Stellar parameters estimation using Gaussian processes

regression

Bu Yude (Shandong University at Weihai)

1. Introduction

Spectral fitting: K24 and ki13

Grids

Spectral fitting: K24 and ki13

Grids Random forestRandom forest

Neural Networks

Neural Networks …….…….

SSPP: measure stellar

parameters

SSPP: measure stellar

parameters

Beijing

1. Introduction

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LASP: measure stellar

parameters

LASP: measure stellar

parameters

beijingJ

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

1. Introduction

Existing methodsExisting methods

Regression methods: Kernel regressionNeural networksGaussian processes regression

Regression methods: Kernel regressionNeural networksGaussian processes regression

Non-Regression methods: MATISSE methods Minimum distance methodsTemplate fitting

Non-Regression methods: MATISSE methods Minimum distance methodsTemplate fitting

1. Introduction

1. Introduction

Gaussian processes regression (GPR): A regression methods originates from ANNs: some types of ANNs become GPs in the limit of infinite sizeSeveral 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.

2. Brief introduction to GPR

2. Brief introduction to GPR

2. Brief introduction to GPR

2. Brief introduction to GPR

2. Brief introduction to GPR

2. Brief introduction to GPR

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).

2. Brief introduction to GPR

2. Brief introduction to GPR

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.

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

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.

3. Data and results

3. Data and results

3. Data and results

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

3. Data and results

3. Data and results

3. Data and results

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

3. Data and Results

3. Data and Results

3. Data and Results

3. Results

3. Results

3. Results

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.

4. Compared with other methods

4. Compared with other methods

4. Compared with other methods

4. Compared with other methods

4. Compared with other methods

4. Compared with other methods

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.

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.

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).

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.

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.

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,…….

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

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

Thanks