Federated Conformal Prediction

Retrieval-augmented generation (RAG) lets language models answer questions more accurately by consulting relevant documents. Many valuable collections, such as medical records, cannot be pooled because of privacy rules. Federated RAG leaves each collection with its owner, or node, which scores candidate answers from its own documents; a central hub combines the scores. Some nodes, called Byzantine, may be compromised, faulty, or misled by instructions hidden in documents, and report arbitrary scores. Conformal prediction returns a set containing the correct answer with a chosen probability, using a cutoff set in a calibration step on questions with known answers. An unknown group of nodes, no larger than a declared bound, may misreport both in this step and at query time. Existing methods assume every node is honest or protect only the calibration step. We observe that the honest nodes are the same in both steps. The hub therefore has all nodes score the same calibration questions, and keeps a candidate only if some plausible group of honest nodes, using its own scores in both steps, would keep it. We prove that the resulting sets contain the correct answer with the chosen probability in finite samples, whatever the Byzantine nodes report. No method using the same information can return smaller sets without risking the loss of an answer the honest nodes support. If nodes fail at random, the guarantee weakens only by the probability that more nodes fail than declared. In simulations, on real question-answering tasks including medical exams, and with language models as nodes, some hijacked, our sets reached the target whenever no more nodes misbehaved than declared, while plain averaging could miss it. They were also clearly smaller than those of simpler methods with the same protection, most of all when the declared bound was generous, so a cautious bound costs little.

Conformal risk control (CRC) provides distribution-free guarantees on segmentation quality by calibrating a prediction-set threshold on held-out data. In federated deployments, the standard approach pools calibration scores across sites into a single threshold. We provide the first quantification, on real multi-institutional brain tumor data (FeTS-2022, 1,251 subjects, 20 institutions), showing that this naive pooled CRC protects the average hospital but violates coverage at 40% of individual institutions, with the worst site exceeding the target false-negative rate by 7.8 percentage points. The naive alternative, per-site local CRC, largely restores coverage but inflates prediction sets by 83x, rendering them clinically useless. We propose a shrinkage-based federated CRC protocol: each site transmits only its empirical risk curve (G scalars) to a server, which computes a shrinkage-regularized threshold per site. A single hyperparameter n0 smoothly trades worst-case coverage for prediction-set efficiency; leave-one-site-out sensitivity analysis identifies n0=19, achieving 2.7/20 violations at 2.0x stretch. We further show that direct Lagrangian optimization of coverage budgets fails, concentrating risk on vulnerable hospitals, and that the finite-sample correction term is essential: removing it triples violations. The marginal CRC guarantee is preserved by construction under the stated site-mixture assumption; per-site coverage is validated across four targets with three seeds. No patient-level images, masks, or per-volume scores leave any site.

Uncertainty quantification is essential in high-stakes machine learning tasks. However, one of the principled solutions, conformal prediction, faces challenges under limited local calibration data, privacy constraints, and data heterogeneity. In multi-agent settings, existing works do not simultaneously and satisfactorily address these challenges with guarantees either limited to averages across agents or losing validity in heterogeneous settings. Hence, we propose personalized federated weighted conformal prediction (PFWCP), a framework that combines local density ratio weighting with weighted quantile aggregation to correct for heterogeneity while preserving privacy. The method yields asymptotically valid marginal and calibration-conditional coverage guarantees for each participating agent and supports protocols with one-shot communication. Theoretical analysis presents an adjustment to the coverage variance, governed by an effective sample size expression, which is necessary in the context of weighted conformal prediction, and experiments on synthetic and real datasets show improved calibration quality over state-of-the-art federated conformal baselines.

Federated Conformal RAG (FC-RAG) provides distribution-free coverage for a bandwidth-limited swarm of weak language models, but only at a fixed horizon. We extend it to anytime-valid sequential coverage: validity at every stopping time, preserved under predictable adaptive control (recalibration, per-node bandwidth escalation, distilled-student refresh), at no extra cost in assumptions over fixed-horizon FC-RAG. Naive composition fails because FC-RAG's marginal coverage bound makes the betting e-process a non-supermartingale on adverse calibration draws, and Ville's inequality cannot be invoked. We give Anytime-FC-RAG, a sequential extension built on a summable per-step calibration-deviation budget that converts the marginal bound into a strict conditional bound on a calibration-good event, paired with a truncated betting e-process that is a nonnegative supermartingale on the entire probability space. From these two ingredients, we obtain four guarantees: time-uniform alarm validity $\mathbb{P}(\sup_t E_t \ge 1/δ_e) \le δ_e + δ_{\mathrm{cal}}$, a Hoeffding-stitched cumulative-miscoverage envelope at the same total budget, safety under any predictable controller (recalibration, bandwidth escalation, student refresh), and training-side error propagation across an unbounded sequence of Federated Probe-Logit Distillation (FPLD) refreshes via a summable training budget. As a practical consequence, an adaptive controller that escalates retrieval bandwidth only when the e-process crosses a warning threshold matches the alarm rate of a fixed-high-bandwidth schedule at substantially lower communication cost. Experiments on a GPT-2-small + MiniLM swarm across MMLU, DBpedia, and AG News verify the predicted alarm rate, detection delay, envelope coverage, and $14$-$57\%$ bandwidth savings; the alarm fires when and only when coverage genuinely breaks.

We propose a Byzantine-resilient federated conformal prediction (FCP) method that leverages partial model sharing, where only a subset of model parameters is exchanged each round. Unlike existing robust FCP approaches that primarily harden the calibration stage, our method protects both the federated training and conformal calibration phases. During training, partial sharing inherently restricts the attack surface and attenuates poisoned updates while reducing communication. During calibration, clients compress their non-conformity scores into histogram-based characterization vectors, enabling the server to detect Byzantine clients via distance-based maliciousness scores and to estimate the conformal quantile using only benign contributors. Experiments across diverse Byzantine attack scenarios show that the proposed method achieves closer-to-nominal coverage with substantially tighter prediction intervals than standard FCP, establishing a robust and communication-efficient approach to federated uncertainty quantification.

Deploying trustworthy AI systems requires principled uncertainty quantification. Conformal prediction (CP) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for CP are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose group-conditional federated conformal prediction (GC-FCP), a federated extension of conditional conformal calibration for a target mixture over prespecified groups. GC-FCP constructs mergeable, atom-stratified coresets from local calibration scores, enabling compact aggregation at the server when the number of active atoms is moderate. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines. The code of our work can be found at https://github.com/HaifengWen/GC-FCP.

Federated learning (FL) faces challenges in uncertainty quantification (UQ). Without reliable UQ, FL systems risk deploying overconfident models at under-resourced agents, leading to silent local failures despite seemingly satisfactory global performance. Existing federated UQ approaches often address data heterogeneity or model heterogeneity in isolation, overlooking their joint effect on coverage reliability across agents. Conformal prediction is a widely used distribution-free UQ framework, yet its applications in heterogeneous FL settings remains underexplored. We provide FedWQ-CP, a simple yet effective approach that balances empirical coverage performance with efficiency at both global and agent levels under the dual heterogeneity. FedWQ-CP performs agent-server calibration in a single communication round. On each agent, conformity scores are computed on calibration data and a local quantile threshold is derived. Each agent then transmits only its quantile threshold and calibration sample size to the server. The server simply aggregates these thresholds through a weighted average to produce a global threshold. Experimental results on seven public datasets for both classification and regression demonstrate that FedWQ-CP empirically maintains agent-wise and global coverage while producing the smallest prediction sets or intervals.

We propose PRISM-FCP (Partial shaRing and robust calIbration with Statistical Margins for Federated Conformal Prediction), a communication-efficient Byzantine-robust federated conformal prediction framework that uses partial model sharing to mitigate stochastic model-poisoning attacks during training and histogram-based filtering to mitigate adversarial calibration submissions. Existing robust FCP approaches primarily address adversarial behavior during calibration, leaving training-stage poisoning to separate robust-training mechanisms. PRISM-FCP instead considers the coupling between the two stages. During training, clients partially share updates by transmitting only $M$ of $D$ parameters per round. Under the stated stochastic attack model, this attenuates the expected energy of each Byzantine client's perturbation contribution to the aggregate by a factor of $M/D$ relative to full sharing. When this benefit outweighs the optimization slowdown caused by partial updates, it can reduce training error and improve interval efficiency. During calibration, the server uses client-provided characterization vectors to filter suspected Byzantine clients before estimating the conformal quantile from the retained clients. Experiments on synthetic benchmarks and the UCI Superconductivity and YearPredictionMSD datasets, including Gaussian, ALIE, and sign-flipping training-stage attacks, demonstrate near-nominal empirical coverage and favorable communication--performance tradeoffs in the studied settings.