arXiv subjects

Xiaoyue Li

Publications and source records attributed to Xiaoyue Li.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Online Estimation of Spiked Eigenvalues with Adaptive Weighting under Persistent Aspect Ratio Heterogeneity

We study online estimation of spiked covariance eigenvalues from observations distributed across $L$ nodes with heterogeneous and persistent effective sample sizes. In the proportional high-dimensional regime, local Rayleigh statistics are deterministically distorted by node-specific aspect ratios $c_{\ell,t}=p/N^{\mathrm{eff}}_{\ell,t}$, and direct aggregation of uncorrected statistics converges to the wrong limit. We propose a correct-then-aggregate framework in which each node removes its deterministic bias via an inverse Rayleigh transfer map, and the server fuses corrected estimates using adaptive soft-max weights based on predictable fluctuation metrics, transmitting only $O(k)$ scalars per active node per round. We establish consistency and asymptotic normality of the global estimator, enabling valid online inference, and derive non-asymptotic bounds quantifying how accuracy improves with the number of nodes and their effective sample sizes. The adaptive weights achieve variance reduction comparable to oracle inverse-variance weighting, confirming the data-driven construction is nearly efficient. Simulation studies validate these properties. An application to cross-venue monitoring of a dominant market factor shows the method tracks systemic risk in real time while substantially reducing communication cost relative to a centralized pooled approach.

math.ST↗

arXiv2026

Adaptive Time-Stepping Euler--Maruyama Scheme for SDEs with Non-Globally Lipschitz Coefficients: Uniform Convergence, Stability and Ergodicity

This paper develops an adaptive time-stepping Euler--Maruyama scheme for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By dynamically adjusting the timestep at each iteration, the proposed scheme effectively prevents numerical instability. We prove the moment boundedness of the numerical solution and establish a $1/2$-order strong convergence rate both on finite-time intervals and uniformly in time. Furthermore, the scheme faithfully inherits the $p$th moment exponential stability of the underlying SDE. For long-time ergodic dynamics, we establish the polynomial ergodicity of the numerical invariant measure. Moreover, we show that the numerical invariant measure converges to the invariant measure of the underlying SDE at an optimal rate of $1/2$ in the $L^q$-Wasserstein distance. Numerical experiments confirm our theoretical results and indicate the superior accuracy and computational performance of the proposed scheme over several fixed-step and existing adaptive methods.

math.NA↗

arXiv2026

Exponential Contraction for Underdamped Langevin Diffusions with Superlinear Forces

Underdamped Langevin diffusions model kinetic sampling and thermally driven inertial dynamics, but quantitative convergence is difficult when degenerate noise is coupled with a nonconvex superlinear force. We prove unit-prefactor exponential contraction in an explicit weighted Kantorovich cost under radial confinement, a hypocoercive Lyapunov condition, and $|\nabla U(x)-\nabla U(y)|\leq L_1(1+|x|^\ell+|y|^\ell)|x-y|$, $0\leq\ell\leq2$. No smallness condition is imposed on $L_1$. At the critical exponent $\ell=2$, a quartic lower bound on $U$ is used together with an anisotropic position--velocity localization to obtain a nonempty endpoint regime. The proof combines regularized reflection--synchronous coupling, an exponential Lyapunov weight, tightness, and an occupation-time argument at the singular coupling direction. The result yields exponential convergence and uniqueness of the invariant Gibbs measure within the finite-cost class. It covers power-law confining potentials below quartic growth and nonconvex quartic Duffing potentials with cubic force.

math.PR↗

arXiv2026

Efficient Multi-Cohort Inference for Long-Term Effects and Lifetime Value in A/B Testing with User Learning

In streaming platforms churn is extremely costly, yet A/B tests are typically evaluated using outcomes observed within a limited experimental horizon. Even when both short- and predicted long-term engagement metrics are considered, they may fail to capture how a treatment affects users' retention. Consequently, an intervention may appear beneficial in the short term and neutral in the long term while still generating lower total value than the control due to users churn. To address this limitation, we introduce a method that estimates long-term treatment effects (LTE) and residual lifetime value change ($\Delta ERLV$) in short multi-cohort A/B tests under user learning. To estimate time-varying treatment effects efficiently, we introduce an inverse-variance weighted estimator that combines multiple cohorts estimates, reducing variance relative to standard approaches in the literature. The estimated treatment trajectory is then modeled as a parametric decay to recover both the asymptotic treatment effect and the cumulative value generated over time. Our framework enables simultaneous evaluation of steady-state impact and residual user value within a single experiment. Empirical results show improved precision in estimating LTE and $\Delta ERLV$ and identify scenarios in which relying on either short-term or long-term metrics alone would lead to incorrect product decisions.

cs.LG↗

arXiv2026

An explicit finite-memory scheme for approximating and sampling invariant measures of stochastic functional differential equations with infinite delay

Efficient sampling and numerical approximation of invariant probability measures (IPMs) on infinite-dimensional function spaces are important problems in scientific computing. In this paper, we study the numerical approximation and sampling of IPMs associated with stochastic functional differential equations with infinite delay (SFDEswID). To this end, we develop a fully explicit ergodicity-preserving truncated Euler--Maruyama scheme for SFDEswID that requires only finite historical storage and accommodates superlinearly growing coefficients. We establish strong convergence of the numerical segment process and show that it admits a unique IPM and is exponentially ergodic in the Wasserstein distance. Building on these results, we prove the convergence of the numerical IPM to the exact one and derive an explicit convergence rate. As a consequence, we obtain a quantitative long-time sampling error estimate of order $O\left(e^{-\lambda_\varepsilon t_n}+\Delta^{\rho_\varepsilon}\right)$. The results provide a rigorous and computationally efficient framework for sampling IPMs and quantifying long-time sampling errors for stochastic systems with infinite delay.

math.NA↗

arXiv2026

An explicit adaptive time-stepping scheme for superlinear stochastic diffusion systems

This paper develops an adaptive time-stepping Euler--Maruyama (EM) scheme for stochastic diffusion systems with superlinearly growing coefficients. The adaptive timestep is chosen according to the superlinear growth of both drift and diffusion coefficients. To prevent excessively small timesteps, a truncated EM scheme is employed as a backstop whenever the adaptive timestep falls below a prescribed threshold. By combining the stochastic analysis with the stopping time technique, we establish the strong convergence of the proposed method and obtain the optimal $1/2$-order strong convergence rate in the $L^q$-sense for $q>2$. {Finally, numerical experiments are carried out for stiff, nonstiff, and stochastic Lorenz systems to validate the theoretical findings. The results indicate that the proposed scheme achieves superior accuracy and performance compared to various fixed-step and adaptive alternatives.

math.NA↗

arXiv2025

Hybrid Stochastic Functional Differential Equations with Infinite Delay: Approximations and Numerics

This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is established for a large class of highly nonlinear hybrid SFDEs with infinite delay. Our new theory makes it possible to numerically approximate the solution of the hybrid SFDE with infinite delay, via the numerical solution of the corresponding hybrid SFDE with finite delay.

math.PR↗

arXiv2025

Discretization, Uniform-in-Time Estimations and Approximation of Invariant Measures for Nonlinear Stochastic Differential Equations with Non-Uniform Dissipativity

The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose an easily applicable explicit Truncated Euler-Maruyama (TEM) scheme and prove its numerical ergodicity in the $L^p$-Wasserstein distance ($p\geqslant 1$). Furthermore, by combining truncation techniques with the coupling method, we establish a uniform-in-time $1/2$-order convergence rate in moments for the TEM scheme. Additionally, leveraging the exponential ergodicity of both the numerical and exact solutions, we derive a $1/2$-order convergence rate for the invariant measures of the TEM scheme and the exact solution in the $L^1$-Wasserstein distance. Finally, two numerical experiments are conducted to validate our theoretical results.

math.NA↗

arXiv2025

The ergodicity of nonlinear McKean-Vlasov stochastic differential equations with common noise

This paper focuses on the ergodicity of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN), where coefficients depend on both the state and the measure. A major challenge in this setting is that the underlying Markov operator loses the semigroup property, precluding standard ergodic analyses. To circumvent this issue, we lift the system by considering the joint flow of the solution and its conditional distribution. We first construct a semigroup associated with the measure pair of the solution and its conditional distribution. Under polynomial growth conditions, we prove the existence and uniqueness of the invariant measure for the lifted system by a coupling method and obtain an explicit exponential convergence rate. We subsequently derive the strong law of large numbers by a decoupling approach. Building on these results, we establish the uniform-in-time propagation of chaos for the associated mean-field interacting particle system. Furthermore, we establish the convergence of the distribution of a single particle and the empirical measure of the particle system to the marginals of the invariant measure. Finally, illustrative examples are provided to verify the theoretical findings.

math.PR↗

arXiv2025

Development of numerical methods for nonlinear hybrid stochastic functional differential equations with infinite delay

This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite historical storage. Leveraging approximation theory, we prove the boundedness of the numerical solution's $p$th moment and establish its convergence, achieving a rate of $1/2$ order under polynomially growing coefficients. Furthermore, we refine the scheme to better capture the underlying exponential stability of the exact solution, in both moment and almost sure senses. Finally, numerical experiments are presented to validate our theoretical results.

math.NA↗

arXiv2025

Propagation of chaos and Razumikhin theorem for the nonlinear McKean-Vlasov SFDEs with common noise

As the limit equations of mean-field particle systems perturbed by common environmental noise, the McKean-Vlasov stochastic differential equations with common noise have received a lot of attention. Moreover, past dependence is an unavoidable natural phenomenon for dynamic systems in life sciences, economics, finance, automatic control, and other fields. Combining the two aspects above, this paper delves into a class of nonlinear McKean-Vlasov stochastic functional differential equations (MV-SFDEs) with common noise. The well-posedness of the nonlinear MV-SFDEs with common noise is first demonstrated through the application of the Banach fixed-point theorem. Secondly, the relationship between the MV-SFDEs with common noise and the corresponding functional particle systems is investigated. More precisely, the conditional propagation of chaos with an explicit convergence rate and the stability equivalence are studied. Furthermore, the exponential stability, an important long-time behavior of the nonlinear MV-SFDEs with common noise, is derived. To this end, the It\^o formula involved with state and measure is developed for the MV-SFDEs with common noise. Using this formula, the Razumikhin theorem is proved, providing an easy-to-implement criterion for the exponential stability. Lastly, an example is provided to illustrate the result of the stability.

math.PR↗

arXiv2024

Big-Thick Data generation via reference and personal context unification

Smart devices generate vast amounts of big data, mainly in the form of sensor data. While allowing for the prediction of many aspects of human behaviour (e.g., physical activities, transportation modes), this data has a major limitation in that it is not thick, that is, it does not carry information about the context within which it was generated. Context - what was accomplished by a user, how and why, and in which overall situation - all these factors must be explicitly represented for the data to be self-explanatory and meaningful. In this paper, we introduce Big-Thick Data as highly contextualized data encoding, for each and every user, both her subjective personal view of the world and the objective view of an all-observing third party taken as reference. We model big-thick data by enforcing the distinction between personal context and reference context. We show that these two types of context can be unified in many different ways, thus allowing for different types of questions about the users' behaviour and the world around them and, also, for multiple different answers to the same question. We validate the model with a case study that integrates the personal big-thick data of one hundred and fifty-eight University students over a period of four weeks with the reference context built using the data provided by OpenStreetMap.

cs.HC↗

arXiv2024

Double-bracket quantum algorithms for high-fidelity ground state preparation

Ground state preparation is a central application for quantum computers but remains challenging in practice. In this work, we quantitatively investigate the performance and gate counts of double-bracket quantum algorithms (DBQAs) for ground state preparation. We propose a practical strategy in which DBQAs refine initial state preparation circuits, and we compile them for Heisenberg chains using controlled-Z and single-qubit gates. Warm-started DBQAs consistently improve both the energy and ground-state fidelity relative to the initial states provided by variational ans\"atze, indicating that DBQAs offer an effective unitary synthesis method. To demonstrate compatibility with near-term hardware, we executed a proof-of-concept example on IBM devices. With error mitigation, we observed a statistically significant improvement over the corresponding warm-start circuit. Furthermore, numerical emulations for the same system size indicate that executing DBQAs on Quantinuum's hardware could achieve similar cost-function gains without requiring error mitigation. These findings suggest that DBQAs are a promising approach for enhancing ground-state approximations on near-term quantum devices.

quant-ph↗

arXiv2024

KAE: A Property-based Method for Knowledge Graph Alignment and Extension

A common solution to the semantic heterogeneity problem is to perform knowledge graph (KG) extension exploiting the information encoded in one or more candidate KGs, where the alignment between the reference KG and candidate KGs is considered the critical procedure. However, existing KG alignment methods mainly rely on entity type (etype) label matching as a prerequisite, which is poorly performing in practice or not applicable in some cases. In this paper, we design a machine learning-based framework for KG extension, including an alternative novel property-based alignment approach that allows aligning etypes on the basis of the properties used to define them. The main intuition is that it is properties that intentionally define the etype, and this definition is independent of the specific label used to name an etype, and of the specific hierarchical schema of KGs. Compared with the state-of-the-art, the experimental results show the validity of the KG alignment approach and the superiority of the proposed KG extension framework, both quantitatively and qualitatively.

cs.AI↗

arXiv2024

Quantum dynamics of dissipative Chern insulator

For open quantum systems,a short-time evolution is usually well described by the effective non-Hermitian Hamiltonians,while long-time dynamics requires the Lindblad master equation,in which the Liouvillian superoperators characterize the time evolution. In this paper, we constructed an open system by adding suitable gain and loss operators to the Chen insulator to investigate the time evolution of quantum states at long times by numerical simulations.Finally,we also propose a topolectrical circuits to realize the dissipative system for experimental observation. It is found found that the opening and closing of the Liouvillian gap leads to different damping behaviours of the system and that the presence of non-Hermitian skin effects leads to a phenomenon of chiral damping with sharp wavefronts.Our study deepens the understanding of quantum dynamics of dissipative system.

quant-ph↗

arXiv2024

Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations

Inspired by the stochastic particle method, this paper develops an easily implementable explicit scheme for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. We prove that the numerical solution of the interacting particle system (IPS) attains the optimal uniform-in-time strong convergence rate of order 1/2, and that it faithfully captures the long-term dynamics of MV-SDEs, including moment boundedness, stability, and ergodicity. In particular, the existence and uniqueness of an exchangeable numerical invariant probability measure for the IPS are established via an appropriately constructed operator semigroup. Concerning the approximation of the invariant measure, we derive a non-asymptotic error bound between the distribution of the one-particle numerical solution and the marginal distribution of the IPS's invariant measure; By the uniform-in-time propagation of chaos, we further obtain an asymptotic error bound between the one-particle marginal of the IPS's numerical invariant measure and the exact invariant measure of the MV-SDE. Numerical experiments are provided to validate the theoretical results.

math.PR↗

arXiv2023

The delay feedback control for the McKean-Vlasov stochastic differential equations with common noise

Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions of the system state such that the controlled system to be boundedness in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in [27] which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The It\^o formula with respect to both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated.

math.PR↗

arXiv2023

Strong convergence of multiscale truncated Euler-Maruyama method for super-linear slow-fast stochastic differential equations

This manuscript is dedicated to the numerical approximation of super-linear slow-fast stochastic differential equations (SFSDEs). Borrowing the heterogeneous multiscale idea, we propose an explicit multiscale Euler-Maruyama scheme suitable for SFSDEs with locally Lipschitz coefficients using an appropriate truncation technique. By the averaging principle, we establish the strong convergence of the numerical solutions to the exact solutions in the pth moment. Additionally, under lenient conditions on the coefficients, we also furnish a strong error estimate. In conclusion, we give two illustrative examples and accompanying numerical simulations to affirm the theoretical outcomes.

math.NA↗