FastBDT: A Speed-Optimized Multivariate Classification Algorithm for the Belle II Experiment

Abstract

during which the fitted classifier is applied to new datapoints with unknown labels. During the fitting-phase, the internal parameters (or model) of a multivariate classifier are adjusted, so that the classifier can statistically distinguish signal and background data-points. The model complexity plays an important role during the fitting-phase and can be controlled by the hyper-parameters of the model. If the model is too simple (too complex) it will be under-fitted (over-fitted) and perform poorly on test data-points with unknown labels.Stochastic gradient-boosted decision trees [8] are widely employed in high energy physics for multivariate classification and regression tasks. The implementation presented in this paper was developed for the Belle II experiment [2], which is located at the SuperKEKB collider in Tsukuba, Japan. Multivariate classification is extensively used in the Belle II Analysis Software Framework (BASF2) [16], for instance during the reconstruction of particle tracks, as part of particle identification algorithms, and to suppress background processes in physics analyses. Often, a large amount of classifiers must be fitted due to hyper-parameter optimization, different background scenarios, to gain improved estimates on the importance of individual features, or to create networks of classifiers which feed into one another. Therefore, Belle II required a default multivariate classification algorithm which is: fast during fitting and application; robust enough to be trained in an automated environment; can be reliably used by non-experts; preferably generates an interpretable model and exhibits a good out-of-the box performance.FastBDT satisfies those requirements and is the default multivariate classification algorithm in BASF2. On the other hand, BASF2 supports other popular multivariate analysis frameworks like TMVA [9], scikit-learn (SKLearn) [19], XGBoost [5] and Tensorflow [1] as well.Abstract Stochastic gradient-boosted decision trees are widely employed for multivariate classification and regression tasks. This paper presents a speed-optimized and cachefriendly implementation for multivariate classification called FastBDT. The concepts used to optimize the execution time are discussed in detail in this paper. The key ideas include: an equal-frequency binning on the input data, which allows replacing expensive floating-point with integer operations, while at the same time increasing the quality of the classification; a cache-friendly linear access pattern to the input data, in contrast to usual implementations, which exhibit a random access pattern. FastBDT provides interfaces to C/ C++, Python and TMVA. It is extensively used in the field of high energy physics (HEP) by the Belle II experiment.

Search for B+→μ+νμ and B+→μPrim1, Bernlochner2, Goldenzweig3 et al. 2020Phys. Rev. D350170View full textAdd to dashboardCite

“…To reduce the sizable background from continuum processes, a multivariate classifier using an optimized implementation of gradient BDTs [39] is used and trained to distinguish B þ → μ þ ν μ signal decays from continuum processes. The BDT exploits the fact that the event topology for nonresonant e þ e − -collision processes differ significantly from the resonant e þ e − → ϒð4SÞ → BB process.…”

The Full Event Interpretation

“…Finally, the FEI uses FastBDT [8], a gradient-boosted decision tree (BDT) implementation, as its default multivariate classification algorithm. The algorithm was originally designed for the FEI to speed up the training and application phase.…”

Tracking and vertexing in BELLE II

“…The CDC track finding combines different algorithms having in common the same starting point: a collection of CDC hits. The very first step implemented is a background filter based on a FastBDT (Fast Boosted Decision Tree), a speed-optimized multivariate classification algorithm developed for the Belle II experiment [5]. For the background rejection, the classification is based on clustered hits shape variables.…”

“…The results of both approaches are then combined, using the collection of track candidates obtained from the global method as a baseline. A multivariate approach based on FastBDT [5], and trained using simulated events, is used to add segments from the local finder to the global track candidates.…”