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This Letter presents a novel, to the best of our knowledge, method to calibrate multi-focus microscopic structured-light three-dimensional (3D) imaging systems with an electrically adjustable camera focal length. We first leverage the conventional method to calibrate the system with a reference focal lengthf0. Then we calibrate the system with other discrete focal lengthsfiby determining virtual features on a reconstructed white plane usingf0. Finally, we fit the polynomial function model using the discrete calibration results forfi. Experimental results demonstrate that our proposed method can calibrate the system consistently and accurately.
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This content will become publicly available on June 16, 2026
A Piecewise Lyapunov Analysis of Sub-quadratic SGD: Applications to Robust and Quantile Regression
Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective functionfthat is locally strongly convex with a sub--quadratic tail. This setting covers many widely used online statistical methods. We introduce a novel piecewise Lyapunov function that enables us to handle functionsfwith only first-order differentiability, which includes a wide range of popular loss functions such as Huber loss. Leveraging our proposed Lyapunov function, we derive finite-time moment bounds under general diminishing stepsizes, as well as constant stepsizes. We further establish the weak convergence, central limit theorem and bias characterization under constant stepsize, providing the first geometrical convergence result for sub--quadratic SGD. Our results have wide applications, especially in online statistical methods. In particular, we discuss two applications of our results. 1) Online robust regression: We consider a corrupted linear model with sub--exponential covariates and heavy--tailed noise. Our analysis provides convergence rates comparable to those for corrupted models with Gaussian covariates and noise. 2) Online quantile regression: Importantly, our results relax the common assumption in prior work that the conditional density is continuous and provide a more fine-grained analysis for the moment bounds.
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- PAR ID:
- 10610275
- Publisher / Repository:
- ACM SIGMETRICS Performance Evaluation Review
- Date Published:
- Journal Name:
- ACM SIGMETRICS Performance Evaluation Review
- Volume:
- 53
- Issue:
- 1
- ISSN:
- 0163-5999
- Page Range / eLocation ID:
- 85 to 87
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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