Neural networks as a tool for parameter estimation in astrophysical data

Abstract

We present a neural net algorithm for parameter estimation in the context of large cosmological data sets. Cosmological data sets present a particular challenge to pattern-recognition algorithms since the input patterns (galaxy redshift surveys, maps of cosmic microwave background anisotropy) are not fixed templates overlaid with random noise, but rather are random realizations whose information content lies in the correlations between data points. We train a ``committee'' of neural nets to distinguish between Monte Carlo simulations at fixed parameter values. Sampling the trained networks using additional Monte Carlo simulations generated at intermediate parameter values allows accurate interpolation to parameter values for which the networks were never trained. The Monte Carlo samples automatically provide the probability distributions and truth tables required for either a frequentist or Bayseian analysis of the one observable sky. We demonstrate that neural networks provide unbiased parameter estimation with comparable precision as maximum-likelihood algorithms but significant computational savings. In the context of CMB anisotropies, the computational cost for parameter estimation via neural networks scales as $N^{3/2}$. The results are insensitive to the noise levels and sampling schemes typical of large cosmological data sets and provide a desirable tool for the new generation of large, complex data sets.

21 pages, 3 figures, submitted to "Neural Networks" special issue on GeoScience and Astronomy

References in corpus (17)

• 4-Year COBE DMR Cosmic Microwave Background Observations: Maps and Basic Results
• Cosmic Topology
• Estimating the Power Spectrum of the Cosmic Microwave Background
• Power Spectrum of Primordial Inhomogeneity Determined from the 4-Year COBE DMR Sky Maps
• Eigenmode Analysis of Galaxy Redshift Surveys I. Theory and Methods
• Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps
• An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps
• On Determining the Spectrum of Primordial Inhomogeneity from the COBE DMR Sky Maps: II. Results of Two Year Data Analysis
• Estimating non-gaussianity in the microwave background
• Neural computation as a tool for galaxy classification : methods and examples
• Physical Parameterization of Stellar Spectra: The Neural Network Approach
• Wide Field Imaging. I. Applications of Neural Networks to object detection and star/galaxy classification
• RMS Anisotropy in the COBE-DMR Four-Year Sky Maps
• Statistical Power, the Bispectrum and the Search for Non-Gaussianity in the CMB Anisotropy
• Power Spectrum Estimators For Large CMB Datasets
• CMB Power Spectrum Estimation via Hierarchical Decomposition
• Bayesian joint estimation of non-Gaussianity and the power spectrum