1. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington A method for exploiting domain information in parameter estimation Coryn Bailer-Jones Max Planck Institute for Astronomy Heidelberg Collaborators: Carola Tiede, Kester Smith, Christian Elting (Gaia @ MPIA group)

2. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington The problem ● estimate stellar astrophysical parameters (APs) from multidimensional (spectral) data, given a grid of templates ● strong and weak APs

3. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington “standard” approaches ● use a labelled grid (e.g. synthetic spectra) ● minimum distance methods (k-nearest neighbours) – what weighting/scaling of data dimensions? – limited by grid resolution ● learn mapping: data APs (global interpolation) – e.g. support vector machines, neural networks,... – implicitly infer sensitivity of the data to the APs

4. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington 1. It's an inverse problem log(Teff) flux in band

5. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington 1. It's an inverse problem log(Teff) flux in band theoretically a global model cannot fit this in general

6. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington 2. We can fit a forward model flux vs. log(T eff ) flux vs. logg

7. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Local grid interpolation

8. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Local grid interpolation

9. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington General case: multiple bands and APs

10. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Estimate sensitivites

11. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington ● use local linear J-dimensional interpolation as forward model ● interpolation over neighbours as measured in AP space – chosen to “bracket” the current AP estimate ● coefficients of the plane are the reciprocal sensitivities Local linear variant

12. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Applying the model ● J=2 (Teff, logg) 234 templates ● I=11 medium photometric bands, SNR=10 per band ● test set: 233 objects ● exampes of iterations for two objects (blue is truth): iteration number

13. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Model performance RMS errors: 1.68 dex in logg 0.042 in log(T eff ) (480K at 5000K) Cf. SVM: 0.99 dex 0.028 (320K) ● systematic in weak AP (intrinsic to data – also seen with other methods) ● difficult task: – only 11 bands at SNR=10 – wide AP range, yet sparse grid – sub-optimal local interpolation (linear)

14. Coryn Bailer-Jones, ADASS XVII, September 2007, Kensington Summary ● global fitting models ignore inverse nature of the mapping ● new approach – local method with local interpolation via fitted forward model – use of sensitivity information for optimal “weighting” of data ● competitive performance on low SNR data (I=11, J=2) ● model under development. Next steps: – (better) nonlinear forward models (smoothness) – local iteration tuning/convergence – extend to higher J (fits are J-dimensional, not I-dimensional) – multiple solutions (degeneracies)