| _version_ | 1866902166121218048 |
|---|---|
| author | SÉRGIO DE ANDRADE, PAULO |
| author_facet | SÉRGIO DE ANDRADE, PAULO |
| contents | This paper introduces a novel framework for extending conformal prediction to dependent data sequences, such as time series. Traditional conformal prediction methods rely on the strong assumption of data exchangeability, which is often violated in practice. To overcome this limitation, we leverage the mathematical theory of martingales. By reformulating the non-conformity scores within a martingale context, we can derive valid prediction intervals without requiring data to be independent and identically distributed. Specifically, we construct a supermartingale from the sequence of prediction errors, and then apply martingale concentration inequalities, such as the Azuma-Hoeffding inequality, to bound the cumulative deviation of these errors. This allows us to calibrate the prediction intervals dynamically, ensuring they maintain a desired level of statistical coverage over time. The proposed Martingale Conformal Prediction (MCP) framework is both theoretically sound, providing finite-sample coverage guarantees under mild dependency assumptions, and computationally feasible. We establish formal proofs of validity and discuss the conditions under which the guarantees hold. The practical utility of our approach is demonstrated through a series of experiments on synthetic and real-world time series data, showing that MCP achieves robust and reliable uncertainty quantification in non-IID settings, outperforming standard methods that fail to account for data dependency. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17690726 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Conformal Prediction for Dependent Data: A Martingale Approach SÉRGIO DE ANDRADE, PAULO This paper introduces a novel framework for extending conformal prediction to dependent data sequences, such as time series. Traditional conformal prediction methods rely on the strong assumption of data exchangeability, which is often violated in practice. To overcome this limitation, we leverage the mathematical theory of martingales. By reformulating the non-conformity scores within a martingale context, we can derive valid prediction intervals without requiring data to be independent and identically distributed. Specifically, we construct a supermartingale from the sequence of prediction errors, and then apply martingale concentration inequalities, such as the Azuma-Hoeffding inequality, to bound the cumulative deviation of these errors. This allows us to calibrate the prediction intervals dynamically, ensuring they maintain a desired level of statistical coverage over time. The proposed Martingale Conformal Prediction (MCP) framework is both theoretically sound, providing finite-sample coverage guarantees under mild dependency assumptions, and computationally feasible. We establish formal proofs of validity and discuss the conditions under which the guarantees hold. The practical utility of our approach is demonstrated through a series of experiments on synthetic and real-world time series data, showing that MCP achieves robust and reliable uncertainty quantification in non-IID settings, outperforming standard methods that fail to account for data dependency. |
| title | Conformal Prediction for Dependent Data: A Martingale Approach |
| url | https://doi.org/10.5281/zenodo.17690726 |