In this paper, we address the problem of spectroscopic redshift estimation in Astronomy. Due to the expansion of the Universe, galaxies recede from each other on average. This movement causes the emitted electromagnetic waves to shift from the blue part of the spectrum to the red part, due to the Doppler effect. Redshift is one of the most important observables in Astronomy, allowing the measurement of galaxy distances. Several sources of noise render the estimation process far from trivial, especially in the low signal-to-noise regime of many astrophysical observations. In recent years, new approaches for a reliable and automated estimation methodology have been sought out, in order to minimize our reliance on currently popular techniques that heavily involve human intervention. The fulfilment of this task has evolved into a grave necessity, in conjunction with the insatiable generation of immense amounts of astronomical data. In our work, we introduce a novel approach based on Deep Convolutional Neural Networks. The proposed methodology is extensively evaluated on a spectroscopic dataset of full spectral energy galaxy distributions, modelled after the upcoming Euclid satellite galaxy survey. Experimental analysis on observations of idealistic and realistic conditions demonstrate the potent capabilities of the proposed scheme.
Photometric observations have been extensively utilized in redshift estimation due to the fact that photometric analysis is substantially less costly and time-consuming, contrary to the spectroscopic case. Popular methods for this kind of estimation include Bayesian estimation with predefined spectral templates @cite_10 , or alternatively some widely used machine-learning models, adapted for this kind of problem, like the Multilayer Perceptron @cite_20 , @cite_8 and Boosted Decision Trees @cite_8 , @cite_38 . However, the limited wavelength resolution of photometry, compared to spectroscopy, introduces a higher level of uncertainty to the given procedures. In spectroscopy, by observing the full Spectral Energy Distribution (SED) of a galaxy, one can easily detect distinctive emission and absorption lines that can lead to a judicious redshift estimation, by measuring the wavelength shift of these spectral characteristics from the rest frame. Due to noisy observations, the main redshift estimation methods involve cross-correlating the SED with predefined spectral templates @cite_6 or PCA decompisitions of a template library. Noisy conditions and potential errors due to the choice of templates are the main reason that most reliable spectroscopic redshift estimation methods heavily depend on human judgment and experience to validate automated results.
@cite_38 @cite_8 @cite_6 @cite_10 @cite_20
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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 (SDSS) 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 & Lahav, 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 experiment's 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 http: github.com IftachSadeh ANNZ. Photometric redshifts are quickly becoming an essential tool of observational cosmology, although their utilization is somewhat hindered by certain shortcomings of the existing methods, e.g., the unreliability of maximum-likelihood techniques or the limited application range of the "training-set" approach. The application of Bayesian inference to the problem of photometric redshift estimation effectively overcomes most of these problems. The use of prior probabilities and Bayesian marginalization facilitates the inclusion of relevant knowledge, such as the expected shape of the redshift distributions and the galaxy type fractions, which can be readily obtained from existing surveys but are often ignored by other methods. If this previous information is lacking or insufficient—for instance, because of the unprecedented depth of the observations—the corresponding prior distributions can be calibrated using even the data sample for which the photometric redshifts are being obtained. An important advantage of Bayesian statistics is that the accuracy of the redshift estimation can be characterized in a way that has no equivalents in other statistical approaches, enabling the selection of galaxy samples with extremely reliable photometric redshifts. In this way, it is possible to determine the properties of individual galaxies more accurately, and simultaneously estimate the statistical properties of a sample in an optimal fashion. Moreover, the Bayesian formalism described here can be easily generalized to deal with a wide range of problems that make use of photometric redshifts. There is excellent agreement between the ≈130 Hubble Deep Field North (HDF-N) spectroscopic redshifts and the predictions of the method, with a rms error of Δz ≈ 0.06(1 + zspec) up to z < 6 and no outliers nor systematic biases. It should be remarked that since these results have not been reached following a training-set procedure, the above value of Δz should be a fair estimate of the expected accuracy for any similar sample. The method is further tested by estimating redshifts in the HDF-N but restricting the color information to the UBVI filters; the results are shown to be significantly more reliable than those obtained with maximum-likelihood techniques. We present a novel way of using neural networks (NN) to estimate the redshift distribution of a galaxy sample. We are able to obtain a probability density function (PDF) for each galaxy using a classification neural network. The method is applied to 58714 galaxies in CFHTLenS that have spectroscopic redshifts from DEEP2, VVDS and VIPERS. Using this data we show that the stacked PDF's give an excellent representation of the true @math using information from 5, 4 or 3 photometric bands. We show that the fractional error due to using N(z_(phot)) instead of N(z_(truth)) is <=1 on the lensing power spectrum P_(kappa) in several tomographic bins. Further we investigate how well this method performs when few training samples are available and show that in this regime the neural network slightly overestimates the N(z) at high z. Finally the case where the training sample is not representative of the full data set is investigated. An IPython notebook accompanying this paper is made available here: this https URL