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The scientific value of the next generation of large continuum surveys would be greatly increased if the redshifts of the newly detected sources could be rapidly and reliably estimated. Given the observational expense of obtaining spectroscopic redshifts for the large number of new detections expected, there has been substantial recent work on using machine learning techniques to obtain photometric redshifts. Here we compare the accuracy of the predicted photometric redshifts obtained from Deep Learning(DL) with the k-Nearest Neighbour (kNN) and the Decision Tree Regression (DTR) algorithms. We find using a combination of near-infrared, visible and ultraviolet magnitudes, trained upon a sample of SDSS QSOs, that the kNN and DL algorithms produce the best self-validation result with a standard deviation of {sigma} = 0.24. Testing on various sub-samples, we find that the DL algorithm generally has lower values of {sigma}, in addition to exhibiting a better performance in other measures. Our DL method, which uses an easy to implement off-the-shelf algorithm with no filtering nor removal of outliers, performs similarly to other, more complex, algorithms, resulting in an accuracy of {Delta}z < 0.1$ up to z ~ 2.5. Applying the DL algorithm trained on our 70,000 strong sample to other independent (radio-selected) datasets, we find {sigma} < 0.36 over a wide range of radio flux densities. This indicates much potential in using this method to determine photometric redshifts of quasars detected with the Square Kilometre Array.
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We present a machine-learning photometric redshift analysis of the Kilo-Degree Survey Data Release 3, using two neural-network based techniques: ANNz2 and MLPQNA. Despite limited coverage of spectroscopic training sets, these ML codes provide photo-zs of quality comparable to, if not better than, those from the BPZ code, at least up to zphot<0.9 and r<23.5. At the bright end of r<20, where very complete spectroscopic data overlapping with KiDS are available, the performance of the ML photo-zs clearly surpasses that of BPZ, currently the primary photo-z method for KiDS. Using the Galaxy And Mass Assembly (GAMA) spectroscopic survey as calibration, we furthermore study how photo-zs improve for bright sources when photometric parameters additional to magnitudes are included in the photo-z derivation, as well as when VIKING and WISE infrared bands are added. While the fiducial four-band ugri setup gives a photo-z bias $delta z=-2e-4$ and scatter $sigma_z<0.022$ at mean z = 0.23, combining magnitudes, colours, and galaxy sizes reduces the scatter by ~7% and the bias by an order of magnitude. Once the ugri and IR magnitudes are joined into 12-band photometry spanning up to 12 $mu$, the scatter decreases by more than 10% over the fiducial case. Finally, using the 12 bands together with optical colours and linear sizes gives $delta z<4e-5$ and $sigma_z<0.019$. This paper also serves as a reference for two public photo-z catalogues accompanying KiDS DR3, both obtained using the ANNz2 code. The first one, of general purpose, includes all the 39 million KiDS sources with four-band ugri measurements in DR3. The second dataset, optimized for low-redshift studies such as galaxy-galaxy lensing, is limited to r<20, and provides photo-zs of much better quality than in the full-depth case thanks to incorporating optical magnitudes, colours, and sizes in the GAMA-calibrated photo-z derivation.
From SDSS commissioning photometric and spectroscopic data, we investigate the utility of photometric redshift techniques to the task of estimating QSO redshifts. We consider empirical methods (e.g. nearest-neighbor searches and polynomial fitting), standard spectral template fitting and hybrid approaches (i.e. training spectral templates from spectroscopic and photometric observations of QSOs). We find that in all cases, due to the presence of strong emission-lines within the QSO spectra, the nearest-neighbor and template fitting methods are superior to the polynomial fitting approach. Applying a novel reconstruction technique, we can, from the SDSS multicolor photometry, reconstruct a statistical representation of the underlying SEDs of the SDSS QSOs. Although, the reconstructed templates are based on only broadband photometry the common emission lines present within the QSO spectra can be recovered in the resulting spectral energy distributions. The technique should be useful in searching for spectral differences among QSOs at a given redshift, in searching for spectral evolution of QSOs, in comparing photometric redshifts for objects beyond the SDSS spectroscopic sample with those in the well calibrated photometric redshifts for objects brighter than 20th magnitude and in searching for systematic and time variable effects in the SDSS broad band photometric and spectral photometric calibrations.
Machine learning techniques, specifically the k-nearest neighbour algorithm applied to optical band colours, have had some success in predicting photometric redshifts of quasi-stellar objects (QSOs): Although the mean of differences between the spectroscopic and photometric redshifts is close to zero, the distribution of these differences remains wide and distinctly non-Gaussian. As per our previous empirical estimate of photometric redshifts, we find that the predictions can be significantly improved by adding colours from other wavebands, namely the near-infrared and ultraviolet. Self-testing this, by using half of the 33 643 strong QSO sample to train the algorithm, results in a significantly narrower spread for the remaining half of the sample. Using the whole QSO sample to train the algorithm, the same set of magnitudes return a similar spread for a sample of radio sources (quasars). Although the matching coincidence is relatively low (739 of the 3663 sources having photometry in the relevant bands), this is still significantly larger than from the empirical method (2%) and thus may provide a method with which to obtain redshifts for the vast number of continuum radio sources expected to be detected with the next generation of large radio telescopes.
Precision photometric redshifts will be essential for extracting cosmological parameters from the next generation of wide-area imaging surveys. In this paper we introduce a photometric redshift algorithm, ArborZ, based on the machine-learning technique of Boosted Decision Trees. We study the algorithm using galaxies from the Sloan Digital Sky Survey and from mock catalogs intended to simulate both the SDSS and the upcoming Dark Energy Survey. We show that it improves upon the performance of existing algorithms. Moreover, the method naturally leads to the reconstruction of a full probability density function (PDF) for the photometric redshift of each galaxy, not merely a single best estimate and error, and also provides a photo-z quality figure-of-merit for each galaxy that can be used to reject outliers. We show that the stacked PDFs yield a more accurate reconstruction of the redshift distribution N(z). We discuss limitations of the current algorithm and ideas for future work.
We present ANNz2, a new implementation of the public software for photometric redshift (photo-z) estimation of Collister and Lahav (2004), which now includes generation of full probability distribution functions (PDFs). ANNz2 utilizes multiple machine learning methods, such as artificial neural networks and boosted decision/regression trees. The objective of the algorithm is to optimize the performance of the photo-z estimation, to properly derive the associated uncertainties, and to produce both single-value solutions and PDFs. In addition, estimators are made available, which mitigate possible problems of non-representative or incomplete spectroscopic training samples. ANNz2 has already been used as part of the first weak lensing analysis of the Dark Energy Survey, and is included in the experiments first public data release. Here we illustrate the functionality of the code using data from the tenth data release of the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. The code is available for download at https://github.com/IftachSadeh/ANNZ .
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