Constraints on fNL from Wilkinson Microwave Anisotropy Probe 7-year data using a neural network classifier

Abstract

We present a multi-class neural network (NN) classifier as a method to measure nonGaussianity, characterised by the local non-linear coupling parameter fNL, in maps of the cosmic microwave background (CMB) radiation. The classifier is trained on simulated non-Gaussian CMB maps with a range of known fNL values by providing it with wavelet coefficients of the maps; we consider both the HealPix (HW) wavelet and the spherical Mexican hat wavelet (SMHW). When applied to simulated test maps, the NN classfier produces results in very good agreement with those obtained using standard chi2 minimization. The standard deviations of the fNL estimates for WMAPlike simulations were {\sigma} = 22 and {\sigma} = 33 for the SMHW and the HW, respectively, which are extremely close to those obtained using classical statistical methods in Curto et al. and Casaponsa et al. Moreover, the NN classifier does not require the inversion of a large covariance matrix, thus avoiding any need to regularise the matrix when it is not directly invertible, and is considerably faster.