Quantile Randomized Kaczmarz Algorithm with Whitelist Trust Mechanism
Sofiia Shvaiko, Longxiu Huang, Elizaveta Rebrova

TL;DR
This paper improves the robustness and efficiency of the QuantileRK algorithm for solving noisy overdetermined linear systems by introducing an online detection mechanism and quantile estimation from small samples.
Contribution
It reanalyzes QRK's convergence, proposes a practical online detector for unreliable rows, and reduces computational cost via subsampling.
Findings
Convergence rate improves as corruption decreases.
The online detector effectively flags unreliable equations.
Subsampling preserves robustness while lowering per-iteration cost.
Abstract
Randomized Kaczmarz (RK) is a simple and fast solver for consistent overdetermined systems, but it is known to be fragile under noise. We study overdetermined linear systems with a sparse set of corrupted equations, where only is observed with . The recently introduced QuantileRK (QRK) algorithm addresses this issue by testing residuals against a quantile threshold, but computing a per-iteration quantile across many rows is costly. In this work we (i) reanalyze QRK and show that its convergence rate improves monotonically as the corruption fraction decreases; (ii) propose a simple online detector that flags and removes unreliable rows, which reduces the effective and speeds up convergence; and (iii) make the method practical by…
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Taxonomy
TopicsStochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques · Statistical Methods and Inference
