Global Stellar Formation Rates or SFRs are crucial to constrain theories of
galaxy formation and evolution. SFR's are usually estimated via spectroscopic
observations which require too much previous telescope time and therefore
cannot match the needs of modern precision cosmology. We therefore propose a
novel method to estimate SFRs for large samples of galaxies using a variety of
supervised ML models.Comment: ESANN 2018 - Proceedings, ISBN-13 978287587048

Brescia, Massimo

Cavuoti, Stefano

Longo, Giuseppe

Riccio, Giuseppe

Veneri, Michele Delli

English

arXiv

Global Stellar Formation Rates or SFRs are crucial to constrain theories of galaxy formation and evolution. SFR's are usually estimated via spectroscopic observations which require too much previous telescope time and therefore cannot match the needs of modern precision cosmology. We therefore propose a novel method to estimate SFRs for large samples of galaxies using a variety of supervised ML models

DELLI VENERI, MICHELE

CAVUOTI, STEFANO

BRESCIA, Massimo

RICCIO, GIUSEPPE

OA@INAF - Istituto Nazionale di Astrofisica

2018Publication Year2020-10-05T14:04:18ZAcceptance in OA@INAFStellar formation rates in galaxies using Machine Learning modelsTitleDELLI VENERI, MICHELE; CAVUOTI, STEFANO; BRESCIA, Massimo; RICCIO, GIUSEPPE; Longo, GiuseppeAuthorshttp://hdl.handle.net/20.500.12386/27588HandleStellar formation rates in galaxies using MachineLearning modelsMichele Delli Veneri1, Stefano Cavuoti1,2,3, Massimo Brescia2, Giuseppe Riccio2and Giuseppe Longo1,31- Universitá degli Studi Federico II - Dipartimento di Fisica “E. Pancini”,via Cintia 6, I-80135 Napoli, Italia2- INAF - Osservatorio Astronomico di Capodimonte,via Moiariello 16, I-80131 Napoli, Italia3- INFN - Napoli Unit, via Cintia 6, I-80135 Napoli, ItaliaAbstract. Global Stellar Formation Rates or SFRs are crucial to constrain theoriesof galaxy formation and evolution. SFR’s are usually estimated via spectroscopicobservations which require too much previous telescope time and therefore cannotmatch the needs of modern precision cosmology. We therefore propose a novelmethod to estimate SFRs for large samples of galaxies using a variety of supervisedML models.1 IntroductionOne of the main parameters used to understand galaxy formation and evolution is theglobal Stellar Formation Rate (SFR) [1] which measures the luminosity-weighted av-erage across local variations in star formation history and physical conditions within agiven galaxy. The identification of proper SFR indicators and their calibration has beenat the center of intensive debate for the last thirty years and many problems must yetbe solved. However, in a broad oversimplification, global SFR indicators are measuresof luminosity, either monochromatic or integrated over some wavelength range chosenin order to be sensitive to the short-lived massive stars. There is a large variety of suchindicators spanning from the UV/optical/near-IR range (∼ 0.1-5 µm) which probe thedirect stellar light emerging from young stars, to the mid/far-IR ( ∼ 5-1000 µm) probingthe stellar light reprocessed by dust. Other indicators rely on the ionizing photon rate, astraced by the gas ionized by massive stars [2, 3]; hydrogen recombination lines, forbid-den metal lines, and in the millimeter range, the free-free (Bremsstrahlung) emission.Finally, other indicators are, at least in principle, derived in the X ray domain, fromX-ray binaries, massive stars, and supernovae; the non-thermal synchrotron emissionproduced by accelerated charged particles, which, following the suggestions in [4], canbe calibrated as an SFR indicator.It is clear, however, that the correct evaluation of SFR from optical/FIR broad banddata is a highly non trivial task due to the complex and still largely poorly understoodcorrelation existing between the SFR and the broad band photometric properties inte-grated over the whole galaxy. From the mathematical point of view, the estimation ofSFR is a typical regression problem and, in a recent work [5] it has been shown howmachine learning methods can be effectively used to estimate stellar formation ratesarXiv:1805.06338v3  [astro-ph.IM]  23 Jan 2019Fig. 1: Left panel: distribution of AVG; right panel: Spectroscopic redshift distributionof the training sample.for objects in large panchromatic sky surveys. In this work we make use of the SFR’sderived in [6] for a subsample of galaxies in the SDSS-DR7. While referring to theoriginal paper for a detailed description, we shall just remind that Brinchman [6] usedthe Charlot & Longhetti model [7] and that the method to obtain SFR estimates for otherclasses of galaxies (AGN, Composite, low S/N SF, low S/N LINER and Unclassifiable)is nearly identical to that described in [6].2 DataIn order to compare the results of our work with those obtained by [5] we used theData Release 7 of the Sloan Digital Sky Survey (hereafter SDSS-DR7) [8]. In factthis data release was used in [6] to derive reliable star formation rates for a subsampleof ∼ 106 galaxies with good spectroscopy. To create our Knowledge Base (or KB),we extracted from the SpecPhoto view of the SDSS-DR7 all objects whose PlateID,FiberID and MJD matched the objects in the the Brinchmann et al. catalogue [6].From the former we extracted the psfMag, fiberMag, petroMag, modelMag, expMagand deVMag magnitudes in the u, g, r, i, and z bands and the spectroscopic redshift;from the latter, the targets i.e. the average total star formation rates (AVG)1. Then thefollowing constrains were applied:1. for SFRs we required a successful estimation (flag = 0 in [6]);2. for redshifts we required a successful spectroscopic estimation (zWarning = 0 in[8])A sample of 572,285 galaxies satisfied those criteria. Then we eliminated from thesample all objects with a ”Null” feature and truncated all magnitude distributions tophysically meaningful values, obtaining a KB of 570,908 galaxies. For each magnitudetype, we produced the u - g, g - r, r - i, and i - z colors, reaching a total of 54 photo-metric features for our KB plus the AVG as a target. The distribution of spectroscopicredshifts and AVGs for the KB is shown in Fig. 1 (right and left panel, respectively) . Tostudy the relationship between redshift and star formation rate, we cross-matched the1 ”Magnitudes” m are the conventional astronomical equivalent of the fluxes fλ. More precisely m =−2.5Log fλ + q0, where q0 is a zero point.Fig. 2: Spectroscopic AVG VS Predicted AVG.The central line gives the bisector, whilethe other two define the 3σ regions. Objects outside these green lines must be consid-ered as ”outliers”.sample of 570,908 galaxies with our catalogue of photometric redshifts for the SDSS-DR9 galaxies [9], retaining 436,490 galaxies out of the 570,908. Thus integrating thefeatures list with: the spectroscopic redshift zSpec and the relative photometric red-shift estimations zPhot derived from [9], we reached a 56-dimensional parameter space(hereafter DR7-KB). Furthermore we created a second database based on the first one(DR9-KB) using the more accurate photometric data from the SDSS-DR9 [10].3 AlgorithmsIn the present work we make use of two Machine Learning (ML) methods, respectivelyRandom Forest (RF) [11] and Multi Layer Perceptron trained by the Quasi Newton Al-gorithm (MLPQNA) [12]. In order to optimize their performances, we apply the k-foldcross validation [13] and two feature selection methods. The latter are respectively, theforward selection [14] based on the feature importance embedded in the RF and PHi-LAB (Parameter Handling including Lasso Analysis as Benchmark). PHiLAB (Bresciaet al. in prep.) is a method designed to solve the known problem of the all-relevantfeature selection, i.e. the identification of the exact parameter space that could be con-sidered as relevant in the context of a problem solution analysis. By performing anexhaustive selection of all relevant features, it enables a deeper understanding of thephysical phenomena governing the specific problem (in this case the star forming rateprediction). The importance of any feature of the given parameter space is evaluated asthe accuracy loss induced by a random perturbation of the original feature among theavailable data entries. For each feature the relative measure of significance is then com-pared to the statistical score obtained by evaluating the regression estimation, by meansof the known LASSO statical method [15], based on the L1-norm regularization. Thecombination of the features supporting the optimal solution of Lasso regression withthose out-coming from the random noising mechanism, is able to furnish a robust andcomplete set of features composing the best parameter space for the current problem[15].4 ExperimentsWe performed a series of experiments divided in five groups (as listed in Table 1). In thefirst group, we used the full DR7-KB (54 or 55 features depending on the experiment)and the k-fold cross validation in order to compare our results with the ones obtained in[5]; in the second, we used the same KB but, instead of the k-fold cross validation, weused the traditional train-validation-test approach [16] in order to evaluate the cross val-idation effect on the performances of our models. In the third group, we replicated thesecond group experiments by replacing the full set of features with the most informa-tive ones selected by the PHiLAB method. In the fourth group we replicated the secondgroup experiments on the DR9-KB, in order to identify the best model to be used toproduce the final SFR catalogue as well to compare the effects of different photometry.In the fifth group, we replicated the third group of experiments on the DR9 KB, usingonly the most informative features selected by the PHiLAB method. The experimentID (see Table 1) is composed of a number and an acronym; the number specifies thegroup while the following acronym indicates the set of features:• M+C: Magnitudes + Colors. We used as input features the combination of mag-nitudes and colors described in section 2 and as a target the AVG;• ZSPEC: Spectroscopic Redshifts. We added to the M+C parameter space thespectroscopic redshift (zSpec) to check if a correlation between SFR and spectro-scopic redshifts exists;• ZPHOT: Photometric Redshifts. We added to the M+C parameter space the pho-tometric redshifts estimates (zPhot) to check if a correlation between SFR andphotometric redshifts exists;• MLPQNA. We used the same KB used for the ZSPEC experiment in the thirdgroup and for the M+C experiment in the fifth group but, instead of the RF, weused the MLPQNA described in [17].5 Results, Conclusions and Future WorksThe statistical results of the experiments described above are summarized in Table 1.In Fig. 2 we plot the spectroscopic AVG vs our output for three experiments: 3 M+C(best experiment on DR7-KB), 5 M+C (same as previous experiment but applied tothe DR9-KB) and, finally, 5 MLPQNA (best experiment on DR9-KB). In Fig. 3 weshow the feature importance for those three experiments. In particular, by focusing theattention on RMSE and η% (percentage of outliers having estimates outside the (> 3σ)boundaries) quantities, group 1 experiments show that the k-fold cross validation tech-nique does not improve the performance on such KB. From group 2 and 3 it appearsevident that the information about photometric redshifts does not improve the SFR esti-mation performance. In fact, this feature is always relegated at the bottom of the featureimportance ranking list. This could be explained by keeping in mind that, due to ob-vious selection effects, in this work only low redshift galaxies (zspec < 0.33) are beenevaluated (see Fig. 1) and thus the photometric redshift does not carry enough informa-tion to boost the performance. On the other hand, the introduction of the spectroscopicTable 1: Results of the experiments; in column 1 we have the ID, in column 2 the size ofthe parameter space, in column 3 the used model, in column 4 the KB, in column 5 theroot mean squared error, in column 6 the median, in column 7 the standard deviationand finally in column 8 the percentage (η%) of outliers having estimates outside the(> 3σ) boundaries.ID feat. Model KB RMSE Median σ η%1 M+C 54 RF DR7 0.247 −0.022 0.247 2.081 ZSPEC 55 RF DR7 0.229 −0.019 0.229 2.261 ZPHOT 55 RF DR7 0.247 −0.022 0.247 2.062 M+C 54 RF DR7 0.245 −0.022 0.245 2.072 ZPHOT 55 RF DR7 0.245 −0.022 0.245 2.053 M+C 32 RF DR7 0.245 −0.022 0.245 2.123 ZPHOT 33 RF DR7 0.245 −0.022 0.245 2.103 ZSPEC 33 RF DR7 0.227 −0.020 0.227 2.323 MLPQNA 33 MLPQNA DR7 0.218 −0.015 0.218 2.264 M+C 54 RF DR9 0.261 −0.020 0.261 1.954 ZPHOT 55 RF DR9 0.262 −0.019 0.262 1.895 M+C 27 RF DR9 0.261 −0.019 0.261 1.945 ZPHOT 28 RF DR9 0.262 −0.019 0.262 1.935 MLPQNA 27 MLPQNA DR9 0.254 −0.015 0.254 2.05redshift in our KB, significantly improved the performance of our models but, due tothe small percentage of the SDSS-DR9 that has measured spectroscopic redshifts whichare not already contained in the KB, this information is of little or no practical utility inproducing a wider catalogue of SFRs. From Table 1, by looking at group four and five,it is evident that our performance on the DR9-KB is worst than that on the DR7-KB;this can be traced to the changes in photometry between the two data releases (changesreflected by the differences in the feature ranking as shown in Fig. 3). Regardless ofthe general improvement of the DR9 photometry over the DR7, the AVG estimation de-pends from the DR7 photometry [6] and thus it carries over all its intrinsic errors latercorrected in the DR9. At this stage of our work, we believe that the loss in performanceis acceptable (∼ 6%). At the moment we are performing also other experiments usingdifferent ML models and different types of SFR estimators (i.e. specific SFR [6]). Thiswill enable the possibility of a direct comparison between our experiments and thosedescribed in [5]. We wish however to emphasize that these results are the best estimatesof SFRs obtained so far with ML based methods and that they can therefore provide aviable alternative to the spectroscopic approach.References[1] P. Madau and M. Dickinson. Cosmic Star-Formation History. ARA&A, 52:415–486, 2014.[2] D. Calzetti, J. Harris, J. S. Gallagher, III, and al. The Ionized Gas in Local Starburst Galaxies: Globaland Small-Scale Feedback from Star Formation. AJ, 127:1405–1430, March 2004.[3] S. Hong, D. Calzetti, M. A. Dopita, and et al. Blair. Large-scale Shock-ionized and Photoionized Gasin M83: The Impact of Star Formation. ApJ, 731:45, April 2011.Fig. 3: Feature Importance Histogram[4] J. J. Condon. Radio emission from normal galaxies. ARA&A, 30:575–611, 1992.[5] K. Stensbo-Smidt, F. Gieseke, C. Igel, A. Zirm, and K.S. Pedersen. Sacrificing information for thegreater good: How to select phot. bands for optimal accuracy. MNRAS, 464(3):2577–2596, 2016.[6] J. Brinchmann, S. Charlot, S.D.M. White, and Tremonti et al. The physical properties of star-forminggalaxies in the low-redshift Universe. MNRAS, 351(4):1151–1179, 2004.[7] S. Charlot and M. Longhetti. Nebular emission from star-forming galaxies. MNRAS, 323:887–903,May 2001.[8] K.N. Abazajian, J.K. Adelman-Mccarthy, M.A. Ageros, S.S. Allam, and C. et al. Allende Prieto. Theseventh data release of the sloan digital sky survey. ApJSS, 182(2):543–558, 2009.[9] M. Brescia, S. Cavuoti, G. Longo, and V. De Stefano. A catalogue of photometric redshifts for thesdss-dr9 galaxies (research note). A& A, 568, 2014.[10] C. P. Ahn, R. Alexandroff, and Allende Prieto et al. The Ninth Data Release of the Sloan Digital SkySurvey: First Spectroscopic Data from the SDSS-III Baryon Oscillation Spectroscopic Survey. ApjSS,203:21, December 2012.[11] L. Breiman. Random forests. Machine Learning, 45(1):5–32, 2001.[12] S. Cavuoti, M. Brescia, V. De Stefano, and G. Longo. Photometric redshift estimation based on datamining with photoraptor. 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Stellar formation rates in galaxies using Machine Learning models

Global Stellar Formation Rates or SFRs are crucial to constrain theories of galaxy formation and evolution. SFR's are usually estimated via spectroscopic observations which require too much previous telescope time and therefore cannot match the needs of modern precision cosmology. We therefore propose a novel method to estimate SFRs for large samples of galaxies using a variety of supervised ML models. © ESANN 2018 - Proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning

Delli Veneri, M.

Cavuoti, S.

Brescia, M.

Riccio, G.

Longo, G.

Archivio della ricerca - Università degli studi di Napoli Federico II

https://openaccess.inaf.it/bitstream/20.500.12386/27588/1/DelliVeneriEtAl-1805.06338.pdf

Stellar formation rates in galaxies using Machine Learning models

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