I am currently developing a boosted decision tree classifier and some of the input variables I am using have a momentum dependence. I would like to provide momentum as an input variable but I am worried that if I do this then the BDT will capitalise on the difference of the signal and background momentum distributions to aid in classification and therefore ultimately result in a momentum bias. To avoid this I would like to reweight background events such that their combined momentum distribution matches that of signal. How exactly do I go about doing this?
All help appreciated,
Could you be more explicit about which quantities are involved? Is there a way to use a transformed variable that eliminates the momentum dependence? For example, if you have something that looks like a gaussian and the mean is momentum dependent, but sigma is the same, just subtract the mean from your input variable.
Sure, the quantities I am concerned about are the following ATLAS b-tagging discriminants: IP2D, IP3D, RNNIP, JetFitter, SV1 and MV2c10rnn. They are themselves multivariate algorithms that are concerned with b-jet identification. As they are multivariate algorithms the momentum dependence is not clear and therefore I don’t think a transformation would be able to eliminate the dependence.
I would like to apply a similar approach to that described in this note on page 13:
I think you are referring to this passage in the text, right? (emphasis is mine)
The training of the multivariate classifier is performed on jets from tt¯ events with b-jets (1 million) being considered as signal, and c- (0.5 million) and light-flavour jets (1 million) being considered as background. The performance is tested on an independent sample of 5 million tt¯ events. The kinematic properties of the jets, namely pT and |η|, illustrated in Figure 9, are included in the training in order to take advantage of the correlations with the other input variables. However, to avoid differences in the kinematic distributions of signal and background (light-flavour jets) being interpreted as discriminating by the training, the signal jets are reweighted in pT and |η| to match the spectrum of the light-flavour background jets. No kinematic reweighting is applied at the evaluation stage of the multivariate classifier.
It seems to me that you should include the momentum (or just pT, as above), to aid in classification. However, when computing the efficiency, the reweighting is done to avoid interpreting a difference in distribution as a difference in training discrimination. That said, it is not clear how this reweigthing was done, so if you know who wrote the article, he/she would be the best person to ask, or at least someone from the experiment. I think this is a bit out of the scope for this forum (I would answer if I knew, but I’m not familiar with the analysis in the article).
Yes that’s the passage I was referring to. Having taken a better look at the TMVA user guide I believe TMVA has event-by-event weighting capabilities so in theory I should be able to capitalise on this to achieve my desired result. Thank you very much for the advice and taking the time to help me.
All the best,