arXiv subjects

Jiaxin Qiu

Publications and source records attributed to Jiaxin Qiu.

7 recordsLinked to original sources

arXiv2026

Spike Estimation from Heteroscedastic Noise via Random Splitting

In this paper, we consider a spiked Wigner type matrix with a heteroscedastic and unknown variance profile. It is well known that in the supercritical regime of the BBP transition, strong spikes can create outliers in the spectrum. Unfortunately, in the heteroscedastic case, in general it is not possible to estimate the spike strength from these observed outlier consistently, as the latter is a solution to a Dyson equation with unknown parameters from the variance profile. In this paper, inspired by the work on sparse matrix completion \citep{BordenaveCosteNadakuditi2023}, we introduce an asymmetrized model by randomly splitting the spiked matrix into two parts, which transforms the noisy Wigner type matrix into a non Hermitian random matrix, while preserving the Hermitian spikes at the cost of a dilution. We establish a BBP type transition for the asymmetrized model, from which we can estimate the strength of the spikes precisely, even without knowing the variance profile of the noise part. We then further apply our approach to study the correlation between two correlated spiked models, where the spike/signal parts of the two models are correlated, and the noise parts are independent but may both be heteroscedastic. By applying our asymmetrization approach to the two models separately and also jointly, we are able to obtain a precise estimate of the correlation between the signal parts of the two models.

math.ST↗

arXiv2026

A spectral approach for online covariance change point detection

Change point detection in covariance structures is a fundamental and crucial problem for sequential data. Under the high-dimensional setting, most of the existing research has focused on identifying change points in historical data. However, there is a significant lack of studies on the practically relevant online change point problem, which means promptly detecting change points as they occur. In this paper, applying the limiting theory of linear spectral statistics for random matrices, we propose a class of spectrum based CUSUM-type statistic. We first construct a martingale from the difference of linear spectral statistics of sequential sample Fisher matrices, which converges to a Brownian motion. Our CUSUM-type statistic is then defined as the maximum of a variant of this process. Finally, we develop our detection procedure based on the invariance principle. Simulation results show that our detection method is highly sensitive to the occurrence of change point and is able to identify it shortly after they arise, outperforming the existing approaches.

math.ST↗

arXiv2024

Robust estimation for number of factors in high dimensional factor modeling via Spearman correlation matrix

Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman sample correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is robust against heavy tails in either the common factors or idiosyncratic errors. The consistency of our estimator is established under mild conditions. Numerical experiments demonstrate the superiority of our estimator compared to existing methods.

stat.ME↗

arXiv2024

PE-Planner: A Performance-Enhanced Quadrotor Motion Planner for Autonomous Flight in Complex and Dynamic Environments

The role of a motion planner is pivotal in quadrotor applications, yet existing methods often struggle to adapt to complex environments, limiting their ability to achieve fast, safe, and robust flight. In this letter, we introduce a performance-enhanced quadrotor motion planner designed for autonomous flight in complex environments including dense obstacles, dynamic obstacles, and unknown disturbances. The global planner generates an initial trajectory through kinodynamic path searching and refines it using B-spline trajectory optimization. Subsequently, the local planner takes into account the quadrotor dynamics, estimated disturbance, global reference trajectory, control cost, time cost, and safety constraints to generate real-time control inputs, utilizing the framework of model predictive contouring control. Both simulations and real-world experiments corroborate the heightened robustness, safety, and speed of the proposed motion planner. Additionally, our motion planner achieves flights at more than 6.8 m/s in a challenging and complex racing scenario.

cs.RO↗

arXiv2023

On eigenvalues of sample covariance matrices based on high dimensional compositional data

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under the high-dimensional regime where the data dimension increases to infinity proportionally with the sample size. The findings reveal that the limiting spectral distribution is the well-known Marchenko-Pastur law. The largest (or smallest non-zero) eigenvalue converges almost surely to the left (or right) endpoint of the limiting spectral distribution, respectively. Moreover, the linear spectral statistics demonstrate a Gaussian limit. Simulation experiments demonstrate the accuracy of theoretical results.

math.ST↗

arXiv2023

SRL-ORCA: A Socially Aware Multi-Agent Mapless Navigation Algorithm In Complex Dynamic Scenes

For real-world navigation, it is important to endow robots with the capabilities to navigate safely and efficiently in a complex environment with both dynamic and non-convex static obstacles. However, achieving path-finding in non-convex complex environments without maps as well as enabling multiple robots to follow social rules for obstacle avoidance remains challenging problems. In this letter, we propose a socially aware robot mapless navigation algorithm, namely Safe Reinforcement Learning-Optimal Reciprocal Collision Avoidance (SRL-ORCA). This is a multi-agent safe reinforcement learning algorithm by using ORCA as an external knowledge to provide a safety guarantee. This algorithm further introduces traffic norms of human society to improve social comfort and achieve cooperative avoidance by following human social customs. The result of experiments shows that SRL-ORCA learns strategies to obey specific traffic rules. Compared to DRL, SRL-ORCA shows a significant improvement in navigation success rate in different complex scenarios mixed with the application of the same training network. SRL-ORCA is able to cope with non-convex obstacle environments without falling into local minimal regions and has a 14.1\% improvement in path quality (i.e., the average time to target) compared to ORCA. Videos are available at https://youtu.be/huhXfCDkGws.

cs.RO↗

arXiv2021

Asymptotic normality for eigenvalue statistics of a general sample covariance matrix when $p/n \to \infty$ and applications

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this CLT result, we first adapt the covariance matrix test problem to the new ultra-high dimensional context. Then as a second application, we develop a new test for the separable covariance structure of a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the second test for separable covariance structure of matrix-valued white noise.

stat.ME↗