Learning approach to the detection of gravitational wave transients

We investigate the class of quadratic detectors (i.e., the statistic is a bilinear function of the data) for the detection of poorly modeled gravitational transients of short duration. We point out that all such detection methods are equivalent to passing the signal through a filter bank and linearly combining the output energy. Existing methods for the choice of the filter bank and of the weight parameters (to be multiplied by the output energy of each filter before summation) rely essentially on the two following ideas: (i) the use of the likelihood function based on a (possibly noninformative) statistical model of the signal and the noise; (ii) the use of Monte Carlo simulations for the tuning of parametric filters to get the best detection probability while keeping the false alarm rate fixed. We propose a third approach according to which the filter bank is "learned" from a set of training data. By-products of this viewpoint are that, contrarily to previous methods, (i) there is no requirement of an explicit description of the probability density function of the data when the signal is present and (ii) the filters we use are nonparametric. The learning procedure may be described as a two step process: first, estimate the mean and covariance of the signal with the training data; second, find the filters which maximize a contrast criterion referred to as the deflection between the "noise only" and "signal + noise" hypotheses. The deflection is homogeneous to the signal-to-noise ratio and it uses the quantities estimated at the first step. We apply this original method to the problem of the detection of supernovae core collapses. We use the catalog of waveforms provided recently by Dimmelmeier to train our algorithm. We expect such a detector to have better performances in this particular problem provided that the reference signals are reliable.