Astronomy Letters

, Volume 44, Issue 12, pp 735–753 | Cite as

Measuring the Probabilistic Photometric Redshifts of X-ray Quasars Based on the Quantile Regression of Ensembles of Decision Trees

  • A. V. MeshcheryakovEmail author
  • V. V. Glazkova
  • S. V. Gerasimov
  • I. V. Mashechkin


We present empirical machine learning algorithms for measuring the probabilistic photometric redshifts (photo-z) of X-ray quasars based on the quantile regression of ensembles of decision trees. Relying on the data of present-day photometric sky surveys (e.g., SDSS, GALEX, WISE, UKIDSS, 2MASS, FIRST), the proposed methods allow one to make high-quality photo-z point predictions for extragalactic objects, to estimate the confidence intervals, and to reconstruct the full probability distribution functions for all predictions. The quality of photo-z predictions has been tested on samples of X-ray quasars from the 1RASS and 3XMM DR7 surveys, which have spectroscopic redshift measurements in the SDSS DR14Q catalog. The proposed approaches have shown the following accuracy (the metrics are the normalized median absolute deviation σNMAD and the percentage of outliers n>0.15): σNMAD, n>0.15 = 0.043, 12% (SDSS + WISE), 0.037, 8% (SDSS + WISE + GALEX) and 0.032, 8.6% (SDSS + WISE + GALEX + UKIDSS) on the RASS sample; σNMAD, n>0.15 = 0.054, 13% (SDSS + WISE), 0.045, 7.6% (SDSS + WISE + GALEX), and 0.037, 6.6% (SDSS + WISE + GALEX + UKIDSS) on the 3XMM sample. The presented photo-z algorithms will become an important tool for analyzing the multi-wavelength data on X-ray quasars in the forthcoming Spectrum–Roentgen–Gamma sky survey.


quasars photometric redshifts machine learning quantile regression decision trees random forest gradient boosting SRG eRosita ART-XC SDSS WISE GALEX UKIDSS 2MASS FIRST ROSAT XMM-Newton 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T.M. C. Abbott, F. B. Abdalla, A. Alarcon, J. Aleksić, S. Allam, et al. (DES Collab.), arXiv:1708.01530 (2017).Google Scholar
  2. 2.
    T. M. C. Abbott, F. B. Abdalla, S. Allam, A. Amara, J. Annis, et al., arXiv:1801.03181 (2018).Google Scholar
  3. 3.
    F. B. Abdalla, M. Banerji, O. Lahav, and V. Rashkov, Mon. Not. R. Astron. Soc. 417, 1891 (2011).ADSCrossRefGoogle Scholar
  4. 4.
    P. A. Abell, J. Allison, S. F. Anderson, J. R. Andrew, et al. (LSST Sci. Collab.), arXiv:0912.0201 (2009).Google Scholar
  5. 5.
    B. Abolfathi, D. S. Aguado, G. Aguilar, C. Allende Prieto, et al., Astrophys. J. Suppl. Ser. 235, 42 (2018).ADSCrossRefGoogle Scholar
  6. 6.
    T. T. Ananna, M. Salvato, S. LaMassa, C. M. Urry, N. Cappelluti, et al., Astrophys. J. 850, 66 (2017).ADSCrossRefGoogle Scholar
  7. 7.
    M. de Backer, A. El Ghouch, and I. van Keilegom, J. Am. Stat. Assoc., 1 (2018).Google Scholar
  8. 8.
    R. Beck, L. Dobos, T. Budavári, A. S. Szalay, and I. Csabai, Mon. Not. R. Astron. Soc. 460, 1371 (2016).ADSCrossRefGoogle Scholar
  9. 9.
    R. Beck, C.-A. Lin, E. E. O. Ishida, F. Gieseke, R. S. de Souza, M. V. Costa-Duarte, M. W. Hattab, and A. Krone-Martins, Mon. Not. R. Astron. Soc. 468, 4323 (2017).ADSCrossRefGoogle Scholar
  10. 10.
    R. H. Becker, R. L. White, and D. J. Helfand, Astrophys. J. 450, 559 (1996).ADSCrossRefGoogle Scholar
  11. 11.
    Th. Boller, M. J. Freyberg, J. Tremper, F. Haberl, W. Voges, and K. Nandra, Astron. Astrophys. 588, 103 (2016).ADSCrossRefGoogle Scholar
  12. 12.
    Jo Bovy, A. D. Myers, J. F. Hennawi, D. W. Hogg, R. G. McMahon, et al., Astrophys. J. 749, 41 (2012).ADSCrossRefGoogle Scholar
  13. 13.
    L. Breiman, Machine Learning 24, 123 (1996).Google Scholar
  14. 14.
    L. Breiman, Ann. Stat. 26, 801 (1998).CrossRefGoogle Scholar
  15. 15.
    L. Breiman, Machine Learning 45, 5 (2001).CrossRefGoogle Scholar
  16. 16.
    L. Breiman, J. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, Belmont, CA, 1984).zbMATHGoogle Scholar
  17. 17.
    M. Brescia, S. Cavuoti, R. D’Abrusco, G. Longo, and A. Mercurio, Astrophys. J. 772, 140 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    A. G. A. Brown, A. Vallenari, T. Prusti, J. H. J. de Bruijne, et al. (Gaia Collab.), arXiv:1804.09365 (2018).Google Scholar
  19. 19.
    G. Bruzual and S. Charlot, Mon. Not. R. Astron. Soc. 344, 1000 (2003).ADSCrossRefGoogle Scholar
  20. 20.
    M. Carrasco Kind and R. J. Brunner, Mon. Not. R. Astron. Soc. 432, 1483 (2013).ADSCrossRefGoogle Scholar
  21. 21.
    R. Caruana and A. Niculescu-Mizil, in Proceedings of the 23rd International Conference on Machine Learning (2006), pp. 161–168.Google Scholar
  22. 22.
    K. C. Chambers, E. A. Magnier, N. Metcalfe, H. A. Flewelling, et al., arXiv:1612.05560 (2016).Google Scholar
  23. 23.
    P. Chaudhuri and W. Loh, Bernoulli 8, 561 (2002).MathSciNetGoogle Scholar
  24. 24.
    T. Chen and C. Guestrin, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, p. 785.CrossRefGoogle Scholar
  25. 25.
    A. V. Dorogush, A. Gulin, G. Gusev, N. Kazeev, L. Ostroumova Prokhorenkova, and A. Vorobev, arXiv:1706.09516 (2017).Google Scholar
  26. 26.
    D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, et al., Astrophys. J. 633, 560 (2005).ADSCrossRefGoogle Scholar
  27. 27.
    M. Fernández-Delgado, E. Cernadas, S. Barro, and D. Amorim, J. Machine Learning Res. 15, 3133 (2014).MathSciNetGoogle Scholar
  28. 28.
    Yo. Freund and R. E. Schapire, J. Comput. Syst. Sci. 55, 119 (1997).CrossRefGoogle Scholar
  29. 29.
    J. Friedman, Comput. Stat. Data Anal. 38, 367 (1999).CrossRefGoogle Scholar
  30. 30.
    J. Friedman, Ann. Stat. 29(5), (2001).Google Scholar
  31. 31.
    P. Geurts, D. Ernst, and L. Wehenkel, Machine Learning 63, 3 (2006).CrossRefGoogle Scholar
  32. 32.
    T. Gneiting, A. E. Raftery, A. H. Westveld, and T. Goldman, Mon.Weather Rev. 133, 1098 (2004).ADSCrossRefGoogle Scholar
  33. 33.
    T. Gneiting, F. Balabdaoui, and A. E. Raftery, Stat. Methodol., Ser. B 69, 243 (2007).CrossRefGoogle Scholar
  34. 34.
    T. Hastie, R. Tibshirani, and J. Friedman, Elements of Statistical Learning, 2nd ed. (Springer, New York, 2009).CrossRefzbMATHGoogle Scholar
  35. 35.
    T. Ho, Pattern Anal. Machine Intell. 20(8), 832 (1998a).Google Scholar
  36. 36.
    T. K. Ho, IEEE Trans. Pattern Anal. Machine Intell. 20, 832 (1998b).Google Scholar
  37. 37.
    D.W. Hogg, arXiv:astro-ph/9905116 (1999).Google Scholar
  38. 38.
    G. Hutsi, M. Gilfanov, A. Kolodzig, and R. Sunyaev, Astron. Astrophys. 572, 28 (2014).ADSCrossRefGoogle Scholar
  39. 39.
    R. G. James, D. Witten, T. Hastie, and R. Tibshirani, An Introduction to Statistical Learning with Applications (Springer, Berlin, 2013).CrossRefzbMATHGoogle Scholar
  40. 40.
    J. T. A. de Jong, G. A. Verdoes Kleijn, T. Erben, H. Hildebrandt, K. Kuijken, et al., Astron. Astrophys. 604, 134 (2017).CrossRefGoogle Scholar
  41. 41.
    G.Ke, Q. Meng, T. Finely, T. Wang,W.Chen, W.Ma, Q. Ye, and T.-Y. Liu, Adv. Neural Inform. Proc. Syst. 30, 3149 (2017).Google Scholar
  42. 42.
    R. Koenker and G. Bassett, Jr., Econometrica 46, 33 (1978).CrossRefGoogle Scholar
  43. 43.
    R. Koenker et al., Quantile Regression (2005).CrossRefzbMATHGoogle Scholar
  44. 44.
    R. Kohavi, Proc. IJCAI 14, 1137 (1995).Google Scholar
  45. 45.
    A. Kolodzig, M. Gilfanov, R. Sunyaev, S. Sazonov, and M. Brusa, Astron. Astrophys. 558, 89 (2013).ADSCrossRefGoogle Scholar
  46. 46.
    A. Lawrence, S. J. Warren, O. Almaini, A. C. Edge, N. C. Hambly, R. F. Jameson, P. Lucas, M. Casali, et al., Mon. Not. R. Astron. Soc. 379, 1599 (2007).ADSCrossRefGoogle Scholar
  47. 47.
    Q. V. Le, T. Sears, and A. Smola, Technical report (NICTA, Sydney, 2005).Google Scholar
  48. 48.
    B. Leistedt and D. W. Hogg, Astrophys. J. 838, 1 (2017).CrossRefGoogle Scholar
  49. 49.
    Yu. Liu and V. Gopalakrishnan, Data 2, 8 (2017).CrossRefGoogle Scholar
  50. 50.
    M. Markatou, H. Tian, S. Biswas, and G. Hripcsak, J. Machine Learning Res. 6, 1127 (2005).MathSciNetGoogle Scholar
  51. 51.
    D. Ch. Martin, J. Fanson, D. Schiminovich, P. Morrissey, P. G. Friedman, et al., Astrophys. J. 619, 1 (1996).CrossRefGoogle Scholar
  52. 52.
    N. Meinshausen, J. Machine Learning Res. 7, 983 (2006).MathSciNetGoogle Scholar
  53. 53.
    A. Merloni, P. Predehl, W. Becker, H. Bohringer, T. Boller, H. Brunner, et al., arXiv:1209.3114 (2012).Google Scholar
  54. 54.
    J. Mitchell and K. F. Wallis, J. Appl. Econometr. 26, 1023 (2012).CrossRefGoogle Scholar
  55. 55.
    X. Morice-Atkinson, B. Hoyle, and D. Bacon, arXiv:1712.03970 (2017).Google Scholar
  56. 56.
    G. Mountrichas, A. Corral, V. A. Masoura, I. Georgantopoulos, A. Ruiz, A. Georgakakis, F. J. Carrera, and S. Fotopoulou, Astron. Astrophys. 608, 39 (2017).ADSCrossRefGoogle Scholar
  57. 57.
    K. P. Murphy, Machine Learning: A Probabilistic Perspective (MIT Press, Boston,MA, 2012).zbMATHGoogle Scholar
  58. 58.
    I. ˆParis, P. Petitjean, E. Aubourg, A. D. Myers, A. Streblyanska, B.W. Lyke, et al., arXiv:1712.05029 (2017).Google Scholar
  59. 59.
    A. Patej and D. J. Eisenstein, Mon. Not. R. Astron. Soc. 477, 5090 (2018).ADSCrossRefGoogle Scholar
  60. 60.
    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, B.O. Grisel, M. Blondel, et al., J.Machine Learning Res. 12, 2825 (2011).Google Scholar
  61. 61.
    P. J. E. Peebles, Nat. Astron. 1, 57 (2017).ADSCrossRefGoogle Scholar
  62. 62.
    K. L. Polsterer, A. D’Isanto, and F. Gieseke, arXiv:1608.08016 (2016).Google Scholar
  63. 63.
    A. Refregier, A. Amara, T. D. Kitching, A. Rassat, R. Scaramella, and J. Weller, arXiv:1001.0061 (2010).Google Scholar
  64. 64.
    S. R. Rosen, N. A. Webb, M. G. Watson, J. Ballet, D. Barret, V. Braito, F. J. Carrera, et al., Astron. Astrophys. 590, 1 (2016).CrossRefGoogle Scholar
  65. 65.
    M. Salvato, O. Ilbert, and B. Hoyle, Nat. Astron., 68 (2018).Google Scholar
  66. 66.
    S. J. Schmidt, J. A. Newman, A. Abate, et al., arXiv:1410.4506 (2014).Google Scholar
  67. 67.
    D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, New York, Chichester, 1992).CrossRefzbMATHGoogle Scholar
  68. 68.
    M. F. Skrutskie, R. M. Cutri, R. Stiening, M. D. Weinberg, S. Schneider, J. M. Carpenter, et al., Astron. J. 131, 1163 (2006).ADSCrossRefGoogle Scholar
  69. 69.
    S. A. Smee, J. E. Gunn, A. Uomoto, N. Roe, and D. Schlegel, Astron. J. 146, 32 (2013).ADSCrossRefGoogle Scholar
  70. 70.
    A. A. Tsyplakov, Prikl. Ekonom. 3, 27 (2012).Google Scholar
  71. 71.
    W. Voges, B. Aschenbach, Th. Boller, H. Brouninger, U. Briel, W. Burkert, et al., Astron. Astrophys. 349, 389 (1999).ADSGoogle Scholar
  72. 72.
    W. Voges, B. Aschenbach, T. Boller, H. Brauninger, U. Briel, W. Burkert, et al., IAU Circ. 7432, 3 (2000).ADSGoogle Scholar
  73. 73.
    D. H. Weinberg, M. J. Mortonson, D. J. Eisenstein, Ch. Hirata, A.G. Riess, and E. Rozo, Phys. Rep. 530, 87 (2013).ADSMathSciNetCrossRefGoogle Scholar
  74. 74.
    D. Wittman, R. Bhaskar, and R. Tobin, Mon. Not. R. Astron. Soc. 457, 4 (2016).CrossRefGoogle Scholar
  75. 75.
    Ch.Wolf, Ch. A. Onken, L. C. Luvaul, B. P. Schmidt, et al., Publ. Astron. Soc. Austral. 35, 10 (2018).ADSGoogle Scholar
  76. 76.
    E. L. Wright, P. R. M. Eisenhardt, A. K. Mainzer, M. E. Ressler, et al., Astron. J. 140, 1868 (2010).ADSCrossRefGoogle Scholar
  77. 77.
    Q. Yang, X.-B. Wu, X. Fan, L. Jiang, I. McGreer, et al., Astron. J. 154, 269 (2017).ADSCrossRefGoogle Scholar
  78. 78.
    M. Zamo and P. Naveau, Math. Geosci. 50, 209 (2017).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. V. Meshcheryakov
    • 1
    Email author
  • V. V. Glazkova
    • 2
  • S. V. Gerasimov
    • 2
  • I. V. Mashechkin
    • 2
  1. 1.Space Research InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

Personalised recommendations