arXiv subjects

Haiyang Peng

Publications and source records attributed to Haiyang Peng.

6 recordsLinked to original sources

arXiv2026

A Deployment Audit of Release-Side Risk in Conformal Triage under Prevalence Shift

Conformal triage converts predictive scores into deployment actions that either release a case, flag it for urgent attention, or defer it to human review. Under an observed change in target-event prevalence, however, marginal coverage and human-review rate can miss whether patients who experience the target event are released without review. To address this gap, we introduce a leakage-aware deployment audit for release-side conformal triage. It first assigns target subjects to three non-overlapping roles: prevalence correction, conformal calibration, and held-out release-side evaluation. This separation then lets the audit evaluate release directly: how many event-positive patients are cleared without review, whether the pilot has enough event labels for calibration, and how the release-review trade-off shifts. Applying this audit to a retrospective non-small-cell lung cancer (NSCLC) target cohort shows why lower review can be misleading: after prevalence correction, the pooled conformal branch lowers review by releasing more patients, some of whom are event-positive. Within the audit, the classwise branch acts as a scarcity diagnostic: the pilot has too few event labels to support a low-review release rule.

cs.LG↗

arXiv2026

NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization

Group synchronization is a fundamental task involving the recovery of group elements from pairwise measurements. For orthogonal group synchronization, the most common approach reformulates the problem as a constrained nonconvex optimization and solves it using projection-based methods, such as the generalized power method. However, these methods rely on exact SVD or QR decompositions in each iteration, which are computationally expensive and become a bottleneck for large-scale problems. In this paper, we propose a Newton-Schulz-based Riemannian Gradient Scheme (NS-RGS) for orthogonal group synchronization that significantly reduces computational cost by replacing the SVD or QR step with the Newton-Schulz iteration. This approach leverages efficient matrix multiplications and aligns perfectly with modern GPU/TPU architectures. By employing a refined leave-one-out analysis, we overcome the challenge arising from statistical dependencies, and establish that NS-RGS with spectral initialization achieves linear convergence to the target solution up to near-optimal statistical noise levels. Experiments on synthetic data and real-world global alignment tasks demonstrate that NS-RGS attains accuracy comparable to state-of-the-art methods such as the generalized power method, while achieving nearly a 2$\times$ speedup.

stat.ML↗

arXiv2025

Convergence Analysis of Reshaped Wirtinger Flow with Random Initialization for Phase Retrieval

This paper investigates phase retrieval using the Reshaped Wirtinger Flow (RWF) algorithm, focusing on recovering target vector $\vx \in \R^n$ from magnitude measurements $y_i = \left| \langle \va_i, \vx \rangle \right|, \; i = 1, \ldots, m,$ under random initialization, where $\va_i \in \R^n$ are measurement vectors. For Gaussian measurement designs, we prove that when $m\ge O(n \log^2 n\log^3 m)$, the RWF algorithm with random initialization achieves $ε$-accuracy within $O\big(\log n + \log(1/ε)\big)$ iterations, thereby attaining nearly optimal sample and computational complexities comparable to those previously established for spectrally initialized methods. Numerical experiments demonstrate that the convergence rate is robust to initialization randomness and remains stable even with larger step sizes.

math.OC↗

arXiv2025

The Condition Number in Phase Retrieval from Intensity Measurements

This paper investigates the stability of phase retrieval by analyzing the condition number of the nonlinear map $Ψ_{\boldsymbol{A}}(\boldsymbol{x}) = \bigl(\lvert \langle {\boldsymbol{a}}_j, \boldsymbol{x} \rangle \rvert^2 \bigr)_{1 \le j \le m}$, where $\boldsymbol{a}_j \in \mathbb{H}^n$ are known sensing vectors with $\mathbb{H} \in \{\mathbb{R}, \mathbb{C}\}$. For each $p \ge 1$, we define the condition number $β_{Ψ_{\boldsymbol{A}}}^{\ell_p}$ as the ratio of optimal upper and lower Lipschitz constants of $Ψ_{\boldsymbol{A}}$ measured in the $\ell_p$ norm, with respect to the metric $\mathrm {dist}_\mathbb{H}\left(\boldsymbol{x}, \boldsymbol{y}\right) = \|\boldsymbol{x} \boldsymbol{x}^\ast - \boldsymbol{y} \boldsymbol{y}^\ast\|_*$. We establish universal lower bounds on $β_{Ψ_{\boldsymbol{A}}}^{\ell_p}$ for any sensing matrix $\boldsymbol{A} \in \mathbb{H}^{m \times d}$, proving that $β_{Ψ_{\boldsymbol{A}}}^{\ell_1} \ge π/2$ and $β_{Ψ_{\boldsymbol{A}}}^{\ell_2} \ge \sqrt{3}$ in the real case $(\mathbb{H} = \mathbb{R})$, and $β_{Ψ_{\boldsymbol{A}}}^{\ell_p} \ge 2$ for $p=1,2$ in the complex case $(\mathbb{H} = \mathbb{C})$. These bounds are shown to be asymptotically tight: both a deterministic harmonic frame $\boldsymbol{E}_m \in \mathbb{R}^{m \times 2}$ and Gaussian random matrices $\boldsymbol{A} \in \mathbb{H}^{m \times d}$ asymptotically attain them. Notably, the harmonic frame $\boldsymbol{E}_m \in \mathbb{R}^{m \times 2}$ achieves the optimal lower bound $\sqrt{3}$ for all $m \ge 3$ when $p=2$, thus serving as an optimal sensing matrix within $\boldsymbol{A} \in \mathbb{R}^{m \times 2}$. Our results provide the first explicit uniform lower bounds on $β_{Ψ_{\boldsymbol{A}}}^{\ell_p}$ and offer insights into the fundamental stability limits of phase retrieval.

cs.IT↗

arXiv2024

Noisy phase retrieval from subgaussian measurements

This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the subgaussian setting, we explore two commonly used assumptions: either the subgaussian measurements satisfy a fourth-moment condition or the target signals exhibit non-peakiness. For each scenario, we introduce a novel spectral initialization method that yields robust initial estimates. Building on this, we employ leave-one-out arguments to show that the classical Wirtinger flow algorithm achieves a linear rate of convergence for both real-valued and complex-valued cases, provided the sampling complexity $m\ge O(n \log^3 m)$, where $n$ is the dimension of the underlying signals. In contrast to existing work, our algorithms are regularization-free, requiring no truncation, trimming, or additional penalty terms, and they permit the algorithm step sizes as large as $O(1)$, compared to the $O(1/n)$ in previous literature. Furthermore, our results accommodate arbitrary noise vectors that meet certain statistical conditions, covering a wide range of noise scenarios, with sub-exponential noise as a notable special case. The effectiveness of our algorithms is validated through various numerical experiments. We emphasize that our findings provide the first theoretical guarantees for recovering non-peaky signals using non-convex methods from Bernoulli measurements, which is of independent interest.

math.OC↗

arXiv2024

PLCNet: Patch-wise Lane Correction Network for Automatic Lane Correction in High-definition Maps

In High-definition (HD) maps, lane elements constitute the majority of components and demand stringent localization requirements to ensure safe vehicle navigation. Vision lane detection with LiDAR position assignment is a prevalent method to acquire initial lanes for HD maps. However, due to incorrect vision detection and coarse camera-LiDAR calibration, initial lanes may deviate from their true positions within an uncertain range. To mitigate the need for manual lane correction, we propose a patch-wise lane correction network (PLCNet) to automatically correct the positions of initial lane points in local LiDAR images that are transformed from point clouds. PLCNet first extracts multi-scale image features and crops patch (ROI) features centered at each initial lane point. By applying ROIAlign, the fix-sized ROI features are flattened into 1D features. Then, a 1D lane attention module is devised to compute instance-level lane features with adaptive weights. Finally, lane correction offsets are inferred by a multi-layer perceptron and used to correct the initial lane positions. Considering practical applications, our automatic method supports merging local corrected lanes into global corrected lanes. Through extensive experiments on a self-built dataset, we demonstrate that PLCNet achieves fast and effective initial lane correction.

cs.CV↗