Optimal Ridge Detection using Coverage Risk
This provides a method for improving density ridge estimation in statistical applications, though it appears incremental as it builds on existing error measures.
The authors tackled the problem of density ridge estimation by introducing coverage risk as an error measure, proposing two risk estimators for selecting tuning parameters, and demonstrating successful recovery of underlying density structures in simulated and cosmology datasets.
We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show that we can select tuning parameters by minimizing the estimated risk. We study the rate of convergence for coverage risk and prove consistency of the risk estimators. We apply our method to three simulated datasets and to cosmology data. In all the examples, the proposed method successfully recover the underlying density structure.