1. Stellar parameters estimation using Gaussian processes regression Bu Yude (Shandong University at Weihai)

2. 1. Introduction Spectral fitting: K24 and ki13 Grids Random forest Neural Networks ……. SSPP: measure stellar parameters Beijing

3. 1. Introduction ? ? ? ? ? ? LASP: measure stellar parameters beijingJ

4. More methods can give more robust estimation of stellar parameters It is necessary to explore new methods to improve the accuracy of existing methods. 2014.8.20

5. 1. Introduction Existing methods Regression methods:  Kernel regression  Neural networks  Gaussian processes regression Regression methods:  Kernel regression  Neural networks  Gaussian processes regression Non-Regression methods:  MATISSE methods  Minimum distance methods  Template fitting Non-Regression methods:  MATISSE methods  Minimum distance methods  Template fitting

6. 1. Introduction

7. 1. Introduction Gaussian processes regression (GPR):  A regression methods originates from ANNs: some types of ANNs become GPs in the limit of infinite size  Several advantages over other methods: GPR has less number of parameters to be determined than ANNs. GPR is easier to determine the optimal algorithm parameters than SVR and KR: it can determine the algorithm parameters automatically, not manually.

8. 2. Brief introduction to GPR

9. 2. Brief introduction to GPR

10. 2. Brief introduction to GPR

11. 2. Brief introduction to GPR

12. 2. Brief introduction to GPR

13. 2. Brief introduction to GPR

14. 2. Brief introduction to GPR In practice, GPR algorithm consists of linear model and nonlinear model, so it is more complicated than above single linear model. In order to facilitate the application of GPR, we provide source code written in matlab in supplementary material of our paper (will publish on MNRAS).

15. 2. Brief introduction to GPR

16. 2. Brief introduction to GPR

17. 3. Data and Results Spectra from SDSS DR10. Select using following criterion: 1. The interstellar extinction in the r band below 0.3; 2. 14 < g < 19.5; 3. −0.2 < g − r < 0.9; 4. 0.7 < u − g < 2.4; 5. {−0.2 < g − r − 0.5(u − g − 0.5) < 0.4}OR {u − g < 1.4 AND g − r < 0.25}; 6. −0.2 < 0.35(g − r) − (r − i) < 0.20. Using the above criterion we can obtain a total of 303,041 spectra, about half of the total stellar spectra included in SDSS DR10.

18. 3. Data and results Criterion 1 is used to select stars from sky regions with modest interstellar dust extinction Criterion 2 is used to select bright stars. Criterions 3 and 4 are used to select stars with colours consistent with the main stellar locus RR Lyrae stars and blue horizontal branch stars Criteria 5 and 6 are used to exclude white dwarf– red dwarf pairs or single hot white dwarfs July 7, 2014, 扬州星系宇宙学前沿研讨会

19. 3. Data and Results We will use PCA to reduce the dimension of the spectra. By a comparison with different number of PCs, we use 40 PCs to derive the stellar parameters.

20. 3. Data and results

23. 3. Data and Results MILES spectra: In our comparison study, to diminish the influence of hot or cold stars, we only select the MILES spectra with 4000K < Teff<15000 K. This selection yields a final sample of 820 MILES stellar spectra. We have also used PCA to reduce the dimension of the spectra, and use 40 PCs to derive stellar parameters

24. 3. Data and results

27. 3. Data and Results ELODIE spectra: we also only use the spectra with 4000K < Teff<15000 K. This selection yields a final sample of 1075 spectra ： 538 for training and 537 for testing. We have reduced the spectral resolution from 42000 to 2000 to using Gaussian convolution to match the SDSS resolution We have also used PCA to reduce the dimension of the spectra, and use 40 PCs to derive stellar parameters

28. 3. Data and Results

31. 3. Results ParameterSpectra TeffSDSS ELODIE MILES 0.25 3 -6 101 328 426

32. 3. Results ParameterSpectra Log gSDSS ELODIE MILES -0.022 -0.046 -0.038 0.38 0.45 0.40

33. 3. Results ParameterSpectra [Fe/H]SDSS ELODIE MILES -0.013 -0.0072 -0.0011 0.24 0.34 0.28

34. 4. Compared with other methods We now compare GPR with three widely used regression methods: KR algorithm (Zhang et al. 2005), ANNs (Haykin 1998) and support vector regression (SVR; Drucker et al. 1997). SDSS spectra will be used in this experiment. We will also use 40 PCs to derive the stellar parameters.

35. 4. Compared with other methods ParameterAlgorithmTime TeffGPR KR ANN SVR 0.25 145 157 43 101 797 794 28s 1642s 41s 4924s

36. 4. Compared with other methods ParameterAlgorithm Log gSDSS KR ANN SVR -0.022 145 157 43 0.38 797 797 794

37. 4. Compared with other methods ParameterAlgorithmTime TeffGPR KR ANN SVR 0.25 145 157 43 101 797 794 28s 1642s 41s 4924s

38. 4. Compared with other methods ParameterAlgorithmTime TeffGPR KR ANN SVR 0.25 145 157 43 101 797 794 28s 1642s 41s 4924s

39. 4. Compared with other methods ParameterAlgorithmTime log gGPR KR ANN SVR - 0.022 -0.00019 -0.021 -0.13 0.38 0.076 0.46 0.69 21s 1548s 43s 4624s

40. 4. Compared with other methods ParameterAlgorithmTime [Fe/H]GPR KR ANN SVR - 0.013 -0.000058 -0.022 -0.020 0.24 0.046 0.34 0.49 22s 1566s 45s 4523s

41. 4. Compared with other methods We find that GPR gives more accurate estimate of three atmospheric parameters than SVR and ANNs, and give more accurate estimate of Teff than KR. Though KR gives more accurate estimate of log g and [Fe/H] than GPR, it takes much longer time than GPR. Overall, GPR is accurate and efficient in extracting the atmospheric parameters.

42. 5. Future work We plan to apply GPR to the LAMOST spectra in a near future. LAMOST can now only provide relative flux calibrated spectra because there is still no network of photometric standard stars for LAMOST (Song et al. 2012). Thus, we can’t apply GPR to LAMOST spectra with the procedure same as those on SDSS spectra. To extract the atmospheric parameters accurately, we have to investigate the performance of the GPR on relative flux calibrated spectra.

43. 5. Future work Our plan consists of following four steps: 1. Derive the Lick line indices of the spectra with S/N>15. It is proved that the Lick indices will not be affected by the shape of continuum, and hence it is suitable for the LAMOST spectra (Song et al. 2012). Of course, to extract the Lick indices accurately, we have to fit pseudo stellar continuum, which has been considered in Song et al. (2012).

44. 5. Future work 2. Construct the GPR model of extracting the atmospheric parameters by using Lick indices. 3. Construct the GPR model of deriving the atmospheric parameters from the spectra with relative flux calibrated spectra. We will use the atmospheric parameters derived by using the Lick indices and LAMOST spectra to construct the GPR model of extracting the atmospheric parameters from relative flux calibrated spectra.

45. 5. Future work 4. Apply the constructed GPR model to the spectra with S/N< 15. For the spectra with S/N<15, we can’t derive the Lick indices accurately. Thus, we will use the GPR model on the relative flux calibrated spectra instead of using the Lick line indices to derive the atmospheric parameters.

46. 5. Future works Use the most recently developed machine learning algorithms to process the spectra, including SDSS spectra and LAMOST spectra. These algorithms include: ELM, SPNs, DBN, RBM,…….

47. 6. References Cui X.-Q. et al., 2012, RAA, 12, 1197 Luo A-L. et al. 2012, RAA, 12, 1243 Wu Y. et al., 2011, RAA, 11, 924 Zhang J.-N., Wu F.-C., Luo A.-L., Zhao Y.-H., 2005, Spectroscopy and Spectral analysis, 25, 2088 Rasmussen C. E.,Williams C. K. I., 2006, Gaussian Processes for Machine Learning. MITPress, London, England

48. 7.Summary We have used spectra from SDSS,MILES and ELODIE to evaluate the performance of GPR. The results show that GPR can accurately derive stellar parameters, especially when using spectra with homogeneous calibrated parameters. We have also compared GPR with three widely used regression methods (ANNs, KR and SVR) using SDSS spectra as the testing data. We find that GPR is more efficient than these three regression methods. July 7, 2014, 扬州星系宇宙学前沿研讨会

49. Thanks