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Federated Binary Matrix Factorization Using Proximal Optimization
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Proposes FeLb, a federated proximal-gradient method for Boolean matrix factorization that shares relaxed coefficient matrices aggregated with a binary-inducing proximal operator, with convergence and differential privacy guarantees.
Problem
Boolean matrix factorization over horizontally distributed binary data where clients cannot share raw data, and naive federation of local BMF methods yields poor reconstructions.
Approach
Relax BMF into a regularized binary matrix factorization solved by iPALM-style proximal gradient steps, with clients sharing only coefficient matrices that the server aggregates via a proximal (binary-inducing) averaging operator; Gaussian/Laplacian noise gives differential privacy.
Key results
- On 8 real-world datasets with 50 clients, FeLb^mu achieves average rank 1.625 in F1, the best among compared federated BMF methods, versus 2.750 for FeLb.
- FeLb^mu reaches F1 0.414 on TCGA and 0.197 on Netflix, while Asso, GreConD, MEBF, Zhang, and ELBMF often fail to finish or score near zero.
- FeLb and FeLb^mu remain robust to XOR noise on synthetic data and retain accuracy under (epsilon, delta)-differential privacy with epsilon up to 2.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · ACS Inc | F1 score: 0.690 -> 0.585 | Hurt |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · ACS Pov | F1 score: 0.797 -> 0.638 | Hurt |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · cs.LG | F1 score: 0.068 -> 0.057 | Hurt |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · Goodreads | F1 score: 0.017 -> 0.125 | Helped |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · HPA Brain | F1 score: 0.642 -> 0.007 | Hurt |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · Movielens | F1 score: 0.017 -> 0.193 | Helped |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · Netflix | F1 score: 0.010 -> 0.197 | Helped |
| Use Felb^mu instead of the strongest listed baseline | Federated BMF · TCGA | F1 score: 0.055 -> 0.414 | Helped |
| Use multiplicative-update steps instead of Lipschitz steps (ablation) | Felb · Goodreads | F1 score: 0.059 -> 0.125 | Helped |
| Use multiplicative-update steps instead of Lipschitz steps (ablation) | Felb · TCGA | F1 score: 0.402 -> 0.414 | Helped |
| Use multiplicative-update steps instead of Lipschitz steps (ablation) | Felb · ACS Inc | F1 score: 0.328 -> 0.585 | Helped |
| Use multiplicative-update steps instead of Lipschitz steps (ablation) | Felb · ACS Pov | F1 score: 0.517 -> 0.638 | Helped |
Surprising findings
- GreConD outperforms the proposed methods on ACS Income and ACS Poverty in F1.
- MEBF outperforms the proposed methods on HPA Brain.
Limitations
- Post-hoc baselines time out on medium and large real-world datasets.
- Experiments assume homogeneous clients with similar data distributions.
- Convergence to Boolean solutions requires an increasing regularization schedule; the theory is a sketch in places.
Experimental setup
Datasets: ACS Income ACS Poverty ArXiv cs.LG abstracts Goodreads HPA Movielens Netflix TCGA synthetic binary matrices with XOR noise
Benchmarks: ACS Income ACS Poverty cs.LG Goodreads HPA Brain Movielens Netflix TCGA synthetic data
Metrics: F1 score RMSD runtime recall similarity
Baselines: ASSO GreConD MEBF ELBMF Zhang et al. relaxation BMF
Builds on: ELBMF iPALM ASSO GreConD MEBF
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