Photometric redshift estimation using spectral connectivity analysis
Bibliographic record
Abstract
The development of fast and accurate methods of photometric redshift estimation is a vital step towards being able to fully utilize the data of next-generation surveys within precision cosmology. In this paper, we apply a specific approach to spectral connectivity analysis (SCA) called diffusion map. SCA is a class of non-linear techniques for transforming observed data (e.g. photometric colours for each galaxy, where the data lie on a complex subset of p-dimensional space) to a simpler, more natural coordinate system wherein we apply regression to make redshift predictions. In previous applications of SCA to other astronomical problems, we demonstrate its superiority vis-a-vis the principal components analysis, a standard linear technique for transforming data. As SCA relies upon eigen-decomposition, our training set size is limited to ≲104 galaxies; we use the Nyström extension to quickly estimate diffusion coordinates for objects not in the training set. We apply our method to 350 738 Sloan Digital Sky Survey (SDSS) main sample galaxies, 29 816 SDSS luminous red galaxies and 5223 galaxies from DEEP2 with Canada–France–Hawaii Telescope Legacy Survey ugriz photometry. For all three data sets, we achieve prediction accuracies at par with previous analyses, and find that the use of the Nyström extension leads to a negligible loss of prediction accuracy relative to that achieved with the training sets. As in some previous analyses, we observe that our predictions are generally too high (low) in the low (high) redshift regimes. We demonstrate that this is a manifestation of attenuation bias, wherein measurement error (i.e. uncertainty in diffusion coordinates due to uncertainty in the measured fluxes/magnitudes) reduces the slope of the best-fitting regression line. Mitigation of this bias is necessary if we are to use photometric redshift estimates produced by computationally efficient empirical methods in precision cosmology.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".