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Improved Coresets for Vertical Federated Learning: Regularized Linear and Logistic Regressions
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Builds coreset constructions for regularized logistic regression (centralized and vertical FL) using l1 Lewis weights and for ridge regression in VFL using local leverage scores, with sizes that shrink as the regularization λ grows.
Problem
Coreset construction for regularized logistic and ridge regression when features are partitioned across clients in vertical federated learning, where communication cost scales with data size.
Approach
Compute local regularized sensitivity scores via l1 Lewis weights (logistic) and l2 leverage scores (ridge) on the augmented matrix [Z; λI] at each client, aggregate them with a factor T, and sample via the unified VFL framework; the total sensitivity is bounded by the statistical dimension, so coreset size decreases with λ and loses the dependence on the condition number.
Key results
- On Credit Card data, AugLewis achieves F1 of 0.9330 train / 0.9343 test at 500 samples versus 0.8192 / 0.8185 for Uniform and 0.8704 / 0.8712 for HLSZ.
- Training on the coreset is reported as roughly 80x to 100x faster than training on the complete Credit Card dataset.
- For VRLR, the ridge-leverage coreset yields lower test RMSE and model closeness than uniform and Huang et al. (2022) leverage sampling across Blog Feedback and Financial datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use regularization-aware Lewis weights instead of Lewis weights that omit regularization | VRLog coreset construction · Credit Card | test F1: 0.9230 -> 0.9343 | Helped |
| Use regularization-aware Lewis weights instead of Lewis weights that omit regularization | VRLog coreset construction · Credit Card | train F1: 0.9220 -> 0.9330 | Helped |
| Use regularization-aware Lewis weights instead of Lewis weights that omit regularization | VRLog coreset construction · KDD Cup | test F1: 0.8688 -> 0.8772 | Helped |
| Use regularization-aware Lewis weights instead of Lewis weights that omit regularization | VRLog coreset construction · KDD Cup | train F1: 0.8715 -> 0.8801 | Helped |
| Use regularized leverage-score sampling instead of uniform or HLSZ sampling | VRLR coreset construction · Wave Energy Converters | test RMSE | Helped |
| Use regularized leverage-score sampling instead of uniform or HLSZ sampling | VRLR coreset construction · Year Prediction | MSE | Helped |
| Use regularized leverage-score sampling instead of competing coreset sampling methods | VRLR coreset construction · Blog Feedback | test RMSE | Helped |
Surprising findings
- Theoretical logistic regression coreset size bound (sum of ℓ1 Lewis weights) is claimed to be independent of √n, yet the paper also notes an earlier-proved bound with √n dependence.
Limitations
- Logistic regression coreset guarantees rely on a µ-complexity assumption on the data.
- Empirical gains on some datasets (e.g., Year Prediction) are described as not significant.
- Experiments use only 3 to 10 clients and simple linear models; no end-to-end VFL deep model evaluation.
Experimental setup
Datasets: Credit Card Fraud Detection Financial (Gold Price) Blog Feedback KDD Cup Wave Energy Converters Year Prediction MSD UJIIndoorLoc
Benchmarks: Credit Card Fraud Detection KDD Cup Blog Feedback Financial Wave Energy Converters Year Prediction UJIIndoorLoc
Metrics: training loss balanced accuracy F1 score test RMSE model closeness training time speedup
Baselines: Uniform sampling HLSZ (Huang et al. 2022) SqLev Lewis weights Leverage score sampling (Huang et al. 2022) Class-wise QR
Builds on: Huang et al. 2022 VFL coreset framework Lewis weights (Cohen & Peng 2015) Mai et al. 2021 logistic regression coresets statistical dimension (Avron et al. 2017)
Closest papers by meaning
- HaCore: Efficient Coreset Construction with Locality Sensitive Hashing for Vertical Federated Learning (AAAI 2025 · similarity 0.88)
- Vertical Federated Learning with Missing Features During Training and Inference (ICLR 2025 · similarity 0.87)
- Bayesian Coreset Optimization for Personalized Federated Learning (ICLR 2024 · similarity 0.86)
- FedCS: Coreset Selection for Federated Learning (CVPR 2025 · similarity 0.86)
- VFLAIR: A Research Library and Benchmark for Vertical Federated Learning (ICLR 2024 · similarity 0.86)
- FedQS: Optimizing Gradient and Model Aggregation for Semi-Asynchronous Federated Learning (NeurIPS 2025 · similarity 0.85)
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