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Robust Variance-Gradient Subsampling for Logistic Regression With Corrupted Large-Scale Data
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DOI：10.1109/tkde.2026.3718313.png)
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Abstract
En 中文
In the era of Big Data, subsampling is often used to obtain manageable and representative subsets for subsequent downstream learning. However, real-world data are frequently corrupted by malicious attacks or system failures, making robust and efficient subsampling essential. Existing robust subsampling methods that rely on small gradients can mitigate contamination in ordinary linear regression, but they typically underperform for logistic regression: observations with small residuals but low informational value are over-selected, which harms downstream learning. To address this, we propose a novel variance-gradient subsampling (VGS) method by combining the variance of the response with the gradient of the loss function to prioritize samples that are less affected by large gradients, while avoiding the over-selection of small residual observations. For robust parameter estimation, we embed VGS into mini-batch gradient descent (MGD) and develop a VGS-based MGD (VGS-MGD) algorithm, along with its fast approximation. The proposed method not only mitigates the lack of robustness in traditional MGD under contamination but also improves time and memory efficiency for large-scale datasets. Under mild regularity conditions, we establish theoretical guarantees, including clean-selection effectiveness for VGS and non-asymptotic error bounds for the proposed algorithms. Extensive simulations and empirical studies showcase the proposed method’s lower estimation error, higher clean-sample ratio, and competitive time and memory efficiency.
Keywords:
Data corruption
large-scale data
logistic regression
mini-batch gradient descent
robust subsampling
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6.8K
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