arXiv subjects

Yuji Li

Publications and source records attributed to Yuji Li.

5 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↗

arXiv2025

Signal detection from spiked noise via asymmetrization

The signal plus noise model $H=S+Y$ is a fundamental model in signal detection when a low rank signal $S$ is polluted by noise $Y$. In the high-dimensional setting, one often uses the leading singular values and corresponding singular vectors of $H$ to conduct the statistical inference of the signal $S$. Especially, when $Y$ consists of iid random entries, the singular values of $S$ can be estimated from those of $H$ as long as the signal $S$ is strong enough. However, when the $Y$ entries are heteroscedastic or heavy-tailed, this standard approach may fail. Especially in this work, we consider a situation that can easily arise with heteroscedastic or heavy-tailed noise but is particularly difficult to address using the singular value approach, namely, when the noise $Y$ itself may create spiked singular values. It has been a recurring question how to distinguish the signal $S$ from the spikes in $Y$, as this seems impossible by examining the leading singular values of $H$. Inspired by the work \cite{CCF21}, we turn to study the eigenvalues of an asymmetrized model when two samples $H_1=S+Y_1$ and $H_2=S+Y_2$ are available. We show that by looking into the leading eigenvalues (in magnitude) of the asymmetrized model $H_1H_2^*$, one can easily detect $S$. We will primarily discuss the heteroscedastic case and then discuss the extension to the heavy-tailed case. As a byproduct, we also derive the fundamental result regarding the outlier of non-Hermitian random matrix in \cite{Tao} under the minimal 2nd moment condition.

math.ST↗

arXiv2024

Flavor Physics at the CEPC: a General Perspective

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $Z$ pole, the expected production of 4 Tera $Z$ bosons will provide unique and highly precise measurements of $Z$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $Z$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\tau$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $WW$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals.

hep-ex↗

arXiv2023

Reconstruction of Unstable Heavy Particles Using Deep Symmetry-Preserving Attention Networks

Reconstructing unstable heavy particles requires sophisticated techniques to sift through the large number of possible permutations for assignment of detector objects to the underlying partons. Anapproach based on a generalized attention mechanism, symmetry preserving attention networks (SPA-NET), has been previously applied to top quark pair decays at the Large Hadron Collider which produce only hadronic jets. Here we extend the SPA-NET architecture to consider multiple input object types, such as leptons, as well as global event features, such as the missing transverse momentum. Inaddition, we provide regression and classification outputs to supplement the parton assignment. We explore the performance of the extended capability of SPA-NET in the context of semi-leptonic decays of top quark pairs as well as top quark pairs produced in association with a Higgs boson. We find significant improvements in the power of three representative studies: a search for ttH, a measurement of the top quark mass, and a search for a heavy Z' decaying to top quark pairs. We present ablation studies to provide insight on what the network has learned in each case.

hep-ex↗