspected to be affected by the change. We provide a theoretical analysis under a sparse heteroscedastic normal change-point model. We establish an information-theoretic detection delay lower bound when individual tests are based on the likelihood ratio or the generalized likelihood ratio statistics and show that the delay of the HC-based method converges in distribution to this bound. In the special case of constant variance, our bound coincides with known results in (Chan, 2017). We demonstrate the effectiveness of the HC-based method compared to other methods in detecting sparse changes through extensive numerical evaluations.

stat.ME↗

arXiv2025

Graph-Based Prediction Models for Data Debiasing

Bias in data collection, arising from both under-reporting and over-reporting, poses significant challenges in critical applications such as healthcare and public safety. In this work, we introduce Graph-based Over- and Under-reporting Debiasing (GROUD), a novel graph-based optimization framework that debiases reported data by jointly estimating the true incident counts and the associated reporting bias probabilities. By modeling the bias as a smooth signal over a graph constructed from geophysical or feature-based similarities, our convex formulation not only ensures a unique solution but also comes with theoretical recovery guarantees under certain assumptions. We validate GROUD on both challenging simulated experiments and real-world datasets -- including Atlanta emergency calls and COVID-19 vaccine adverse event reports -- demonstrating its robustness and superior performance in accurately recovering debiased counts. This approach paves the way for more reliable downstream decision-making in systems affected by reporting irregularities.

stat.ME↗

arXiv2025

Modeling Discrete Coating Degradation Events via Hawkes Processes

Forecasting the degradation of coated materials has long been a topic of critical interest in engineering, as it has enormous implications for both system maintenance and sustainable material use. Material degradation is affected by many factors, including the history of corrosion and characteristics of the environment, which can be measured by high-frequency sensors. However, the high volume of data produced by such sensors can inhibit efficient modeling and prediction. To alleviate this issue, we propose novel metrics for representing material degradation, taking the form of discrete degradation events. These events maintain the statistical properties of continuous sensor readings, such as correlation with time to coating failure and coefficient of variation at failure, but are composed of orders of magnitude fewer measurements. To forecast future degradation of the coating system, a marked Hawkes process models the events. We use the forecast of degradation to predict a future time of failure, exhibiting superior performance to the approach based on direct modeling of galvanic corrosion using continuous sensor measurements. While such maintenance is typically done on a regular basis, degradation models can enable informed condition-based maintenance, reducing unnecessary excess maintenance and preventing unexpected failures.

stat.AP↗

arXiv2025

Sinkhorn Distributionally Robust Optimization

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.

math.OC↗

arXiv2025

Sepsyn-OLCP: An Online Learning-based Framework for Early Sepsis Prediction with Uncertainty Quantification using Conformal Prediction

Sepsis is a life-threatening syndrome with high morbidity and mortality in hospitals. Early prediction of sepsis plays a crucial role in facilitating early interventions for septic patients. However, early sepsis prediction systems with uncertainty quantification and adaptive learning are scarce. This paper proposes Sepsyn-OLCP, a novel online learning algorithm for early sepsis prediction by integrating conformal prediction for uncertainty quantification and Bayesian bandits for adaptive decision-making. By combining the robustness of Bayesian models with the statistical uncertainty guarantees of conformal prediction methodologies, this algorithm delivers accurate and trustworthy predictions, addressing the critical need for reliable and adaptive systems in high-stakes healthcare applications such as early sepsis prediction. We evaluate the performance of Sepsyn-OLCP in terms of regret in stochastic bandit setting, the area under the receiver operating characteristic curve (AUROC), and F-measure. Our results show that Sepsyn-OLCP outperforms existing individual models, increasing AUROC of a neural network from 0.64 to 0.73 without retraining and high computational costs. And the model selection policy converges to the optimal strategy in the long run. We propose a novel reinforcement learning-based framework integrated with conformal prediction techniques to provide uncertainty quantification for early sepsis prediction. The proposed methodology delivers accurate and trustworthy predictions, addressing a critical need in high-stakes healthcare applications like early sepsis prediction.

cs.LG↗

arXiv2025

Computing high-dimensional optimal transport by flow neural networks

Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.

stat.ML↗

arXiv2025

Distribution-Free Online Change Detection for Low-Rank Images

We present a distribution-free CUSUM procedure designed for online change detection in a time series of low-rank images, particularly when the change causes a mean shift. We represent images as matrix data and allow for temporal dependence, in addition to inherent spatial dependence, before and after the change. The marginal distributions are assumed to be general, not limited to any specific parametric distribution. We propose new monitoring statistics that utilize the low-rank structure of the in-control mean matrix. Additionally, we study the properties of the proposed detection procedure, assessing whether the monitoring statistics effectively capture a mean shift and evaluating the rate of increase in the average run length relative to the control limit in both the in-control and out-of-control cases. The effectiveness of our procedure is demonstrated through simulated and real data experiments.

stat.ME↗

arXiv2025

Spatial Conformal Inference through Localized Quantile Regression

Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on assumptions such as normality, which often break down in large-scale, diverse datasets, leading to unreliable prediction intervals. While machine learning methods have emerged as powerful alternatives, they primarily focus on point predictions and provide limited mechanisms for uncertainty quantification. Conformal prediction, a distribution-free framework, offers valid prediction intervals without relying on parametric assumptions. However, existing conformal prediction methods are either not tailored for spatial settings, or existing ones for spatial data have relied on rather restrictive i.i.d. assumptions. In this paper, we propose Localized Spatial Conformal Prediction (LSCP), a conformal prediction method designed specifically for spatial data. LSCP leverages localized quantile regression to construct prediction intervals. Instead of i.i.d. assumptions, our theoretical analysis builds on weaker conditions of stationarity and spatial mixing, which is natural for spatial data, providing finite-sample bounds on the conditional coverage gap and establishing asymptotic guarantees for conditional coverage. We present experiments on both synthetic and real-world datasets to demonstrate that LSCP achieves accurate coverage with significantly tighter and more consistent prediction intervals across the spatial domain compared to existing methods.

stat.ML↗

arXiv2025

Neural Spatiotemporal Point Processes: Trends and Challenges

Spatiotemporal point processes (STPPs) are probabilistic models for events occurring in continuous space and time. Real-world event data often exhibit intricate dependencies and heterogeneous dynamics. By incorporating modern deep learning techniques, STPPs can model these complexities more effectively than traditional approaches. Consequently, the fusion of neural methods with STPPs has become an active and rapidly evolving research area. In this review, we categorize existing approaches, unify key design choices, and explain the challenges of working with this data modality. We further highlight emerging trends and diverse application domains. Finally, we identify open challenges and gaps in the literature.

cs.LG↗

arXiv2024

Variable Selection for Kernel Two-Sample Tests

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a subset of variables with a pre-specified size that maximizes the variance-regularized kernel MMD statistic. We focus on three commonly used types of kernels: linear, quadratic, and Gaussian. From a computational perspective, we derive mixed-integer programming formulations and propose exact and approximation algorithms with performance guarantees to solve these formulations. From a statistical viewpoint, we derive the rate of testing power of our framework under appropriate conditions. These results show that the sample size requirements for the three kernels depend crucially on the number of selected variables, rather than the data dimension. Experimental results on synthetic and real datasets demonstrate the superior performance of our method, compared to other variable selection frameworks, particularly in high-dimensional settings.

stat.ML↗

arXiv2024

Spatio-Temporal Conformal Prediction for Power Outage Data

In recent years, increasingly unpredictable and severe global weather patterns have frequently caused long-lasting power outages. Building resilience, the ability to withstand, adapt to, and recover from major disruptions, has become crucial for the power industry. To enable rapid recovery, accurately predicting future outage numbers is essential. Rather than relying on simple point estimates, we analyze extensive quarter-hourly outage data and develop a graph conformal prediction method that delivers accurate prediction regions for outage numbers across the states for a time period. We demonstrate the effectiveness of this method through extensive numerical experiments in several states affected by extreme weather events that led to widespread outages.

stat.ML↗

arXiv2024

Detecting algorithmic bias in medical-AI models using trees

With the growing prevalence of machine learning and artificial intelligence-based medical decision support systems, it is equally important to ensure that these systems provide patient outcomes in a fair and equitable fashion. This paper presents an innovative framework for detecting areas of algorithmic bias in medical-AI decision support systems. Our approach efficiently identifies potential biases in medical-AI models, specifically in the context of sepsis prediction, by employing the Classification and Regression Trees (CART) algorithm with conformity scores. We verify our methodology by conducting a series of synthetic data experiments, showcasing its ability to estimate areas of bias in controlled settings precisely. The effectiveness of the concept is further validated by experiments using electronic medical records from Grady Memorial Hospital in Atlanta, Georgia. These tests demonstrate the practical implementation of our strategy in a clinical environment, where it can function as a vital instrument for guaranteeing fairness and equity in AI-based medical decisions.

stat.ML↗

arXiv2024

Posterior sampling via Langevin dynamics based on generative priors

Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Despite many recent developments, generating diverse posterior samples remains a challenge, as existing methods require restarting the entire generative process for each new sample, making the procedure computationally expensive. In this work, we propose efficient posterior sampling by simulating Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.

stat.ML↗

arXiv2024

Multi-Agent Reinforcement Learning for Joint Police Patrol and Dispatch

Police patrol units need to split their time between performing preventive patrol and being dispatched to serve emergency incidents. In the existing literature, patrol and dispatch decisions are often studied separately. We consider joint optimization of these two decisions to improve police operations efficiency and reduce response time to emergency calls. Methodology/results: We propose a novel method for jointly optimizing multi-agent patrol and dispatch to learn policies yielding rapid response times. Our method treats each patroller as an independent Q-learner (agent) with a shared deep Q-network that represents the state-action values. The dispatching decisions are chosen using mixed-integer programming and value function approximation from combinatorial action spaces. We demonstrate that this heterogeneous multi-agent reinforcement learning approach is capable of learning joint policies that outperform those optimized for patrol or dispatch alone. Managerial Implications: Policies jointly optimized for patrol and dispatch can lead to more effective service while targeting demonstrably flexible objectives, such as those encouraging efficiency and equity in response.

cs.LG↗

arXiv2024

Regularization for Adversarial Robust Learning

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models. While various heuristics aim to optimize the distributionally robust risk using the $\infty$-Wasserstein metric, such a notion of robustness frequently encounters computation intractability. To tackle the computational challenge, we develop a novel approach to adversarial training that integrates $ϕ$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We develop stochastic gradient methods with biased oracles to solve this problem efficiently, achieving the near-optimal sample complexity. Moreover, we establish its regularization effects and demonstrate it is asymptotic equivalence to a regularized empirical risk minimization framework, by considering various scaling regimes of the regularization parameter and robustness level. These regimes yield gradient norm regularization, variance regularization, or a smoothed gradient norm regularization that interpolates between these extremes. We numerically validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.

cs.LG↗