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Photometric redshifts for X-ray-selected active galactic nuclei in the eROSITA era

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Machine learning matches template fitting for photometric redshifts of X-ray-selected AGN, with more conservative error estimates.

desk verdict Solid ML-vs-SED photo-z comparison with a released catalogue; the central claim holds, but the eROSITA projection is conditional on a training sample that the authors' own new test shows is not yet in hand. read the letter →

arxiv 1909.00606 v1 pith:A5ZOF4D3 submitted 2019-09-02 astro-ph.IM astro-ph.GA

M. Brescia , M. Salvato , S. Cavuoti , T. T. Ananna , G. Riccio , S. M. LaMassa , C. M. Urry , G. Longo This is my paper · ORCID
classification astro-ph.IMastro-ph.GA
keywords photometricredshiftsactivegalacticnucleieROSITAmachinelearningneuralnetworksSEDfittingStripe82Xredshiftprobabilitydensityfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that machine learning can produce photometric redshifts for X-ray-selected active galactic nuclei (AGN) that are just as accurate and reliable as the traditional template-fitting approach, even though AGN are notoriously hard to fit because both the host galaxy and the nucleus contribute light. This matters because eROSITA will detect about three million AGN across the whole sky and needs quick, trustworthy distance estimates from patchy multi-wavelength data. The authors test this on the Stripe 82X field, which matches eROSITA's depth and data coverage, using the MLPQNA neural network. They find that when optical, near-infrared, and mid-infrared photometry are all available, machine learning and SED fitting perform comparably in accuracy, outlier fraction, and the realism of redshift probability distributions. They also find that the machine-learned probability distributions are more conservative, giving faint and unreliable sources appropriately low confidence, whereas template fitting can be overconfident for its outliers.

What carries the argument

The central object is MLPQNA, a multi-layer perceptron neural network trained with a quasi-Newton algorithm, which maps photometric magnitudes and colours into a redshift estimate. Around it, the paper uses PhiLAB, a hybrid feature-selection algorithm based on shadow features and LASSO, to identify the most informative photometric features, and METAPHOR, a workflow that perturbs the photometry 999 times to build a redshift probability density function from 1000 machine-learning estimates.

What would settle it

Go to the released photo-z catalogue and compare the merged MLPQNA photo-z against the 257 new spectroscopic redshifts from LaMassa et al. (2019): the paper reports $\sigma_{\rm NMAD}$ of 0.154 and an outlier fraction of 38.4%, versus 0.056 and 12.7% on the original training-representative sample. If that fainter sample is representative of what eROSITA will detect, the paper's claim that reliable photo-z can be obtained for a large fraction of eROSITA AGN is contradicted by its own numbers.

Watch

Extended reading notes

Core claim

On the central claim: in Stripe 82X, when SDSS, VHS, WISE, and IRAC photometry are all available, the MLPQNA neural network reaches a normalized median absolute deviation of $\sigma_{\rm NMAD}=0.056$ and an outlier fraction of 12.7 percent, compared with 0.059 and 13.3 percent for the SED-fitting catalogue it is tested against. At the X-ray flux limit that eROSITA will reach, the machine-learning results are slightly better—fewer outliers and no systematic bias—when the training sample is restricted to the bright sources eROSITA will detect. The paper also claims that the redshift probability density functions produced by METAPHOR are reliable and generally more conservative than those from SED fitting, which often assigns high confidence to its own outliers, and it recommends that science use the full probability distributions rather than point estimates. It explicitly states that the remaining bottleneck is the representativeness of the training sample: on a blind test of 257 new fainter sources, both methods degrade, with MLPQNA's outlier fraction rising to 32–41 percent.

Load-bearing premise

The paper's central eROSITA projection assumes that a large, representative spectroscopic training sample covering the full range of AGN types, luminosities, and redshifts can be assembled; the blind test on the 257 new fainter sources shows that when this fails, ML accuracy degrades to outlier fractions of 32–41%.

Editorial extensions

If this is right

  • If eROSITA has a representative spectroscopic training set, reliable ML photometric redshifts can be computed for roughly two-thirds of its AGN using current all-sky photometry, before optical spectroscopy arrives.
  • The gap between the 12.7% outlier fraction on the original sample and the 32–41% on the fainter blind test means training representativeness is the deciding factor for the eROSITA forecast.
  • With the already-deeper unWISE data and future SpherEx coverage, the accuracy of ML photo-z should improve further.
  • When fewer photometric bands are available, SED fitting remains the more reliable method, so the two approaches are complementary rather than interchangeable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The disagreement between ML and SED-fitting outliers could be used as a flag for peculiar or variable sources, since the two methods rarely fail on the same objects.
  • The feature analysis's finding that colours dominate over single magnitudes suggests that other AGN surveys should prioritise multi-band colour coverage over deeper single-band photometry.
  • The overconfident PDZ from template fitting in broad-band-only data implies that luminosity functions and clustering measurements built from such fits may underestimate their redshift errors; this can be tested by comparing to samples with narrow-band photometry.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper tests whether machine-learning photometric redshifts (photo-z), computed with the MLPQNA neural network, are competitive with SED-fitting (LePhare) for X-ray-selected AGN, using the multi-wavelength Stripe 82X catalogue. The authors perform a feature-selection analysis with PhiLAB, compute photo-z for various photometric sub-samples, derive redshift probability density functions with METAPHOR, and release a photo-z catalogue. Their main quantitative claim is that when optical, near-IR, and mid-IR photometry are all available, MLPQNA and LePhare perform comparably in accuracy, outlier fraction, and PDZ realism, with both methods degrading when photometric coverage is reduced. The paper also projects that reliable photo-z can be obtained for a large fraction of eROSITA sources in the Southern hemisphere before spectroscopic follow-up, conditional on assembling a representative spectroscopic training sample.

Significance. If the underlying comparison holds, the paper is a useful step toward producing photo-z for the roughly three million AGN expected from eROSITA, where SED fitting alone may be too slow or too template-dependent. The manuscript's strengths include a released photo-z catalogue, a blind four-fold cross-validation design on the original sample, and an external test on 257 newly obtained spectroscopic redshifts that the authors themselves use to expose the limitations of a non-representative training set. The explicit discussion of the training-sample requirement in Section 8 is honest and is a constructive contribution to the methodology for AGN photo-z. The feature-selection analysis with PhiLAB also provides practical guidance on which photometric bands and colours matter most. However, as discussed below, the feature-selection procedure is not fully blind and the eROSITA-scale extrapolation is not yet supported by the data; these issues are fixable but require revision.

major comments (2)
  1. [Section 3.1 and Section 4, Tables 3-9] The feature-selection step with PhiLAB is performed on the full BEST sample before the four-fold split into training and test folds. Because the same objects that later appear in the test folds contribute to the selection of the feature set, the reported sigma_NMAD and outlier fractions for MLPQNA are not obtained under a fully blind procedure: the model is blind to the test redshifts, but the feature engineering is not. This inflates the apparent performance of MLPQNA and weakens the direct comparison with LePhare. The authors should either perform feature selection inside each training fold (nested cross-validation) or provide evidence that the feature ranking is insensitive to the inclusion of the test-fold objects.
  2. [Section 6, Table 10, and Section 8] The paper's central eROSITA projection is conditional on assembling a spectroscopic training sample representative of the eROSITA population, but that condition is not demonstrated. The paper's own Table 10 shows the consequence when the condition fails: for the 257 new fainter sources from LaMassa et al. (2019), sigma_NMAD rises to 0.104-0.163 and the outlier fraction to 32-41% for MLPQNA across photometric subsets. This is the most direct empirical evidence available about extrapolation to the faint eROSITA population, and it does not support the statement that reliable photo-z can be obtained for a large fraction of Southern-hemisphere sources before spectroscopic follow-up. The authors should either temper the conclusion to present this as a forward requirement rather than an achieved capability, or provide a concrete assessment of how the required representative training sample could be assembled and what sample size or completeness would mitigate the degradation seen in Table 10.
minor comments (5)
  1. [Section 6 and Table 10] The number of new spectroscopic redshifts is given as 257 in the text, 258 in Table 10, and 258 in the caption of Figure 2; please make these numbers consistent.
  2. [Section 5.1, Table 5] The photometric-error cut experiments change both the sample size and the redshift distribution, so the small variations in sigma_NMAD and eta among the three cuts are not clearly significant; a brief statement about the statistical uncertainty of these differences would help.
  3. [Section 7, Table 11] The comparison of METAPHOR and LePhare PDZs depends on the chosen bin sizes (0.01 for both, but with different ranges and normalization conventions). The paper acknowledges this in part, but the claim that METAPHOR is 'superior' in all classes would be strengthened by a sensitivity test to binning.
  4. [Table 8 and Table 9] Table 9 reports statistics for sources in common across all samples but does not state the number of such sources; adding this number would make the table clearer.
  5. [Section 1] The phrase 'they are not the same for the two methods' is vague; specifying whether the difference refers to the outlier populations, the PDZ widths, or the systematic offsets would make the abstract more informative.

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity in the central ML-vs-SED comparison; minor feature-selection-before-split leakage in the parameter-space optimization keeps the score at 2.

  1. fitted input called prediction [Section 4, Tables 3-4, with the k-fold protocol described in Section 3.4]
    "Using ΦLAB on the BE ST sample, we valuated the most relevant features... The photo-z estimation experiment performed with the largest selected parameter space... provided statistical results comparable with the BE ST magcolopt case... the knowledge base has been manually split into 4 not-overlapped sub-sets. In this way by taking each time 3 of these sub-sets as training set and leaving the fourth as blind test set, an overall blind test on the entire knowledge base sample can be performed... All quantities are calculated on blind test sets only."

    ΦLAB performs a supervised feature-selection regression (shadow features plus LASSO) on the BEST sample using the spectroscopic redshifts of all objects, before the 4-fold split described in Sec. 3.4. The folds used to report 'blind test sets only' metrics therefore contain sources whose zspec already influenced which photometric features were selected. The improvement attributed to feature selection (σNMAD 0.079→0.056 and η 16.09→12.74 in Table 3, with similar gains in Table 4) is thus partly in-sample: the feature set is a fitted input that was not re-selected inside each training fold.

full rationale

The central claim that MLPQNA and SED fitting perform comparably for X-ray-selected AGN is anchored to external spectroscopic redshifts: accuracy, outlier fractions, and PDZ reliability are all measured against zspec from SDSS/BOSS/eBOSS and the independent LaMassa et al. (2019) sample. That benchmark is not circular even though the comparison SED redshifts come from A17, a prior paper with overlapping authors, because both methods are scored on the same external zspec rather than on each other. The self-citations to MLPQNA, METAPHOR, and ΦLAB describe the authors' own algorithms, but the algorithms are evaluated on independent data and the citations do not force the outcome. The eROSITA projection is explicitly conditional on assembling a representative training sample and is therefore a stated precondition, not a circular justification; its weakness is that the precondition is not yet demonstrated, which is a correctness risk rather than circularity. The only concrete circularity-adjacent issue is the feature-selection-before-split protocol: ΦLAB selected features using the full BEST sample, after which 4-fold cross-validation was reported as blind. This leaks test-set label information into the feature choice and makes the claimed improvement from feature optimization partly in-sample. It does not invalidate the external-zspec anchoring of the main photo-z comparison, so the score is 2 rather than higher.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. The free parameters are analysis choices and undisclosed model hyperparameters. The main inherited assumption is that Stripe 82X data and a future representative spectroscopic sample will mirror the eROSITA all-sky situation, which the paper itself shows is not yet satisfied.

free parameters (3)
  • MLPQNA hyperparameters (hidden layers, nodes, learning rate, epochs, regularization)
    The architecture and training parameters are not specified in the paper; they are tuned by the authors and referenced from earlier work, but no grid or validation procedure is disclosed.
  • Photometric error threshold for sub-sampling = 0.3 mag
    Section 5.1 selects 0.3 as the best tradeoff after comparing 0.3, 0.25 and 0.2 mag cuts, although sigma does not improve monotonically with tighter cuts.
  • Feature set for photo-z computation = BESTmagcolopt (20 features)
    Section 4 chooses the mixed magnitude-plus-colour parameter space as the best candidate; this choice is made using PhiLAB on the full BEST sample prior to cross-validation.
assumptions (4)
  • domain assumption Stripe 82X ancillary photometry represents what will be available for eROSITA over the Southern sky.
    Sections 1 and 8 assume the wavelength coverage and depth of available all-sky surveys (PanStarrs, SkyMapper, DES, VHS, WISE) will mimic the Stripe 82X data, enabling extrapolation of the measured accuracy to eROSITA.
  • domain assumption The spectroscopic sample available at the time of A17 is representative of the target population.
    Section 6 relies on this for the training set; the later blind test with 257 fainter sources from LaMassa et al. (2019) shows this assumption is violated for fainter objects.
  • ad hoc to paper Feature analysis performed on the BEST (yellow-area) sample applies unchanged to all other photometric sub-samples.
    Section 5 states the authors assume the feature analysis is not affected by the different sub-samples, because the samples are not large enough to re-run the analysis per sub-sample.
  • domain assumption Sources missing photometry in some bands can be handled by subsetting rather than imputation, with the resulting sub-samples remaining jointly usable.
    Section 3 explains that magnitudes instead of fluxes force exclusion of sources with missing bands; the paper assumes the subsets are adequate for training and testing.

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Cite this review

Pith. "Pith review of Photometric redshifts for X-ray-selected active galactic nuclei in the eROSITA era." pith.science (2026). https://pith.science/paper/A5ZOF4D3

@misc{pith2026190900606,
  author       = {Pith},
  title        = {Pith review of: Photometric redshifts for X-ray-selected active galactic nuclei in the eROSITA era},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A5ZOF4D3}},
  note         = {Machine review of arXiv:1909.00606}
}
read the original abstract

With the launch of eROSITA (extended Roentgen Survey with an Imaging Telescope Array), successfully occurred on 2019 July 13, we are facing the challenge of computing reliable photometric redshifts for 3 million of active galactic nuclei (AGNs) over the entire sky, having available only patchy and inhomogeneous ancillary data. While we have a good understanding of the photo-z quality obtainable for AGN using spectral energy distribution (SED)-fitting technique, we tested the capability of machine learning (ML), usually reliable in computing photo-z for QSO in wide and shallow areas with rich spectroscopic samples. Using MLPQNA as example of ML, we computed photo-z for the X-ray-selected sources in Stripe 82X, using the publicly available photometric and spectroscopic catalogues. Stripe 82X is at least as deep as eROSITA will be and wide enough to include also rare and bright AGNs. In addition, the availability of ancillary data mimics what can be available in the whole sky. We found that when optical, and near- and mid-infrared data are available, ML and SED fitting perform comparably well in terms of overall accuracy, realistic redshift probability density functions, and fraction of outliers, although they are not the same for the two methods. The results could further improve if the photometry available is accurate and including morphological information. Assuming that we can gather sufficient spectroscopy to build a representative training sample, with the current photometry coverage we can obtain reliable photo-z for a large fraction of sources in the Southern hemisphere well before the spectroscopic follow-up, thus timely enabling the eROSITA science return. The photo-z catalogue is released here.

Figures

Figures reproduced from arXiv: 1909.00606 by the authors.

Figure 1
Figure 1. Map of the original multi-wavelength coverage of Stripe 82X area discussed in A17. The total area extends for ∼ 2.5° in Declination and 120° in Right Ascension. The dots represent X-ray sources, respectively, from XMM-Newton AO13 (red), AO10 (blue), archival XMM-Newton sources (yellow) and Chandra sources (black). While standard photo-z are generated for the entire area (in red), the selection of the best features d… view at source ↗
Figure 2
Figure 2. Redshift and magnitude distribution for the sources with spectroscopic redshift. The blue sources were presented in A17 and have been used in this work as training and blind test samples. The 258 yellow sources are on average fainter and were recently presented in LaMassa et al. (2019). They are used as additional blind test sample. 3 THE ALGORITHMS We first performed a feature analysis on the sub-sample of sources … view at source ↗
Figure 3
Figure 3. Results of the feature analysis performed with ΦLAB. The importance of each feature is estimated for the case in which only magnitudes are considered for the sample BEST magopt [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Results of the feature analysis performed with ΦLAB. The importance of each feature is estimated for the case in which magnitudes and colours are considered for the sample BESTmag￾colopt. This is demonstrated in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Comparison between spectroscopic redshift and photo-z for the sources cut at the eROSITA flux and divided on the basis of available photometric points. For comparison, the result from A17 is reported in the lower right panel of the figure. By comparing the accuracy and…
Figure 6
Figure 6. Figure 6: The same as the last two bottom-right panels of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Difference between spectroscopic redshift and photo-z computed via MLPQNA and LePhare for the sub-sample of 1689 sources with SDSS, VHS, WISE and IRAC photometry, regardless their X-ray flux. Sources that are outliers for MLPQNA (LePhare) are plot in cyan (orange). For…
Figure 8
Figure 8. Figure 8: One-to-one comparison of accuracy for photo-z com￾puted via MLPQNA with different combinations of photometry. For this plot only sources present in all the subsamples have ben used. using METAPHOR with respect to the PDZ computed in A17 with LePhare. For the analysis d…
Figure 9
Figure 9. Figure 9: Details of the comparison between photo-z computed via SED fitting (A17) and MLPQNA for the sample for which spectro￾scopic information is, respectively, available (left panel) and not available (right panel). The cyan points indicate the sources for which the redshift…
Figure 10
Figure 10. Figure 10: Example of PDZ obtained by METAPHOR and Le￾Phare for the object ID1431 (SDSS J221448.69+002508.7). The true redshift is represented by the black dashed line. The coloured areas represent the PDZ BEST. In this specific case, the PDZs are both limited to the redshift ra…
Figure 11
Figure 11. Figure 11: PDZ BEST cumulative distribution for the entire spectroscopic sample (left) and for the outliers in the respective sub￾samples used in this work (right), compared with the results from A17. The comparison is missing sdssVI and sdssI, only for brevity. While the majori…

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Forward citations

Cited by 1 Pith paper

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.