arXiv subjects

Jiazhen Xu

Publications and source records attributed to Jiazhen Xu.

13 recordsLinked to original sources

arXiv2026

Quantifying Periodicity in Non-Euclidean Object-Valued Time Series

Non-Euclidean object-valued time series are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of many time series. However, quantifying periodicity in general non-Euclidean random objects remains largely unexplored. In this work, we introduce a novel nonparametric framework for quantifying periodicity in random objects within a general metric space that lacks Euclidean structure. Our approach formulates periodicity estimation as a model selection problem and provides methodologies for period estimation, data-driven tuning parameter selection, and periodic component extraction. Our theoretical contributions include deriving uniform convergence rates for general Fréchet regression under temporal dependence, establishing the consistency of period estimation without relying on linearity properties used in the literature for Euclidean data, providing theoretical support for data-driven tuning parameter selection, and deriving uniform convergence results for periodic component estimation. Through extensive simulation studies covering three distinct types of time-varying random objects such as compositional data, networks, and functional data, we showcase the excellent accuracy achieved by our approach in periodicity quantification. Finally, we apply our method to various real datasets, including compositional data arising in U.S. electricity generation, New York City transportation networks, and Germany's water consumption curves, highlighting its practical relevance in identifying and quantifying meaningful periodic patterns.

stat.ME↗

arXiv2026

Spherically Embedded Time Series with Unknown Trend and Periodic Components

Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity driven by latent trend and periodic components. Traditional Euclidean time series methods fail to account for the intrinsic non-Euclidean geometry of the sphere, leaving a critical gap in rigorous methodologies for modelling and forecasting nonstationary spherically embedded time series. To address this methodological gap, we propose a unified geometric framework to analyse nonstationary spherically embedded time series. Central to our approach is a novel nonparametric spherical trend-periodicity decomposition model that uses an optimal-transport-based removal operation to sequentially extract the smooth trend and periodic components while preserving spherical topology. The resulting de-trended and de-seasonalised stationary residuals can be further modelled using a spherical autoregressive model, formalising a novel trend-periodic spherical autoregressive model. Theoretical foundations for the modelling procedure are established on the consistency under temporal dependence. Extensive simulations corroborate these theoretical guarantees and demonstrate the superior finite-sample predictive performance of the trend-periodic spherical autoregressive model. Finally, we validate the practical utility of our methodology through applications to electricity generation compositions and bike trip volume profiles, yielding significantly enhanced forecasting accuracy while providing interpretable insights into the underlying structural dynamics.

stat.ME↗

arXiv2026

Uniform Convergence of Generalized Conditional Fréchet Means with Applications to Weighted Fréchet Aggregation and Exceedance Set Estimation

The statistical analysis of object oriented data in non-Euclidean spaces heavily relies on generalized conditional Fréchet means, notably in the context of Fréchet regression. However, establishing the uniform convergence of these estimators presents several theoretical challenges. The difficulties are caused primarily by the absence of linear structures in general metric spaces, rendering standard techniques for verifying the asymptotic uniform equicontinuity of the estimator largely intractable. To overcome this limitation, this paper introduces an alternative theoretical framework for establishing uniform convergence that bypasses the need to verify uniform equicontinuity, under a novel structural condition on the empirical cost function of the generalized conditional Fréchet means. We demonstrate that this analytical condition is satisfied by various prominent Fréchet regression models across broad classes of metric spaces. Leveraging these foundational uniform convergence guarantees, we subsequently extend two widely used frameworks from Euclidean to non-Euclidean spaces: (i) a weighted Fréchet aggregation framework that facilitates both distributed regression and robust median-of-means regression; and (ii) an exceedance set estimation framework to identify critical covariate regions where the conditional generalized Fréchet mean surpasses a prescribed threshold, alongside a metric to quantify the aggregate magnitude of the exceedance. The theoretical properties of these proposed methods are empirically validated through Monte Carlo simulations and an application to dynamic transportation networks in New York City.

stat.ME↗

arXiv2026

Fire on Motion: Optimizing Video Pass-bands for Efficient Spiking Action Recognition

Spiking neural networks (SNNs) have gained traction in vision due to their energy efficiency, bio-plausibility, and inherent temporal processing. Yet, despite this temporal capacity, most progress concentrates on static image benchmarks, and SNNs still underperform on dynamic video tasks compared to artificial neural networks (ANNs). In this work, we diagnose a fundamental pass-band mismatch: Standard spiking dynamics behave as a temporal low pass that emphasizes static content while attenuating motion bearing bands, where task relevant information concentrates in dynamic tasks. This phenomenon explains why SNNs can approach ANNs on static tasks yet fall behind on tasks that demand richer temporal understanding.To remedy this, we propose the Pass-Bands Optimizer (PBO), a plug-and-play module that optimizes the temporal pass-band toward task-relevant motion bands. PBO introduces only two learnable parameters, and a lightweight consistency constraint that preserves semantics and boundaries, incurring negligible computational overhead and requires no architectural changes. PBO deliberately suppresses static components that contribute little to discrimination, effectively high passing the stream so that spiking activity concentrates on motion bearing content. On UCF101, PBO yields over ten percentage points improvement. On more complex multi-modal action recognition and weakly supervised video anomaly detection, PBO delivers consistent and significant gains, offering a new perspective for SNN based video processing and understanding.

cs.CV↗

arXiv2026

Spherical Spatial Autoregressive Model for Spherically Embedded Spatial Data

Spherically embedded spatial data are spatially indexed observations whose values naturally reside on or can be equivalently mapped to the unit sphere. Such data are increasingly ubiquitous in fields ranging from geochemistry to demography. However, analysing such data presents unique difficulties due to the intrinsic non-Euclidean nature of the sphere, and rigorous methodologies for statistical modelling, inference, and uncertainty quantification remain limited. This paper introduces a unified framework to address these three limitations for spherically embedded spatial data. We first propose a novel spherical spatial autoregressive model that leverages optimal transport geometry and then extend it to accommodate exogenous covariates. Second, for either scenario with or without covariates, we establish the asymptotic properties of the estimators and derive a distribution-free Wald test for spatial dependence, complemented by a bootstrap procedure to enhance finite-sample performance. Third, we contribute a novel approach to uncertainty quantification by developing a conformal prediction procedure specifically tailored to spherically embedded spatial data. The practical utility of these methodological advances is illustrated through extensive simulations and applications to Spanish geochemical compositions and Japanese age-at-death mortality distributions.

stat.ME↗

arXiv2025

Time-step Mixup for Efficient Spiking Knowledge Transfer from Appearance to Event Domain

The integration of event cameras and spiking neural networks holds great promise for energy-efficient visual processing. However, the limited availability of event data and the sparse nature of DVS outputs pose challenges for effective training. Although some prior work has attempted to transfer semantic knowledge from RGB datasets to DVS, they often overlook the significant distribution gap between the two modalities. In this paper, we propose Time-step Mixup knowledge transfer (TMKT), a novel fine-grained mixing strategy that exploits the asynchronous nature of SNNs by interpolating RGB and DVS inputs at various time-steps. To enable label mixing in cross-modal scenarios, we further introduce modality-aware auxiliary learning objectives. These objectives support the time-step mixup process and enhance the model's ability to discriminate effectively across different modalities. Our approach enables smoother knowledge transfer, alleviates modality shift during training, and achieves superior performance in spiking image classification tasks. Extensive experiments demonstrate the effectiveness of our method across multiple datasets. The code will be released after the double-blind review process.

cs.CV↗

arXiv2025

Breaking the Modality Wall: Time-step Mixup for Efficient Spiking Knowledge Transfer from Static to Event Domain

The integration of event cameras and spiking neural networks (SNNs) promises energy-efficient visual intelligence, yet scarce event data and the sparsity of DVS outputs hinder effective training. Prior knowledge transfers from RGB to DVS often underperform because the distribution gap between modalities is substantial. In this work, we present Time-step Mixup Knowledge Transfer (TMKT), a cross-modal training framework with a probabilistic Time-step Mixup (TSM) strategy. TSM exploits the asynchronous nature of SNNs by interpolating RGB and DVS inputs at various time steps to produce a smooth curriculum within each sequence, which reduces gradient variance and stabilizes optimization with theoretical analysis. To employ auxiliary supervision from TSM, TMKT introduces two lightweight modality-aware objectives, Modality Aware Guidance (MAG) for per-frame source supervision and Mixup Ratio Perception (MRP) for sequence-level mix ratio estimation, which explicitly align temporal features with the mixing schedule. TMKT enables smoother knowledge transfer, helps mitigate modality mismatch during training, and achieves superior performance in spiking image classification tasks. Extensive experiments across diverse benchmarks and multiple SNN backbones, together with ablations, demonstrate the effectiveness of our method.

cs.CV↗

arXiv2025

Change Point Detection for Random Objects with Periodic Behavior

Time-varying random objects have been increasingly encountered in modern data analysis. Moreover, in a substantial number of these applications, periodic behaviour of the random objects has been observed. We develop a novel procedure to identify and localize abrupt changes in the distribution of non-Euclidean random objects with periodic behaviour. The proposed procedure is flexible and broadly applicable, accommodating a variety of suitable change point detectors for random objects. We further construct a specific detector used in the proposed procedure which is nonparametric and effectively captures the entire distribution of these random objects. The theoretical results cover the limiting distribution of the detector under the null hypothesis of no change point, the power of the test in the presence of change points under local alternatives and the consistency in estimating the number and locations of change points, whether dealing with a single change point or multiple ones. We demonstrate that the most competitive method currently in the literature for change point detection in random objects is degraded by periodic behaviour, as periodicity leads to blurring of the changes that this procedure aims to discover. Through comprehensive simulation studies, we demonstrate the superior power and accuracy of our approach in both detecting change points and pinpointing their locations. Our main application is to weighted networks, represented through graph Laplacians. The proposed method delivers highly interpretable results, as evidenced by the identification of meaningful change points in the New York City Citi Bike sharing system that align with significant historical events.

stat.ME↗

arXiv2025

Cross Knowledge Distillation between Artificial and Spiking Neural Networks

Recently, Spiking Neural Networks (SNNs) have demonstrated rich potential in computer vision domain due to their high biological plausibility, event-driven characteristic and energy-saving efficiency. Still, limited annotated event-based datasets and immature SNN architectures result in their performance inferior to that of Artificial Neural Networks (ANNs). To enhance the performance of SNNs on their optimal data format, DVS data, we explore using RGB data and well-performing ANNs to implement knowledge distillation. In this case, solving cross-modality and cross-architecture challenges is necessary. In this paper, we propose cross knowledge distillation (CKD), which not only leverages semantic similarity and sliding replacement to mitigate the cross-modality challenge, but also uses an indirect phased knowledge distillation to mitigate the cross-architecture challenge. We validated our method on main-stream neuromorphic datasets, including N-Caltech101 and CEP-DVS. The experimental results show that our method outperforms current State-of-the-Art methods. The code will be available at https://github.com/ShawnYE618/CKD

cs.CV↗

arXiv2025

Robust Functional Principal Component Analysis for Non-Euclidean Random Objects

Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly encountered in modern data analysis. These data structures represent elements within general metric spaces that lack local or global linear structures, rendering traditional functional data analysis methods inapplicable. Moreover, the existing methodology for time-varying random objects does not work well in the presence of outlying objects. In this paper, we propose a robust method for analysing time-varying random objects. Our method employs pointwise Fréchet medians and then constructs pointwise distance trajectories between the individual time courses and the sample Fréchet medians. This representation effectively transforms time-varying objects into functional data. A novel robust approach to functional principal component analysis based on a Winsorized U-statistic estimator of the covariance structure is introduced. The proposed robust analysis of these distance trajectories is able to identify key features of time-varying objects and is useful for downstream analysis. To illustrate the efficacy of our approach, numerical studies focusing on dynamic networks are conducted. The results indicate that the proposed method exhibits good all-round performance and surpasses the existing approach in terms of robustness, showcasing its superior performance in handling time-varying objects data.

stat.ME↗

arXiv2024

Real-time Vehicle-to-Vehicle Communication Based Network Cooperative Control System through Distributed Database and Multimodal Perception: Demonstrated in Crossroads

The autonomous driving industry is rapidly advancing, with Vehicle-to-Vehicle (V2V) communication systems highlighting as a key component of enhanced road safety and traffic efficiency. This paper introduces a novel Real-time Vehicle-to-Vehicle Communication Based Network Cooperative Control System (VVCCS), designed to revolutionize macro-scope traffic planning and collision avoidance in autonomous driving. Implemented on Quanser Car (Qcar) hardware platform, our system integrates the distributed databases into individual autonomous vehicles and an optional central server. We also developed a comprehensive multi-modal perception system with multi-objective tracking and radar sensing. Through a demonstration within a physical crossroad environment, our system showcases its potential to be applied in congested and complex urban environments.

cs.RO↗

arXiv2024

Generalized Score Matching

Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is difficult or impossible to implement. To date, applications of score matching have focused more on continuous IID models. Motivated by various data modelling problems, this article proposes a unified asymptotic theory of generalized score matching developed under the independence assumption, covering both continuous and discrete response data, thereby giving a sound basis for score-matchingbased inference. Real data analyses and simulation studies provide convincing evidence of strong practical performance of the proposed methods.

stat.ME↗

arXiv2022

Generalized Score Matching for Regression

Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to avoid explicit computation of the normalizing constant. In the literature, score matching has so far only been developed for models in which the observations are independent and identically distributed (IID). However, the IID assumption does not hold in the traditional fixed design setting for regression-type models. To deal with the estimation of these covariate-dependent models, this paper presents a new score matching approach for independent but not necessarily identically distributed data under a general framework for both continuous and discrete responses, which includes a novel generalized score matching method for count response regression. We prove that our proposed score matching estimators are consistent and asymptotically normal under mild regularity conditions. The theoretical results are supported by simulation studies and a real-data example. Additionally, our simulation results indicate that, compared to approximate maximum likelihood estimation, the generalized score matching produces estimates with substantially smaller biases in an application to doctoral publication data.

math.ST↗