Determining the optimal noise scale for the convolution kernel bandwidth is crucial for effectively distinguishing between signal and background events. A systematic approach to finding this optimal scale could involve a combination of empirical testing and theoretical modeling based on the expected characteristics of the signal.
One method to achieve this is through cross-validation techniques, where different bandwidths are tested on a validation dataset to evaluate their performance in terms of signal enrichment in the selected signal region (SR). By measuring metrics such as the proportion of signal events within the SR and the overall sensitivity of the method, one can identify the bandwidth that maximizes these metrics.
Additionally, incorporating prior knowledge about the expected signal characteristics—such as the expected width of the signal peak or the typical scale of variations in the feature space—can inform the selection of the convolution kernel bandwidth. For instance, if prior studies suggest that the signal events are concentrated within a specific range of feature values, the bandwidth can be adjusted to reflect this range, ensuring that the filtering process retains relevant signal information while suppressing background noise.
Moreover, Bayesian optimization techniques could be employed to systematically explore the bandwidth parameter space, allowing for a more efficient search for the optimal noise scale. By modeling the relationship between bandwidth and detection performance, one can iteratively refine the choice of bandwidth based on observed outcomes, leading to a more data-driven and systematic determination of the optimal convolution kernel bandwidth.