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REVIEW 3 major objections 6 minor 69 references

Machine learning based Photometric Redshifts for Galaxies in the North Ecliptic Pole Wide field: catalogs of spectroscopic and photometric redshifts

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

Pith's one-line read The paper claims that a random forest trained on 4,421 spectroscopic galaxies—including 2,572 new MMT/Hectospec redshifts—produces photometric redshifts for 77,755 sources in the AKARI North Ecliptic Pole Wide field with dispersion 0.028…

desk verdict Solid catalog paper with real new spec-z data; the headline accuracy claims need a population-matched caveat. read the letter →

arxiv 2502.00692 v1 pith:QRIDK6FD submitted 2025-02-02 astro-ph.CO astro-ph.GA

classification astro-ph.COastro-ph.GA
keywords photometricredshiftsrandomforestNorthEclipticPoleAKARIsurveyspectroscopicMMT/Hectospecgalaxycataloguncertaintycalibration
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

Photometric redshifts—galaxy distances estimated from multi-band colors rather than spectra—are the only way to map the North Ecliptic Pole Wide (NEPW) field in bulk, since spectroscopy covers only a bright subset. This paper expands that subset with 2,572 new MMT/Hectospec measurements, combines them with earlier work into 4,421 galaxies with $z_{\rm spec}<2$, and trains a random forest to convert 26-band photometry into redshifts for all 77,755 sources with Subaru/HSC photometry. On held-out spectroscopic galaxies the model achieves a dispersion of $\sigma_{\Delta z/(1+z)}=0.028$, a catastrophic-outlier fraction of $\eta=7.3\%$, and a bias of $-0.01$, all better than the SED-fitting redshifts previously published for the same field. The paper further argues that the standard deviation of the 1,000 decision-tree predictions, $\sigma_{\rm DT}$, tracks both the probability of a bad redshift and the size of the measurement error, turning point predictions into per-object uncertainties. If these claims hold, the field gains the first homogeneous redshift catalog reaching $r\approx26$ and $z\sim2$, a foundation for the upcoming JWST, Euclid, and SPHEREx studies of this region.

What carries the argument

The load-bearing object is the random forest regression model: an ensemble of 1,000 decision trees, each grown on a bootstrap sample of the 4,421 spectroscopic galaxies and splitting on a random subset of the 56 input features (26 magnitudes, their uncertainties, and four Subaru/HSC colors: $g-r$, $r-i$, $i-z$, $z-Y$). Missing photometry is replaced with a dummy value of 1000 so the tree learns to ignore absent bands. The mechanism that carries the uncertainty claim is $\sigma_{\rm DT}$, the standard deviation of the 1,000 individual tree outputs for a single object; the paper calibrates $\sigma_{\rm DT}$ against the observed $(z_{\rm spec}-z_{\rm phot})$ scatter to produce a per-source error $\sigma_{spz}$, and validates that the normalized residuals are standard normal. The decision tree at the base is defined by recursive splits chosen to minimize the residual sum of squares in redshift.

What would settle it

Obtain deep spectra for a few hundred $r>23$ galaxies in the NEPW field that the catalog assigns $z>0.8$ with $\sigma_{\rm DT}<0.3$. If the catastrophic-outlier fraction among those objects is much larger than the quoted 7.3%, or if $(z_{\rm spec}-z_{\rm phot})/\sigma_{spz}$ deviates strongly from a standard normal, the generalization and uncertainty-calibration claims fail.

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Extended reading notes

Core claim

The central claim is that a deliberately simple random forest, trained only on photometry and spectroscopic redshifts, matches or beats template-based SED fitting in the NEPW field while also supplying an error estimate. Compared against $z_{\rm spec}$ for held-out galaxies, $z_{\rm phot,RF}$ has dispersion $\sigma_{\Delta z/(1+z)}=0.028$, outlier fraction $\eta=7.3\%$, and bias $\langle\Delta z/(1+z)\rangle=-0.01$; the SED-fit comparison point is $0.049$ and $8.9\%$, respectively. The paper's second claim is that $\sigma_{\rm DT}$—the spread among the 1,000 individual tree predictions for one object—is a usable reliability indicator: the cumulative catastrophic-outlier fraction rises with $\sigma_{\rm DT}$, a cut at $\sigma_{\rm DT}=0.3$ keeps the outlier fraction below about five percent for the 52,167 sources retained, and a redshift-dependent calibration $\sigma_{spz}(\sigma_{\rm DT})$ makes $(z_{\rm spec}-z_{\rm phot})/\sigma_{spz}$ approximately standard normal. The paper also reports that accuracy is insensitive to which photometric details enter the input, including magnitude uncertainties, dummy values for missing bands, and whether colors are included.

Load-bearing premise

The accuracy numbers come from a held-out subset of the spectroscopic sample, which is mostly bright ($r<21$), 9-$\mu$m-selected, and at $z<0.8$; the paper assumes those numbers describe the full 77,755-source catalog, which reaches $r\approx26$ and $z\sim2$ where training examples are scarce.

Editorial extensions

If this is right

  • The NEPW band-merged catalog gains a homogeneous redshift for all 77,755 sources with HSC photometry, so infrared luminosity functions, cluster searches, and AGN-host studies can be carried out without relying on sparse spectroscopy.
  • Users can apply the $\sigma_{\rm DT}<0.3$ criterion to select a subset of 52,167 galaxies whose catastrophic-outlier fraction is below about five percent.
  • The random forest outperforms SED fitting on the same 26-band photometry in this field, suggesting machine-learning redshifts should be the default for the NEPW catalog.
  • Each catalog entry carries a per-object uncertainty $\sigma_{spz}$, so downstream measurements can propagate redshift errors rather than applying a single global scatter.
  • Because the accuracy metrics are insensitive to which input features are used, the model is robust to the heterogeneous, partially missing photometry that plagues multi-band merging.

Reading between the lines

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

  • The $\sigma_{\rm DT}$-to-uncertainty calibration is a generic byproduct of random forests, so the same recipe could attach error bars to any random-forest regression, not just photometric redshifts.
  • Since the training sample is dominated by bright, 9-$\mu$m-selected, $z<0.8$ galaxies, the quoted accuracy probably does not hold at the faint, high-redshift end; a dedicated spectroscopic campaign at $r>23$, $z>0.8$ would be the natural stress test.
  • The top-ranked input features are all Subaru/HSC bands, implying that further gains, especially at high redshift, require deeper near-infrared photometry rather than more optical band choices.
  • The same pipeline, retrained on the new sample, could be transplanted directly to other AKARI or Euclid fields, producing catalogs whose errors are calibrated in a consistent way.
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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

3 major / 6 minor

Summary. This paper presents new MMT/Hectospec spectroscopic redshifts in the North Ecliptic Pole Wide (NEPW) field, combines them with literature redshifts to form a training sample of 4,421 galaxies at z<2, and trains a random forest on 26-band photometry (plus four HSC colors and magnitude uncertainties) to estimate photometric redshifts for 77,555 HSC-detected sources. The authors report good test-set performance relative to held-out spectroscopic redshifts: dispersion σ_{Δz/(1+z)}=0.028, outlier fraction η=7.3%, and bias −0.01 (Section 3.3, Figure 4). They also propose using the spread of individual decision-tree predictions, σ_DT, to flag unreliable measurements and to assign per-object uncertainties (Section 3.4, Figures 5 and 7), and they test robustness to input-feature choices and to problematic photometry (Sections 4.3 and 4.5). The final product is a value-added catalog with photometric and spectroscopic redshifts, intended as a legacy resource for the NEPW field.

Significance. If the quoted accuracy holds for the full catalog, this is a useful legacy dataset for a field that will be targeted by JWST, Euclid, and SPHEREx, and the 2,572 new spectroscopic redshifts are a valuable contribution in their own right. The random forest approach is clearly described and the robustness tests over input-feature variations are a strength. The central weakness is that the headline accuracy metrics are measured only on the spectroscopic training population, whose selection function differs from that of the full 77,555-source catalog; the paper itself shows growing residuals for fainter and higher-redshift bins. That limitation does not invalidate the catalog for the bright, low-redshift population, but it does mean the accuracy claims need to be re-framed or supplemented before the paper can be accepted.

major comments (3)
  1. [Section 3.3, Figure 4, and Section 2.2] The headline accuracy metrics (σ=0.028, η=7.3%, bias=−0.01) are derived from 100 random 10% splits of the 4,421 spectroscopic galaxies, but this validation sample inherits the selection function described in Section 2.2: the MMT targets were mainly AKARI 9 µm selected galaxies with r<21, supplemented by r-bright galaxies, while the photometric catalog of 77,555 sources reaches r~26 and includes sources without 9 µm detections. The paper's own Figure 10 shows that the residual zspec−zphot increases for fainter and higher-redshift bins, and Section 4.4 notes that only 8% of the training set is at z>0.8. The claim that the quoted accuracy characterizes the full catalog is therefore not supported by the presented validation. Please provide accuracy metrics in bins of r-band magnitude and redshift (with selection-matched weights if possible), or explicitly state in the abstract and catalog description that the metrics apply only to the spectroscopic-like population.
  2. [Section 4.4 and abstract] The paper states in Section 4.4 that the random forest is only able to interpolate and that the training set spans zspec=[0,1.758], yet the abstract advertises photometric redshifts 'up to z~2'. Predictions for sources at z>1.758 are extrapolations with no validation points, so the advertised redshift range is inconsistent with the validated range. I request that the redshift range of the catalog be limited to the training support, or that high-redshift validation be provided, with extrapolated sources clearly flagged or removed from the accuracy claims.
  3. [Section 3.4, Figures 5 and 7] The uncertainty calibration is self-referential. The σ_spz(σ_DT) relation is defined from the 1σ scatter of (zspec−zphot) in bins of σ_DT using the uncertainty test sample, and then the right panel of Figure 7 validates the Gaussianity of the normalized residuals on that same sample. In addition, the reliability threshold σ_DT=0.3 is chosen from the same cumulative outlier curve in Figure 5. This procedure cannot detect optimistic bias from overfitting to the calibration sample. Please validate the uncertainty and reliability estimates on an independent sample, for example via a nested cross-validation or a separate calibration split, and report the empirical coverage of the quoted 1σ uncertainties.
minor comments (6)
  1. [Section 5 and Table 2] The number of catalog sources is listed as 77,555 in the abstract and Table 2, but the first bullet of Section 5 says 77,775; please harmonize the count.
  2. [Figure 10] The caption of Figure 10 describes redshift subsamples 0.0<z<0.3, 0.3<z<0.7, and 0.7<z<2.0, while the main text and figure legend use 0.0–0.4, 0.4–0.8, and 0.8–2.0; these boundaries should be made consistent.
  3. [Table 4] The row for Set_no err is confusing: the 'magnitude uncertainty' column says 'excluded', but the 'included HSC photometry' column still lists 'mag., mag. uncertainties, and colors'; revise the table so that each row clearly states what is included and what is excluded.
  4. [Section 2.2] The redshift-measuring package RVSNUpy is described only as forthcoming work and is not made publicly available; for reproducibility, please provide a software repository or a detailed algorithm description with the paper.
  5. [Section 4.1 and Figure 8] Only the top five permutation importances are displayed; please provide a full list or electronic table of importances for all 56 input features so that the insignificance of the remaining features can be verified.
  6. [Abstract and Table 2] The survey area is given as 5.4 deg² in the abstract and Section 1, but Table 2 lists 5.6 deg²; the quoted area should be consistent across the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline photo-z accuracy is measured against external spectroscopic redshifts.

full rationale

The central claim — that the random forest photo-z estimates have dispersion 0.028, outlier fraction 7.3%, and bias -0.01 — is evaluated by comparing held-out random-forest predictions with spectroscopic redshifts (Section 3.3, Figure 4). Spectroscopic redshifts are external to the model and were not constructed from the photo-z predictions, so the accuracy metric is an independent benchmark. Hyperparameters are tuned on cross-validated test splits, which may cause mild optimism but is not circular. The sigma_DT uncertainty calibration (Section 3.4) is an empirical relation between tree-scatter and residual scatter, fitted and then checked on the same cross-validated spectroscopic sample; this is a self-calibration rather than an independent validation, but it does not determine the headline redshift accuracy and is not a fitted parameter renamed as a prediction. The generalization concern — that the spectroscopic training sample is brighter and lower-redshift than the full 77,755-source catalog, while the random forest can only interpolate within z <= 1.758 — is a real correctness risk, explicitly acknowledged in Section 4.4, but it is not circularity under the review criteria. No load-bearing step reduces to its own inputs by construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim depends mainly on the fidelity of the input photometry and spectroscopic labels, on the validity of the dummy-value imputation, and on the representativeness of the training sample for the full catalog. No new physical entities are introduced. The model hyperparameters and the sigma_DT reliability threshold are data-tuned choices, not physical parameters.

free parameters (6)
  • depth (max tree depth) = 25
    Chosen from the RMS convergence test in Figure 3 left; a hyperparameter tuned on the training/validation split.
  • n_estimators (number of bootstrapped sub-training sets) = 1000
    Chosen from RMS convergence in Figure 3 right; tuned on validation.
  • max_features (features per split) = 7 (sqrt(56))
    Chosen by the sqrt rule from James et al. 2021; not tuned on data, but a modeling choice.
  • dummy value for missing photometry = 1000
    Chosen by hand to be far from real photometry; robustness tested with -1000, -100, 100 variants in Section 4.3.
  • sigma_DT reliability threshold = 0.3
    Chosen in Section 3.4 from Figure 5 so that the cumulative outlier fraction stays below 5% for 98% of the sample; a data-derived criterion applied to the catalog.
  • redshift range cut = z < 2
    Selected in Section 2.2 because the number of high-z galaxies is too small; this limits the claimed catalog range to z ~ 2 even though training max is z=1.758.
assumptions (5)
  • domain assumption The input 26-band photometry from the NEPW band-merged catalog (Kim et al. 2021b) is accurate and consistently calibrated across bands.
    All photometric redshift estimates rest on this photometry; problematic HSC photometry is tested in Section 4.5 but the general reliability of the catalog is taken from prior work.
  • domain assumption The compiled spectroscopic redshifts from the literature and from this survey are accurate enough to serve as training labels.
    The random forest is trained on these redshifts; any systematic error in the spec-z sample propagates into the photo-z estimates. Quoted r-value cuts (r>4 absorption, r>20 emission) are used in Section 2.2.
  • ad hoc to paper Missing photometry values can be replaced with an extreme dummy value (1000) without systematically biasing the predictions.
    The dummy-value replacement is a modeling choice tested in Section 4.3, but the test sets are drawn from the spectroscopic sample and may not cover all missing-data patterns in the full catalog.
  • standard math The random forest interpolates within the training feature space but cannot extrapolate beyond it.
    This is stated in Section 4.4; it underlies the caveat that z~2 estimates exceed the training maximum of z=1.758.
  • domain assumption The spectroscopic training sample is representative of the full 77,755 source catalog in feature space.
    The accuracy metrics are computed on held-out spectroscopic galaxies, and are assumed to transfer to the full catalog. The training targets were selected from AKARI 9 micron and r-band bright galaxies (Section 2.2), which may bias representativeness.

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Cite this review

Pith. "Pith review of Machine learning based Photometric Redshifts for Galaxies in the North Ecliptic Pole Wide field: catalogs of spectroscopic and photometric redshifts." pith.science (2026). https://pith.science/paper/QRIDK6FD

@misc{pith2026250200692,
  author       = {Pith},
  title        = {Pith review of: Machine learning based Photometric Redshifts for Galaxies in the North Ecliptic Pole Wide field: catalogs of spectroscopic and photometric redshifts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QRIDK6FD}},
  note         = {Machine review of arXiv:2502.00692}
}
read the original abstract

We perform an MMT/Hectospec redshift survey of the North Ecliptic Pole Wide (NEPW) field covering 5.4 square degrees, and use it to estimate the photometric redshifts for the sources without spectroscopic redshifts. By combining 2572 newly measured redshifts from our survey with existing data from the literature, we create a large sample of 4421 galaxies with spectroscopic redshifts in the NEPW field. Using this sample, we estimate photometric redshifts of 77755 sources in the band-merged catalog of the NEPW field with a random forest model. The estimated photometric redshifts are generally consistent with the spectroscopic redshifts, with a dispersion of 0.028, an outlier fraction of 7.3%, and a bias of -0.01. We find that the standard deviation of the prediction from each decision tree in the random forest model can be used to infer the fraction of catastrophic outliers and the measurement uncertainties. We test various combinations of input observables, including colors and magnitude uncertainties, and find that the details of these various combinations do not change the prediction accuracy much. As a result, we provide a catalog of 77755 sources in the NEPW field, which includes both spectroscopic and photometric redshifts up to z~2. This dataset has significant legacy value for studies in the NEPW region, especially with upcoming space missions such as JWST, Euclid, and SPHEREx.

Figures

Figures reproduced from arXiv: 2502.00692 by the authors.

Figure 1
Figure 1. The field of view of our own spectroscopic survey of the NEPW field. The gray dots indicate the sources iden￾tified in the infrared range in the AKARI NEPW field sur￾vey. We plot 10 percent of all samples detected by AKARAI for clarity. Blue dots show the sources with spectroscopic redshifts measured in previous studies. Orange dots display the sources with spectroscopic redshifts measured from our MMT/Hectospec sur… view at source ↗
Figure 2
Figure 2. Properties of spectroscopically observed sources in our NEPW sample as a function of spectroscopic redshifts. The top panel shows the distribution of (a) all available spectroscopic redshifts and (b) spectroscopic redshifts measured in this study. The vertical dashed line indicates the median of the redshifts. The middle panel shows the RVSNUpy r-value distribution as a function of the spectroscopic redshift measure… view at source ↗
Figure 3
Figure 3. (Left) RMS of the redshift measurements for training (blue) and test (orange) sets as a function of the depth. The shaded region displays the 1σ distributions of RMS. The dashed vertical line denotes the depth of 25. (Right) RMS of the test set as a function of the number of bootstrapped sub-training sets. The dashed vertical line denotes 1000 of the number of bootstrapped sub-training sets. i-z, z-Y ). We use color… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: (Left) Comparison between the photometric redshifts measured with our random forest model (zphot,RF) and the spectroscopic redshifts (zspec). Orange cross symbols indicate the catastrophic outliers with |∆z|/(1 + z) > 0.15. The quoted numbers are the accuracy metrics o…
Figure 5
Figure 5. Figure 5: Cumulative fraction of catastrophic outliers and cumulative number of photometric measurements as a func￾tion of σDT. The orange line and shaded region indicate the cumulative fractions of catastrophic outliers and their 1σ scatter. The black line and shaded region ind…
Figure 6
Figure 6. Figure 6: shows the comparison between zphot,RF and zphot,SED for the two groups separated at σDT = 0.3. In general, zphot,RF with σDT < 0.3 are consistent with zphot,SED. The objects with inconsistent zphot,RF and zphot,SED have σDT larger than 0.3. At zphot,SED < 0.8, 0.0 0.5 …
Figure 7
Figure 7. Figure 7: (Left) Difference between zspec and zphot,RF as a function of σDT. For clarity, we display only 5 percent of the data points. The blue line indicates the mean distribution, and the orange and green area corresponds to 1σspz and 3σspz distributions. The vertical dashed …
Figure 8
Figure 8. Figure 8: shows the result of the permutation impor￾tance computation for our 56 input features. There are five features with permutation importance larger than 0.03; yHSC, iHSC, zHSC, rHSC, gHSC −rHSC. Not surpris￾ingly, all top five features are from HSC photometry be￾cause al…
Figure 9
Figure 9. Figure 9: The accuracy metrics of the photometric redshift estimation depends on the input features. The top, middle, and bottom panels show the medians of σz/(1+z), η, and ⟨∆z/(1 + z)⟩ of each set with their 1σ scatter, respectively. The dotted lines in the top two panels indic…
Figure 11
Figure 11. Figure 11: shows the differences between HSC z -band and Maidanak I-band magnitudes normalized by their uncertainties: (zHSC - IMaidanak)/p δz2 HSC + δI2 Maidanak for the sources with overlapped photometry. The dashed line shows the best-fit Gaussian to the distribution. There a…
Figure 12
Figure 12. Figure 12: The accuracy metrics of the photometric redshift estimation for five different input datasets that handle the problematic HSC photometry, differently. The top, middle, and below panels show the medians of σz/(1+z), η, and ⟨∆z/(1 + z)⟩ of each set with their 1σ scatter…

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