The aim of this talk is to describe a heuristic based on continuous time branching processes which gives very easily, a wide array of asymptotic results for random network models in terms of the Malthusian rate of growth and the stable age distribution of associated branching process. These techniques allow us to solve not only first passage percolation problems rigorously but also understand functionals such as the degree distribution of shortest path trees, congestion across edges as well as asymptotics for ``betweeness centrality'' a concept of crucial interest in social networks, in terms of Cox processes and extreme value distributions. These techniques also allow one to exactly solve models of ``weak disorder'' in the context of the stochastic mean field model of distance.
In this presentation, we propose an extension to existing biometric systems by applying a calibration function to the $n$ matching scores. We introduce a computationally-light calculation that can be applied either as a post-processing filter or embedded directly into an algorithm to yield perfectly calibrated probability-based scores. In addition to attaching a meaningful confidence measure to the output, the proposed methodology is also shown to improve the overall performance of a biometric system.
We apply our calibration theorem to an actual data set consisting of nearly 60,000 iris images. By comparing the detection error trade-off ($DET$) curves, we show that our score calibration post-processing filter reduces the area under the $DET$ curve from $2.41$ to $0.17$, and reduces the equal error rate ($EER$) from $5.40 \%$ to $2.84 \%$.
This is joint work with Dmitry Gorodnichy at the Canada Border Services Agency.