Beyond Point Photo-z Estimates: Normalizing Flows for Tomographic N(z) Reconstruction with DESI DR1
Abstract
Accurate calibration of tomographic redshift distributions, N(z) is essential for cosmological analysis of weak lensing data. We investigate conditional normalizing flows (NFs) and compare their performance with random forest (RF) and quantile random forest (QRF) models. We consider DESI galaxy and quasar targets from DESI DR1 spectroscopic data and with the photometry from Legacy Surveys DR10. We train on 1.1 million sources and test on 2.0 million sources in a non-overlapping sky region (0<zspec<4.5). For point estimation, the NF achieves the lowest scatter and outlier fraction at 0<zspec<1.6 and outperforms both baselines across all three metrics at zspec>1.6. By introducing distribution-level metrics like Wasserstein distance and JS divergence, we find that stacking NF posterior PDFs provides more accurate tomographic N(z) reconstruction than QRF, particularly at high redshifts. For zmedian>2.5, the NF achieves a smaller absolute mean-redshift bias (0.060±0.031 versus $0.318$) and higher probability overlap (0.905±0.008 versus $0.787$) than QRF. We apply redshift-dependent post-hoc PDF calibration derived from a held-out validation sample. After calibration, the absolute mean-redshift biases in four bins spanning 0.2<zmedian<1.0 range from $0.0016$ to $0.0019$, with central values below referring benchmark 0.002(1+z). In the highest-redshift bin, calibration further reduces the bias to 0.016±0.011. Our results demonstrate the potential of NF PDFs for tomographic N(z) reconstruction while highlighting challenges in transferring models across galaxy populations.
Related
- X-reconstruction: 3D Tomographic Reconstruction in Astrophysics. I. Mathematical Formulation for Systems in the Optically Thin Regime
- Basis function expansions of the two-point correlation function and reconstruction of the cosmological distance scale
- Recovering Weak Signals with Normalizing Flows
- Neural Posterior Estimation for Tomographic Weak Lensing Mass Mapping
- A Prediction for DESI Full-Shape: Increasing Tomographic Ωm(z) Trend
BibTeX
@misc{chen2026beyond,
title = {{Beyond Point Photo-$z$ Estimates: Normalizing Flows for Tomographic $N(z)$ Reconstruction with DESI DR1}},
author = {Zhuo Chen and Antoine Rocher and Kwan Chuen Chan and Jean-Paul Kneib},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00121},
eprint = {2611.00121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00121},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond Point Photo-z Estimates: Normalizing Flows for Tomographic N(z) Reconstruction with DESI DR1
AU - Zhuo Chen
AU - Antoine Rocher
AU - Kwan Chuen Chan
AU - Jean-Paul Kneib
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00121
UR - https://arxiv.org/abs/2611.00121
AB - Accurate calibration of tomographic redshift distributions, N(z) is essential for cosmological analysis of weak lensing data. We investigate conditional normalizing flows (NFs) and compare their performance with random forest (RF) and quantile random forest (QRF) models. We consider DESI galaxy and quasar targets from DESI DR1 spectroscopic data and with the photometry from Legacy Surveys DR10. We train on 1.1 million sources and test on 2.0 million sources in a non-overlapping sky region (0<z_spec<4.5). For point estimation, the NF achieves the lowest scatter and outlier fraction at 0<z_spec<1.6 and outperforms both baselines across all three metrics at z_spec>1.6. By introducing distribution-level metrics like Wasserstein distance and JS divergence, we find that stacking NF posterior PDFs provides more accurate tomographic N(z) reconstruction than QRF, particularly at high redshifts. For z_median>2.5, the NF achieves a smaller absolute mean-redshift bias (0.060±0.031 versus $0.318$) and higher probability overlap (0.905±0.008 versus $0.787$) than QRF. We apply redshift-dependent post-hoc PDF calibration derived from a held-out validation sample. After calibration, the absolute mean-redshift biases in four bins spanning 0.2<z_median<1.0 range from $0.0016$ to $0.0019$, with central values below referring benchmark 0.002(1+z). In the highest-redshift bin, calibration further reduces the bias to 0.016±0.011. Our results demonstrate the potential of NF PDFs for tomographic N(z) reconstruction while highlighting challenges in transferring models across galaxy populations.
ER -