Signal probability estimation with penalized likelihood method on weighted data

In this work we consider the problem faced by astrophysicists where high energy signal neutrinos must be separated from overwhelming background events. We propose a modification to the usual penalized likelihood approach, to take account of the usage of importance sampling techniques in the generation of the simulated training data. Each simulated maltivariate data point has two associated weights, which define its contribution to the signal or background count. We wish to find the most powerful decision boundary at a certain significance level to optimally separate signal from background neutrinos. In this modified penalized likelihood method, the estimation of the logit function involves two major optimization steps and the use of KL (Kullback-Leibler) distance criterion for model tuning. We compare this approach with a non-standard SVM (support vector machine) approach. Results on simulated multivariate normal data and simulated neutrino data are presented. For the neutrino data, since the truth is unknown, we show a way to check whether the proposed method is working properly.