Pixelwise Split Conformal Prediction for Global Temperature Emulation via Leave-One-Out Ensemble Distillation

Bünyamin Korkut, Yunus Emre Karaoğlan, Ozan Çetin, Yusuf H. Sahin, Alper Ünal
Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 329:1010-1028, 2026.

Abstract

Neural emulators of climate model output rarely come with statistically principled uncertainty estimates. We study how split conformal prediction (SCP) can be repurposed from a post-hoc uncertainty wrapper into a training-time spatial prior for ensemble distillation. Given nine CMIP6 Earth System Models, we train nine leave-one-out (LOO) UNet++ teachers and calibrate each on its held-out target member, producing per-pixel calibration quantiles with the standard marginal split-CP validity interpretation at each spatial location and for each teacher, under exchangeability. From these calibration residual statistics, we derive calibration-informed center weights that score, for each pixel, how consistently each teacher tracks the bias-corrected ensemble consensus, and pixel-loss weights that re-weight the distillation objective so that the student is pushed harder on historically difficult regions. On global monthly near-surface air temperature emulation across a 192$\times$288 grid, the student achieves a test MAE of 0.9625 K versus 0.9782 K for a strong UNet++ baseline (-1.61%), decreases the error of 96.4% of grid cells, and reaches empirical pixelwise coverage of 90.6%. This student coverage is reported as an empirical calibration check rather than as a formal conformal guarantee for the distilled predictor. Our source code is available at https://github.com/bunyaminkorkut/COPA-Global-Temperature-Emulation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v329-korkut26a, title = {Pixelwise Split Conformal Prediction for Global Temperature Emulation via Leave-One-Out Ensemble Distillation}, author = {Korkut, B{\"u}nyamin and Emre Karao{\u{g}}lan, Yunus and {\c{C}}etin, Ozan and Sahin, Yusuf H. and {\"U}nal, Alper}, booktitle = {Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {1010--1028}, year = {2026}, editor = {Ahlberg, Ernst and Johansson, Ulf and Boström, Henrik and Carlevaro, Alberto and Hallberg Szabadváry, Johan and Carlsson, Lars}, volume = {329}, series = {Proceedings of Machine Learning Research}, month = {02--04 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v329/main/assets/korkut26a/korkut26a.pdf}, url = {https://proceedings.mlr.press/v329/korkut26a.html}, abstract = {Neural emulators of climate model output rarely come with statistically principled uncertainty estimates. We study how split conformal prediction (SCP) can be repurposed from a post-hoc uncertainty wrapper into a training-time spatial prior for ensemble distillation. Given nine CMIP6 Earth System Models, we train nine leave-one-out (LOO) UNet++ teachers and calibrate each on its held-out target member, producing per-pixel calibration quantiles with the standard marginal split-CP validity interpretation at each spatial location and for each teacher, under exchangeability. From these calibration residual statistics, we derive calibration-informed center weights that score, for each pixel, how consistently each teacher tracks the bias-corrected ensemble consensus, and pixel-loss weights that re-weight the distillation objective so that the student is pushed harder on historically difficult regions. On global monthly near-surface air temperature emulation across a 192$\times$288 grid, the student achieves a test MAE of 0.9625 K versus 0.9782 K for a strong UNet++ baseline (-1.61%), decreases the error of 96.4% of grid cells, and reaches empirical pixelwise coverage of 90.6%. This student coverage is reported as an empirical calibration check rather than as a formal conformal guarantee for the distilled predictor. Our source code is available at https://github.com/bunyaminkorkut/COPA-Global-Temperature-Emulation.} }
Endnote
%0 Conference Paper %T Pixelwise Split Conformal Prediction for Global Temperature Emulation via Leave-One-Out Ensemble Distillation %A Bünyamin Korkut %A Yunus Emre Karaoğlan %A Ozan Çetin %A Yusuf H. Sahin %A Alper Ünal %B Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2026 %E Ernst Ahlberg %E Ulf Johansson %E Henrik Boström %E Alberto Carlevaro %E Johan Hallberg Szabadváry %E Lars Carlsson %F pmlr-v329-korkut26a %I PMLR %P 1010--1028 %U https://proceedings.mlr.press/v329/korkut26a.html %V 329 %X Neural emulators of climate model output rarely come with statistically principled uncertainty estimates. We study how split conformal prediction (SCP) can be repurposed from a post-hoc uncertainty wrapper into a training-time spatial prior for ensemble distillation. Given nine CMIP6 Earth System Models, we train nine leave-one-out (LOO) UNet++ teachers and calibrate each on its held-out target member, producing per-pixel calibration quantiles with the standard marginal split-CP validity interpretation at each spatial location and for each teacher, under exchangeability. From these calibration residual statistics, we derive calibration-informed center weights that score, for each pixel, how consistently each teacher tracks the bias-corrected ensemble consensus, and pixel-loss weights that re-weight the distillation objective so that the student is pushed harder on historically difficult regions. On global monthly near-surface air temperature emulation across a 192$\times$288 grid, the student achieves a test MAE of 0.9625 K versus 0.9782 K for a strong UNet++ baseline (-1.61%), decreases the error of 96.4% of grid cells, and reaches empirical pixelwise coverage of 90.6%. This student coverage is reported as an empirical calibration check rather than as a formal conformal guarantee for the distilled predictor. Our source code is available at https://github.com/bunyaminkorkut/COPA-Global-Temperature-Emulation.
APA
Korkut, B., Emre Karaoğlan, Y., Çetin, O., Sahin, Y.H. & Ünal, A.. (2026). Pixelwise Split Conformal Prediction for Global Temperature Emulation via Leave-One-Out Ensemble Distillation. Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 329:1010-1028 Available from https://proceedings.mlr.press/v329/korkut26a.html.

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