ILIUM: A forward-modelling based algorithm for parameter estimation from multidimensional data

C.A.L. Bailer-Jones

ILIUM is a new algorithm for estimating parameters from multidimensional data based on forward modelling. It performs an iterative local search to effectively achieve a nonlinear interpolation of a template grid. In contrast to many machine learning approaches, it avoids fitting an inverse model and the problems associated with this. The algorithm makes explicit use of the sensitivities of the data to the parameters with the goal of better treating parameters which only have a weak impact on the data. The forward modelling approach naturally provides uncertainty (full covariance) estimates in the predicted parameters as well as a goodness-of-fit for observations, thus providing a simple means of identifying outliers.

The algorithm has been used to estimate stellar astrophysical parameters (APs) from simulations of the very low resolution spectrophotometry to be obtained by Gaia. The AP accuracy is competitive with that of a support vector machine. For zero extinction stars covering a wide range of metallicity, surface gravity and temperature, ILIUM can estimate Teff to an accuracy of 0.3% at G=15 and to 4% for (lower signal-to-noise ratio) spectra at G=20, the Gaia limiting magnitude (mean absolute errors are quoted). [Fe/H] and logg can be estimated to accuracies of 0.1-0.4dex for stars with G>=18.5, depending on what priors we can place on the APs. If extinction varies a priori over a wide range (0-10mag) - which will be the case with Gaia because it is an all sky survey - then logg and [Fe/H] can still be estimated to 0.3 and 0.5dex respectively at G=15, but much poorer at G=18.5. Teff and Av can also be estimated quite accurately (3-4% and 0.1-0.2\mag respectively at G=15), but there is a strong and ubiquitous degeneracy in these parameters which limits our ability to estimate either accurately at faint magnitudes. Using the forward model we can map these degeneracies (in advance), and thus provide a complete probability distribution over solutions. Additional information from the Gaia parallaxes, other surveys or suitable priors can help reduce these degeneracies.

ILIUM is described in this article
The ILIUM forward modelling algorithm for multivariate parameter estimation and its application to derive stellar parameters from Gaia spectrophotometry
C.A.L. Bailer-Jones, 2010, MNRAS 403, 96-116

More on ILIUM can be found in a series of Gaia DPAC technical notes. The above paper is based on the first four, but does not include all details and includes some additional results.

  • ILIUM. An iterative local interpolation method for parameter estimation
  • Application of ILIUM to the estimation of the Teff-[Fe/H] pair from BP/RP
  • ILIUM III. Further observations, tests and developments Functions
  • ILIUM IV. Three-dimensional forward model and demonstration of a strong and ubiquitous Teff-Av degeneracy in BP/RP
  • ILIUM V. Further degeneracy mapping, application to the semi-empirical library and the use of the forward model and MCMC to build likelihood maps

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    Coryn Bailer-Jones, calj at
    Last modified: 26 January 2010