# Decomposition-Based Modular Conformal Prediction for Two-Stage Modeling

arXiv: https://arxiv.org/abs/2510.04406 · HTML: https://mlsanity.com/paper/2510.04406/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 14 of 14)

- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Propagating Uncertainty in Multi-Stage Bayesian Convolutional Neural Networks with Application to Pulmonary Nodule Detection](https://mlsanity.com/paper/1712.00497/) (2017)
- [Conformal Structured Prediction](https://mlsanity.com/paper/2410.06296/) (2024)
- [Propagation and Attribution of Uncertainty in Medical Imaging Pipelines](https://mlsanity.com/paper/2309.16831/) (2023)
- [Confidence Calibration for Systems with Cascaded Predictive Modules](https://mlsanity.com/paper/2309.12510/) (2023)

## Abstract (arXiv)

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit and understand modular structure. We introduce a conformal prediction framework for two-stage sequential models, where an upstream predictor generates intermediate representations for a downstream model. By decomposing the overall prediction residual into stage-specific components, our method enables practitioners to attribute uncertainty to specific pipeline stages. We develop a risk-controlled parameter selection procedure using family-wise error rate (FWER) control to calibrate stage-wise scaling parameters, and introduce an adaptive extension for non-stationary settings. Experiments on synthetic distribution shifts, as well as real-world supply chain and stock market data, demonstrate that our approach improves coverage under structural, stage-wise shifts compared to standard conformal methods, while identifying stage-wise error contribution. This framework offers diagnostic advantages and robust coverage that standard conformal methods lack.