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Distributed Conformal Prediction via Message Passing
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Proposes two message-passing conformal prediction protocols for decentralized calibration over arbitrary graphs: Q-DCP (smoothed, regularized distributed ADMM quantile regression) and H-DCP (consensus-based histogram estimation with hyperparameter-free coverage).
Problem
Conformal prediction calibration when calibration data is distributed across devices with limited local data that can only communicate with neighbors over an arbitrary graph, without a central server.
Approach
Decentralize split conformal prediction's quantile computation via two schemes: ADMM-based distributed quantile regression with a smooth, strongly convex pinball-loss surrogate (Q-DCP), and consensus averaging of quantized local score histograms (H-DCP), with coverage guarantees derived for both under non-i.i.d. weighted mixture settings.
Key results
- On CIFAR-100 with K=20 devices and alpha=0.1, Q-DCP (epsilon0=0.1, T=1500) matches centralized CP set size on a complete graph and maintains coverage above 1-alpha across chain, cycle, star, torus, and complete topologies, with sparser graphs giving larger sets.
- With a poorly chosen hyperparameter pair (epsilon0=1e-4), Q-DCP can violate the coverage target on well-connected graphs, while H-DCP maintains coverage at all tested communication loads.
- In a star-topology comparison at alpha=0.1, Q-DCP (0.913 coverage, 11.35 set size) and H-DCP/WFCP (0.92, 12.16) are comparable to FCP (0.918, 11.98), whereas FedCP-QQ is over-conservative (0.996 coverage, 45.32 set size).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Q-DCP instead of centralized CP on the complete graph with T=1500 and ε₀=0.1 | Q-DCP · CIFAR100 | set size | No clear effect |
| Use Q-DCP with poorly selected hyperparameters (ε₀=10⁻⁴ and s₀=−8−20α) | Q-DCP · CIFAR100, different network topologies | coverage | Hurt |
| Use Q-DCP with well-selected hyperparameters rather than H-DCP at equal communication load | Q-DCP and H-DCP · CIFAR100 torus graph, 1−α=0.9 | set size | Helped |
| Use Q-DCP with 16-bit rather than higher numerical precision | Q-DCP · CIFAR100 torus graph, 1−α=0.9 | set size | Hurt |
| Use H-DCP across the considered communication loads instead of poorly tuned Q-DCP | H-DCP and Q-DCP · CIFAR100 torus graph, 1−α=0.9 | coverage | Helped |
| Increase the Q-DCP smoothness parameter κ from small to large values (ablation) | Q-DCP · CIFAR100 torus graph | set size | Mixed |
| Decrease the Q-DCP regularization parameter μ (ablation) | Q-DCP · CIFAR100 torus graph | set size | Hurt |
| Decrease μ when s₀ and ε₀ violate the stated assumption (ablation) | Q-DCP · CIFAR100 torus graph | coverage | Helped |
| Increase the H-DCP quantization level M under limited consensus iterations (ablation) | H-DCP · CIFAR100, different network graphs | set size | Mixed |
| Increase network connectivity while holding Q-DCP iteration count fixed | Q-DCP · CIFAR100 Erdős–Rényi graphs | set size | Helped |
| Use ε₀=0.1 as network size K grows, violating the stated assumption | Q-DCP · CIFAR100 Erdős–Rényi graphs | coverage | Hurt |
Surprising findings
- Q-DCP can fail to achieve the coverage guarantee with poorly chosen regularization hyperparameters, even at high numerical precision, since errors compound across iterations on well-connected graphs.
- H-DCP requires a communication load roughly M times larger than Q-DCP per iteration (M=1000 levels), yet the paper reports comparable performance under equal total bit budgets only for suitable settings.
Limitations
- Q-DCP's coverage guarantee depends on hyperparameters (epsilon0, mu, s0) and the spectral gap of the graph, which must be known or chosen carefully.
- H-DCP incurs a per-iteration communication cost M times larger than Q-DCP (M=1000 quantization levels in experiments).
- Experiments are limited to CIFAR-100 and a small PathMNIST setting with a single small model; the topology-dependent convergence requires many iterations on sparse graphs.
Experimental setup
Datasets: CIFAR-100 PathMNIST
Benchmarks: CIFAR-100 PathMNIST
Metrics: coverage normalized set size (inefficiency) communication load in bits
Baselines: centralized CP FCP FedCP-QQ WFCP
Builds on: split conformal prediction FCP WFCP FedCP-QQ ADMM
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