1 Luis Alvarez, 1 Olac Fuentes and 1,2 Roberto Terlevich

1. Extracting Stellar Population Parameters of Galaxies from Photometric Data Using Evolution Strategies and Locally Weighted Linear Regression 1Luis Alvarez,1Olac Fuentes and 1,2Roberto Terlevich 1Instituto Nacional de Astrofísica Óptica y Electrónica, Mexico 2Institute of Astronomy, University of Cambridge, U.K.

2. Content • Problem definition • Data • Methods • Evolution strategies • Hybrid algorithm: ES-LWLR • Experiments • Results • Conclusions • Future work

3. Problem definition • Nowadays, there is a great amount of high quality photometric data that are being analyzed by different methods, with the aim of obtaining a better understanding of the structure and evolution of the Universe. • Among the important information that can be extracted from galactic photometric data are: ages and proportions of stellar populations, redshift and reddening. • The goal of this work is to develop fast and accurate algorithms for extracting stellar population parameters from photometric data of galaxies. • We are interested in using photometric instead of spectroscopic data because photometric can be obtained from very weak galaxies.

4. Photometric vs. Spectroscopic Data

5. Data • The data are spectra of artificial galaxies formed by combining three spectra of synthetic stellar populations of different ages (F1, F2 and F3). Each artificial galaxy is reddened (R) and redshifted (z). The photometric data are obtained after applying filters to the galaxy. • The experiments use a set of nine synthetic stellar population spectra of high resolution. Also, another set with nine low resolution spectra is obtained from the original one by sampling. combination F2, F3 p1, p2, R, z

6. Data (in detail) 1.To combine three spectra Fi , where each spectrum belong to a different stellar age, according to percentages Pi. 2. To apply the reddening Reddening (R) is the preferential scattering of the shorter wavelengths of light due to gas and interstellar dust. 3. To apply the redshift Redshift (z) is a shift toward longer wavelengths of the radiation caused by the emitting object moving away from the observer. It is to the expanssion of the Universe. 4. To filter the spectrum Finally, from the redshifted spectrum we calculate fifteen photometric filter values by averaging the fluxes in fiftten windows of equal width distributed uniformly along the spectrum.

7. Optimization approach • The problem is posed as an optimization task. The objective function is the sum of cuadratic differences between photometric query data (pd) and photometric data predicted by a model.

8. Methods • Traditional methods • Template fitting (used for estimating age and reddening) • Neural networks (photometric redshifts) • Nearest Neighbors (photometric redshifts) • Evolution Strategies • They implement biological evolution concepts by means of genetic operators: combination, mutation and selection. • They optimize parameters by generating a random population of solutions that is evolved using genetic operators. The evolved population contains candidate solutions that are closer to an acceptable solution. • They are appropriate for this problem because they are noise tolerant, work well in high dimensional spaces and they do not get stuck in local minima.

9. Hybrid algorithm ES-LWLR • Key Idea: We can use the individuals created in previous generations as training data for a learning algorithm. • Use the best individuals of each generation to build a local linear model (M: PD->SPP) to generate a new individual, possibly closer to the global solution than the best in the current population. • The model is built using Locally Weighted Linear Regression (LWLR), an instance-based learning algorithm. • The resulting hybrid algorithm ES-LWLR converges faster than ES alone to an acceptable solution.

10. Using LWLR • Evolution strategies create individuals encoding parameters of stellar populations SPP = (F2,F3,P1,P2,,R, z), these are used to obtain the corresponding photometric data, then the objective function is evaluated for each individual. If the relation SPP->PD is reversed, a linear model can be created for estimating the SPP from This model is used for predicting a new set of parameters for the query photometric data pd. LWLR estimates the coeficcients of the relation Y-1.

11. Experiments • Performance measures • Time (in seconds, using a PC Pentium 4 2.4Ghz RAM 128Kb) • Mean absolute error (MAE) of SPP. • Evolution strategies parameters • μ= 50, λ=100, Δσ=0.25, generations=50 • The test set of pd for ES algorithm is formed from: - 100 SPP using high resolution spectra, - 100 SPP using low resolution spectra, - 100 SPP using high resolution noisy spectra, and - 100 SPP using low resolution noisy spectra. (all random) Another set test of equal size is formed for ES-LWLR algorithm.

12. Results

13. Results (2) Objective function ˆ pd: query photometric data, pd: photometric data predicted by the model.

14. Conclusions • The problem of extracting stellar population parameters from photometric data is posed as an optimization problem and then solved using Evolution Strategies. • The idea of forming a linear model, using the solutions in each evolution-estrategy generation, that predicts a new individual accelerates the convergence and increases the accuracy. • In spectra with Gaussian noise, the performance of ES and the hybrid algorithm (ES-LWLR) is similar.

15. Future Work • Improvement of the hybrid algorithm • Use ES-(μ,λ) version to possibly improve the performance in noisy spectra. • Design a strategy that stores the best individuals of each generation, then forms the linear model after n generations, because the solutions of (μ,λ) version are more sparse than the solutions of the (μ+λ) version used in this work. • Improve the population by adding more than one individual by means of a weighted average between the query pd and the best pd predicted.

16. Future Work • Improvement of the application • Refine the models used: reddening, filters, method of combining spectra. • Experiment with different filter sets. • Form a training set of real spectra with the aid of an expert in the domain who would have to verify the labeling of the test set. • Experiment with real data.

17. Thanks!Questions?