From 292436b5fcc95cded617c5dbfff6d1100da531a3 Mon Sep 17 00:00:00 2001 From: Margaret Lazarovits Date: Mon, 10 Jul 2023 11:23:01 -0500 Subject: [PATCH 1/5] added section on parametric cuts to remove mass sculting --- content/training/Decorrelation.md | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/content/training/Decorrelation.md b/content/training/Decorrelation.md index aa745c6..4557e05 100644 --- a/content/training/Decorrelation.md +++ b/content/training/Decorrelation.md @@ -30,13 +30,16 @@ Generally, the best method for making a neural network or BDT's output independe 1. Add a distance correlation function to the loss function that calculates the non-linear correlation between the NN output and some variables that you care about, e.g. jet mass, that you can force the network to minimize which decorrelates the two variables. ([Disco](https://arxiv.org/pdf/2001.05310.pdf)) +## Parametric Cut +When designing jet taggers, variables of interest for discriminators include N-subjettiness derived quantities. Often, these quantities will be correlated with, for example, the $p_T$ of the jet. One example of this type of correlation is called "mass scuplting" and happens when the distribution of the discriminating variable in background begins to exhibit a shape similar to that of the signal with successive cuts. This correlation can have confounding effects in the tagger and one way to remove these effects is to parametrically cut on the discriminant. + +One such prescription to remove these correlations is described [here](https://arxiv.org/abs/1603.00027) and focuses on removing the $p_T$ dependence in the soft-drop mass variable $\rho$. The authors note that there is a $p_T$ dependence in the N-subjettiness ratio $\tau_2/\tau_1$ as a function of the QCD jet scaling (soft-drop) variable, defined as $\rho = log(m^2)(p_T^2)$, which leads to mass sculpting. In order to alleviate this issue, the authors introduce a modified version of the soft-drop variable, $\rho' = \rho + log(p_T/\mu)$ where $\mu$ is chosen to be 1 GeV. It can also be noted that there is a linear depedence between $\tau_2/\tau_1$ and $\rho'$. Here, the authors remedy this by modelling the linear depedence with $\tau_{21}' + \tau_2/\tau_1 - M \times \rho'$ where $\M$ is fit from the data. Applying both these transformations flattens out the relationship between the ratio and the soft-drop variable and removes the mass sculpting effects. It is imperative that the transformation between variables are smooth, as discontinuous functions may lead to artificial features in the data. + + ## Notes to delete later Based on a question we received on [CMSTalk](https://cms-talk.web.cern.ch/t/bdt-score-mass-decorrelation/13184) we should create a new document covering decorrelation methods, an example of which would be decorrelating w.r.t the mass distribution. -1. Follow the [prescription](https://arxiv.org/abs/1603.00027) published by the JetMET group, which talks about designing V taggers. Basically changes the cut on the discriminant as a smooth analytical function of the variable of interest, say M_{X} (hereon referred to as MX). - 1. You can use a variant of DDT that defines a numerical function for every value of (MX,pt) (or MX,MY) plane; this function is smoothed (which is important, since non-smoothing may result in an artificial bump in data). You can read a lot about this in the documentation supporting EXO-17-001. This is usually called a “DDT map”. - 1. Methods used by the "mass parameterized BDT" used in the HH Multi-lepton search (HIG-21-002). This was talked about in an [ML forum presentation](https://indico.cern.ch/event/818774/contributions/3420466/attachments/1840727/3019731/ML_Forum_talk_May8_2019.pdf). 1. **Randomization method**: From 6a40ef8b7a3e61677c2d66687c0a5940b85652fd Mon Sep 17 00:00:00 2001 From: Margaret Lazarovits Date: Tue, 11 Jul 2023 09:47:01 -0500 Subject: [PATCH 2/5] added methods for mass parameterized BDT --- content/training/Decorrelation.md | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) diff --git a/content/training/Decorrelation.md b/content/training/Decorrelation.md index 4557e05..9b8ba80 100644 --- a/content/training/Decorrelation.md +++ b/content/training/Decorrelation.md @@ -36,6 +36,17 @@ When designing jet taggers, variables of interest for discriminators include N-s One such prescription to remove these correlations is described [here](https://arxiv.org/abs/1603.00027) and focuses on removing the $p_T$ dependence in the soft-drop mass variable $\rho$. The authors note that there is a $p_T$ dependence in the N-subjettiness ratio $\tau_2/\tau_1$ as a function of the QCD jet scaling (soft-drop) variable, defined as $\rho = log(m^2)(p_T^2)$, which leads to mass sculpting. In order to alleviate this issue, the authors introduce a modified version of the soft-drop variable, $\rho' = \rho + log(p_T/\mu)$ where $\mu$ is chosen to be 1 GeV. It can also be noted that there is a linear depedence between $\tau_2/\tau_1$ and $\rho'$. Here, the authors remedy this by modelling the linear depedence with $\tau_{21}' + \tau_2/\tau_1 - M \times \rho'$ where $\M$ is fit from the data. Applying both these transformations flattens out the relationship between the ratio and the soft-drop variable and removes the mass sculpting effects. It is imperative that the transformation between variables are smooth, as discontinuous functions may lead to artificial features in the data. +## Methods for mass parameterized BDTs +A dihiggs multilepton search (HIG-21-002) made use of a BDT for signal discrimination, parameterized by the dihiggs invariant mass. In order to avoid correlations in the BDT output and invariant mass of the dihiggs system, they looked at three different methods of decorrelation: randomization, oversampling, and variable profiling. All of the methods utilized a (more or less) 50/50 dataset train/test split where one iteration of the BDT was trained on "even" numbered events and the datacards were produced with the "odd" numbered events. This procedure was repeated for the opposite configuration. Then, to deteremine if the BDT was correctly interpolating the signal masses, one mass point was omitted from training and the results of this BDT were compared to a BDT trained on only this single, omitted mass point. For each train/test configuration (even/odd or odd/even), the BDT's performance gain, as well as loss, were evaluated with ROC curves with two ommitted mass points (done separately). + +In the randomization method, a generator-level dihiggs invariant mass was randomly assigned to each background event the BDT was trained on. For the oversampling method, every signal mass point was assigned to a duplicate of each background event. Obviously the oversampling method leads to slower execution but the same effective statistics for all backgrounds and each signal mass. Conversely, the randomization approach is quicker, but leads to reduced effective statistics. Lastly, to improve performance over lower signal masses, each BDT input variable was profiled as a function of $m_{HH}$. This profile was fit with a polynomial function, and then each point in the input distribution is divided by the fit function value. This corrected ratio is used as the new input to the BDT. The authors also found that splitting the BDT training into high and low mass regions helped. + +In the end, oversampling, especially when combined with input variable corrections, provided a sizable performance gain (5.6%) over the randomization method. This gain is determined from ROC curves made for each training iteration (even/odd or odd/event) and each method. The performance loss is also a 5% improvement over the randomization method. + +For more information on these methods, see the HIG-21-002 [ML forum presentation](https://indico.cern.ch/event/818774/contributions/3420466/attachments/1840727/3019731/ML_Forum_talk_May8_2019.pdf)). + + + ## Notes to delete later Based on a question we received on [CMSTalk](https://cms-talk.web.cern.ch/t/bdt-score-mass-decorrelation/13184) we should create a new document covering decorrelation methods, an example of which would be decorrelating w.r.t the mass distribution. @@ -45,10 +56,10 @@ Based on a question we received on [CMSTalk](https://cms-talk.web.cern.ch/t/bdt- 1. **Randomization method**: Assign a mass value to the background event, chosen randomly out of the array of available signal mass values for which we have signal MC. This method is fast, but you are effectively reducing the available background per signal mass by the number of mass points. - 1. **Oversampling method**: + 2. **Oversampling method**: Make N copies of the background event, where N stands for the total number of signal masses for which we have signal MC, and assign each copy one of the mass values. This method is slower than the *randomization method*, but the stats per mass bin are the same. - 1. **Simplified method**: + 3. **Simplified method**: Profile the input variables vs the signal mass in all of the signal MC and then do a polynomial fit to the distribution. Then correct/reweight the BDT input variables so that the input variable correlation with signal mass is flat. 1. Konstantin Matchev et. al. covered this in ([1911.12299](https://link.springer.com/article/10.1007/JHEP03(2021)291)). The example used in the question is covered in section 4 of the paper, with figure 4 being an example of the achievable decorrelation. The authors also produced a Python module called [ThickBrick](https://prasanthcakewalk.gitlab.io/thickbrick/) which implements their prescription. A demo of ThickBrick was given at [PyHEP2020](https://www.youtube.com/watch?v=rM19CoMNkfA). From d5a9d2e48163dae9f403323a51bd41bfef19172b Mon Sep 17 00:00:00 2001 From: Margaret Lazarovits Date: Fri, 4 Aug 2023 15:07:08 -0500 Subject: [PATCH 3/5] first draft of decorrelation docs --- content/training/Decorrelation.md | 13 +------------ 1 file changed, 1 insertion(+), 12 deletions(-) diff --git a/content/training/Decorrelation.md b/content/training/Decorrelation.md index 9b8ba80..a78eb3c 100644 --- a/content/training/Decorrelation.md +++ b/content/training/Decorrelation.md @@ -47,21 +47,10 @@ For more information on these methods, see the HIG-21-002 [ML forum presentation +So far we have seen decorrelation achieved by using inputs that are decorrelated for the classifier and regularizing the output to penalize learning correlations. Another approach can be to learn decorrelation by maximizing performance metrics that more closely align with the sensitivity of the analysis, like in [this paper](https://link.springer.com/article/10.1007/JHEP03(2021)291) and their corresponding Python-based package, [ThickBrick](https://prasanthcakewalk.gitlab.io/thickbrick/). In this case, the authors study the dependence of the event selection threshold on the signal purity in a given bin of the distribution of an observable. They demonstrate that the threshold increases with signal purity, "implying that the threshold is stronger in the x-'bins' of higher purity." This parametric event selection threshold "naturally leads to decorrelation of the event selection criteria from the event variable x." The failure to incorporate the dependencies on observable distributions is framed as a misalignment between the ML-based selector and the sensitivity of the physics analysis. A demo of their package, ThickBrick, was given at [PyHEP2020](https://www.youtube.com/watch?v=rM19CoMNkfA). -## Notes to delete later -Based on a question we received on [CMSTalk](https://cms-talk.web.cern.ch/t/bdt-score-mass-decorrelation/13184) we should create a new document covering decorrelation methods, an example of which would be decorrelating w.r.t the mass distribution. -1. Methods used by the "mass parameterized BDT" used in the HH Multi-lepton search (HIG-21-002). This was talked about in an [ML forum presentation](https://indico.cern.ch/event/818774/contributions/3420466/attachments/1840727/3019731/ML_Forum_talk_May8_2019.pdf). - 1. **Randomization method**: - Assign a mass value to the background event, chosen randomly out of the array of available signal mass values for which we have signal MC. This method is fast, but you are effectively reducing the available background per signal mass by the number of mass points. - 2. **Oversampling method**: - Make N copies of the background event, where N stands for the total number of signal masses for which we have signal MC, and assign each copy one of the mass values. This method is slower than the *randomization method*, but the stats per mass bin are the same. - 3. **Simplified method**: - Profile the input variables vs the signal mass in all of the signal MC and then do a polynomial fit to the distribution. Then correct/reweight the BDT input variables so that the input variable correlation with signal mass is flat. -1. Konstantin Matchev et. al. covered this in ([1911.12299](https://link.springer.com/article/10.1007/JHEP03(2021)291)). The example used in the question is covered in section 4 of the paper, with figure 4 being an example of the achievable decorrelation. The authors also produced a Python module called [ThickBrick](https://prasanthcakewalk.gitlab.io/thickbrick/) which implements their prescription. A demo of ThickBrick was given at [PyHEP2020](https://www.youtube.com/watch?v=rM19CoMNkfA). - -[*] According to CMS-DP-2020-002 and the ParticleNet authors, (3) worked better than (4) and both are preferable to the DDT methods in (5). You can also do (3) and then apply DDT (5) on top of that to take care of any residual differences. \ No newline at end of file From 6e63812aa302a474b9c5da95c6bac038c73e8a68 Mon Sep 17 00:00:00 2001 From: Margaret Lazarovits Date: Mon, 30 Oct 2023 10:36:59 -0500 Subject: [PATCH 4/5] edited Decorrelation docs - added graphics and more explanation to some sections --- content/images/BDTscores_EXO19020.png | Bin 0 -> 375991 bytes content/images/DisCoPresentation_MLForum.png | Bin 0 -> 125562 bytes content/images/ML_Forum_talk_May8_2019.png | Bin 0 -> 219770 bytes content/training/Decorrelation.md | 33 ++++++++++++------- 4 files changed, 21 insertions(+), 12 deletions(-) create mode 100644 content/images/BDTscores_EXO19020.png create mode 100644 content/images/DisCoPresentation_MLForum.png create mode 100644 content/images/ML_Forum_talk_May8_2019.png diff --git a/content/images/BDTscores_EXO19020.png b/content/images/BDTscores_EXO19020.png new file mode 100644 index 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z8!=!PrF`vsxsxZl>J9ma`!r)$q?pl*(v1yb51xY%{#C^I=Rbgd5QqYfSn)R&*RwVJkJqNk^9TO_@A{u*`Tuw|9$x8HpylD< S1kk(y{v<`^L@I>zzx*HJ*URbv literal 0 HcmV?d00001 diff --git a/content/training/Decorrelation.md b/content/training/Decorrelation.md index a78eb3c..56cefa4 100644 --- a/content/training/Decorrelation.md +++ b/content/training/Decorrelation.md @@ -10,42 +10,51 @@ Below, we detail various methods for common scenarios focusing on BDT (boosted d ## Impartial Training Data -Generally, the best method for making a neural network or BDT's output independent of some known variable is to remove any bias in the training dataset, which is commonly done by adding or removing information. +Generally, the best method for making a neural network's or BDT's output independent of some known variable is to remove any bias in the training dataset, which is commonly done by adding or removing information. ### Adding Information -1. Training on a mix of signals with different masses can help prevent the BDT from learning the mass. +- Training on a mix of signals with different masses can help prevent the BDT from learning the mass. ### Removing Information -1. If you have any input variables that are highly correlated with the mass, you may want to omit them. There may be a loss of raw discrimination power with this approach, but the underlying interpretation will be more sound. +- If you have any input variables that are highly correlated with the mass, you may want to omit them. There may be a loss of raw discrimination power with this approach, but the underlying interpretation will be more sound. ## Reweighting -1. "Reweighting all the input samples to match a reference kinematic distribution. This can be the mass directly, or an ingredient in the invariant mass, such as the pt. I describe this as reweighting to a reference distribution rather than flattening, because a completely flat distribution can require very large weights that skew the training. Making all the samples’ distributions match is usually enough to prevent the BDT from sculpting the background mass. This technique was ultimately what we used in EXO-19-020 (see AN-19-061 for more details)." - Kevin Pedro - 1. This is what is done for the ImageTop tagger and ParticleNet group of taggers. +- One method to achieve correlation by weighting data is reweighting the network's input samples to match a reference distribution. Examples input variables include mass, or an input to invariant mass, like the $p_T$. This method is distinct from flattening the data since it is weighted to match a target distribution rather than a flat distribution. Flattening can also require very large weights that could potentially affect training. This is one way to avoid having the network sculpt, or learn, a certain kinematic quantity, like the background mass. An example of this technique is given in [EXO-19-020](https://arxiv.org/abs/2112.11125). + - This is what is done for the ImageTop tagger and ParticleNet group of taggers. +![reweighted_BDT_scores](../images/BDTscores_EXO19020.png) +BDT scores from EXO-10-020 where the jet $p_T$ distribution is reweighted to match a reference distribution for each sample. ## Adversarial Approach -1. Modify the loss function to enforce uniformity in the variable of interest (i.e. the mass). Check out these links ([1](https://arxiv.org/abs/1410.4140), [2](https://github.com/arogozhnikov/hep_ml), [3](https://github.com/arogozhnikov/hep_ml/blob/master/notebooks/BoostingToUniformity.ipynb)). "I’ve personally found that the “flatness loss function” (eq. 2.9, corresponding to BinFlatnessLossFunction in the python package) works best here." - Kevin Pedro - 1. This is what is done for the DeepAK8-MD taggers. +Adversarial approaches to decorrelation revolve around including a penalty, or regularization, term in the loss function in training. The loss function can be modified to enforce uniformity in the variable of interest (i.e. mass). Check out these links ([1](https://arxiv.org/abs/1410.4140), [2](https://github.com/arogozhnikov/hep_ml), [3](https://github.com/arogozhnikov/hep_ml/blob/master/notebooks/BoostingToUniformity.ipynb)) for some examples of this. One way to technically implement this type of approach is using the "flatness loss function" (i.e. [BinFlatnessLossFunction](https://arogozhnikov.github.io/hep_ml/losses.html?highlight=binflatnesslossfunction#hep_ml.losses.BinFlatnessLossFunction) in the hep-ml package). This type of decorrelation what is done for the DeepAK8-MD taggers. -1. Add a distance correlation function to the loss function that calculates the non-linear correlation between the NN output and some variables that you care about, e.g. jet mass, that you can force the network to minimize which decorrelates the two variables. ([Disco](https://arxiv.org/pdf/2001.05310.pdf)) +Another type of regularization one can do to acheive decorrelation is penalizing the loss function on a certain type of correlation, for example distance. In the seminal distance correlation in HEP-ML paper (([DisCo Fever: Robust Networks Through Distance Correlation](https://arxiv.org/pdf/2001.05310.pdf))), distance is in this case is defined as distance correlation (DisCo), a measure derived from distance covariance, first introduced [here](https://projecteuclid.org/journals/annals-of-applied-statistics/volume-3/issue-4/Brownian-distance-covariance/10.1214/09-AOAS312.full). This distance correlation function calculates the non-linear correlation between the NN output and some variables that you care about, e.g. jet mass, that you can force the network to minimize which decorrelates the two variables by including it as a penalty term in the loss function. An extension of this can be found in the Double-DisCo method, given below, which highlights the distance correlation term in the loss function at the bottom. + +![disco_method](../images/DisCoPresentation_MLForum.png) + +Source: [ABCD Disco with MDMM](https://indico.cern.ch/event/1330198/contributions/5599632/attachments/2727547/4740694/presentation_MLForum.pdf) (ML Forum) +Many thanks to Kevin Pedro for his input on this section and the previous one. ## Parametric Cut When designing jet taggers, variables of interest for discriminators include N-subjettiness derived quantities. Often, these quantities will be correlated with, for example, the $p_T$ of the jet. One example of this type of correlation is called "mass scuplting" and happens when the distribution of the discriminating variable in background begins to exhibit a shape similar to that of the signal with successive cuts. This correlation can have confounding effects in the tagger and one way to remove these effects is to parametrically cut on the discriminant. -One such prescription to remove these correlations is described [here](https://arxiv.org/abs/1603.00027) and focuses on removing the $p_T$ dependence in the soft-drop mass variable $\rho$. The authors note that there is a $p_T$ dependence in the N-subjettiness ratio $\tau_2/\tau_1$ as a function of the QCD jet scaling (soft-drop) variable, defined as $\rho = log(m^2)(p_T^2)$, which leads to mass sculpting. In order to alleviate this issue, the authors introduce a modified version of the soft-drop variable, $\rho' = \rho + log(p_T/\mu)$ where $\mu$ is chosen to be 1 GeV. It can also be noted that there is a linear depedence between $\tau_2/\tau_1$ and $\rho'$. Here, the authors remedy this by modelling the linear depedence with $\tau_{21}' + \tau_2/\tau_1 - M \times \rho'$ where $\M$ is fit from the data. Applying both these transformations flattens out the relationship between the ratio and the soft-drop variable and removes the mass sculpting effects. It is imperative that the transformation between variables are smooth, as discontinuous functions may lead to artificial features in the data. +One such prescription to remove these correlations is described [here](https://arxiv.org/abs/1603.00027) and focuses on removing the $p_T$ dependence in the soft-drop mass variable $\rho$. The authors note that there is a $p_T$ dependence in the N-subjettiness ratio $\tau_2/\tau_1$ as a function of the QCD jet scaling (soft-drop) variable, defined as $\rho = log(m^2)(p_T^2)$, which leads to mass sculpting. In order to alleviate this issue, the authors introduce a modified version of the soft-drop variable, $\rho' = \rho + log(p_T/\mu)$ where $\mu$ is chosen to be 1 GeV. It can also be noted that there is a linear depedence between $\tau_2/\tau_1$ and $\rho'$. Here, the authors remedy this by modelling the linear depedence with $\tau_{21}' + \tau_2/\tau_1 - M \times \rho'$ where $M$ is fit from the data. Applying both these transformations flattens out the relationship between the ratio and the soft-drop variable and removes the mass sculpting effects. It is imperative that the transformation between variables are smooth, as discontinuous functions may lead to artificial features in the data. ## Methods for mass parameterized BDTs -A dihiggs multilepton search (HIG-21-002) made use of a BDT for signal discrimination, parameterized by the dihiggs invariant mass. In order to avoid correlations in the BDT output and invariant mass of the dihiggs system, they looked at three different methods of decorrelation: randomization, oversampling, and variable profiling. All of the methods utilized a (more or less) 50/50 dataset train/test split where one iteration of the BDT was trained on "even" numbered events and the datacards were produced with the "odd" numbered events. This procedure was repeated for the opposite configuration. Then, to deteremine if the BDT was correctly interpolating the signal masses, one mass point was omitted from training and the results of this BDT were compared to a BDT trained on only this single, omitted mass point. For each train/test configuration (even/odd or odd/even), the BDT's performance gain, as well as loss, were evaluated with ROC curves with two ommitted mass points (done separately). +Finally, when using a BDT that is parameterized by a mass quantity of interest, the output can be decorrelated from that mass by three different methods: randomization, oversampling, and variable profiling. Randomization entails randomly pairing a mass quanitity to a background training event so the BDT does not learn any meaningful associations between the mass and the output. For oversampling, this is a bootstrapping method where every input background event is paired with a potential mass point so the effective statistics for all the mass points are the same. Finally, variable profiling has the user profile each BDT input as a function of the mass quantity of interest. Examples of each of these methods is given below in the context of a di-higgs search. -In the randomization method, a generator-level dihiggs invariant mass was randomly assigned to each background event the BDT was trained on. For the oversampling method, every signal mass point was assigned to a duplicate of each background event. Obviously the oversampling method leads to slower execution but the same effective statistics for all backgrounds and each signal mass. Conversely, the randomization approach is quicker, but leads to reduced effective statistics. Lastly, to improve performance over lower signal masses, each BDT input variable was profiled as a function of $m_{HH}$. This profile was fit with a polynomial function, and then each point in the input distribution is divided by the fit function value. This corrected ratio is used as the new input to the BDT. The authors also found that splitting the BDT training into high and low mass regions helped. +A di-higgs multilepton search (HIG-21-002) made use of a BDT for signal discrimination, parameterized by the di-higgs invariant mass. In order to avoid correlations in the BDT output and invariant mass of the di-higgs system, they looked at decorrelation via randomization, oversampling, and variable profiling. All of the methods utilized a (more or less) 50/50 dataset train/test split where one iteration of the BDT was trained on "even" numbered events and the datacards were produced with the "odd" numbered events. This procedure was repeated for the opposite configuration. Then, to deteremine if the BDT was correctly interpolating the signal masses, one mass point was omitted from training and the results of this BDT were compared to a BDT trained on only this single, omitted mass point. For each train/test configuration (even/odd or odd/even), the BDT's performance gain, as well as loss, were evaluated with ROC curves with two ommitted mass points (done separately). + +In the randomization method, a generator-level di-higgs invariant mass was randomly assigned to each background event the BDT was trained on. For the oversampling method, every signal mass point was assigned to a duplicate of each background event. Obviously the oversampling method leads to slower execution but the same effective statistics for all backgrounds and each signal mass. Conversely, the randomization approach is quicker, but leads to reduced effective statistics. Lastly, to improve performance over lower signal masses, each BDT input variable was profiled as a function of $m_{HH}$. This profile was fit with a polynomial function, and then each point in the input distribution is divided by the fit function value. This corrected ratio is used as the new input to the BDT. The authors also found that splitting the BDT training into high and low mass regions helped. In the end, oversampling, especially when combined with input variable corrections, provided a sizable performance gain (5.6%) over the randomization method. This gain is determined from ROC curves made for each training iteration (even/odd or odd/event) and each method. The performance loss is also a 5% improvement over the randomization method. For more information on these methods, see the HIG-21-002 [ML forum presentation](https://indico.cern.ch/event/818774/contributions/3420466/attachments/1840727/3019731/ML_Forum_talk_May8_2019.pdf)). - +![mass_param_BDT](../images/ML_Forum_talk_May8_2019.png) +Source: HIG-21-002 ML forum presentation So far we have seen decorrelation achieved by using inputs that are decorrelated for the classifier and regularizing the output to penalize learning correlations. Another approach can be to learn decorrelation by maximizing performance metrics that more closely align with the sensitivity of the analysis, like in [this paper](https://link.springer.com/article/10.1007/JHEP03(2021)291) and their corresponding Python-based package, [ThickBrick](https://prasanthcakewalk.gitlab.io/thickbrick/). In this case, the authors study the dependence of the event selection threshold on the signal purity in a given bin of the distribution of an observable. They demonstrate that the threshold increases with signal purity, "implying that the threshold is stronger in the x-'bins' of higher purity." This parametric event selection threshold "naturally leads to decorrelation of the event selection criteria from the event variable x." The failure to incorporate the dependencies on observable distributions is framed as a misalignment between the ML-based selector and the sensitivity of the physics analysis. A demo of their package, ThickBrick, was given at [PyHEP2020](https://www.youtube.com/watch?v=rM19CoMNkfA). From 729d4180e4eef35aff45abcbf64b35d7f13fcaaa Mon Sep 17 00:00:00 2001 From: Margaret Lazarovits Date: Wed, 1 Nov 2023 10:23:00 -0500 Subject: [PATCH 5/5] updated graphics with public results, included ABCDisco example --- content/training/Decorrelation.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/content/training/Decorrelation.md b/content/training/Decorrelation.md index 56cefa4..1538636 100644 --- a/content/training/Decorrelation.md +++ b/content/training/Decorrelation.md @@ -29,11 +29,11 @@ BDT scores from EXO-10-020 where the jet $p_T$ distribution is reweighted to mat ## Adversarial Approach Adversarial approaches to decorrelation revolve around including a penalty, or regularization, term in the loss function in training. The loss function can be modified to enforce uniformity in the variable of interest (i.e. mass). Check out these links ([1](https://arxiv.org/abs/1410.4140), [2](https://github.com/arogozhnikov/hep_ml), [3](https://github.com/arogozhnikov/hep_ml/blob/master/notebooks/BoostingToUniformity.ipynb)) for some examples of this. One way to technically implement this type of approach is using the "flatness loss function" (i.e. [BinFlatnessLossFunction](https://arogozhnikov.github.io/hep_ml/losses.html?highlight=binflatnesslossfunction#hep_ml.losses.BinFlatnessLossFunction) in the hep-ml package). This type of decorrelation what is done for the DeepAK8-MD taggers. -Another type of regularization one can do to acheive decorrelation is penalizing the loss function on a certain type of correlation, for example distance. In the seminal distance correlation in HEP-ML paper (([DisCo Fever: Robust Networks Through Distance Correlation](https://arxiv.org/pdf/2001.05310.pdf))), distance is in this case is defined as distance correlation (DisCo), a measure derived from distance covariance, first introduced [here](https://projecteuclid.org/journals/annals-of-applied-statistics/volume-3/issue-4/Brownian-distance-covariance/10.1214/09-AOAS312.full). This distance correlation function calculates the non-linear correlation between the NN output and some variables that you care about, e.g. jet mass, that you can force the network to minimize which decorrelates the two variables by including it as a penalty term in the loss function. An extension of this can be found in the Double-DisCo method, given below, which highlights the distance correlation term in the loss function at the bottom. +Another type of regularization one can do to acheive decorrelation is penalizing the loss function on a certain type of correlation, for example distance. In the seminal distance correlation in HEP-ML paper (([DisCo Fever: Robust Networks Through Distance Correlation](https://arxiv.org/pdf/2001.05310.pdf))), distance is in this case is defined as distance correlation (DisCo), a measure derived from distance covariance, first introduced [here](https://projecteuclid.org/journals/annals-of-applied-statistics/volume-3/issue-4/Brownian-distance-covariance/10.1214/09-AOAS312.full). This distance correlation function calculates the non-linear correlation between the NN output and some variables that you care about, e.g. jet mass, that you can force the network to minimize which decorrelates the two variables by including it as a penalty term in the loss function. An extension of this can be found in the Double DisCo method, given below, which highlights the distance correlation term in the loss function at the bottom. The Double DisCo network leverages the ABCD method for background estimation, which is why it requires two separate discriminants. Below is the Double DisCo NN architecture used in MLG-23-003. Notice the two separate discriminant paths consisting of a Dense layer, a Dropout layer, and another Dense layer before outputting a single discriminant per path. -![disco_method](../images/DisCoPresentation_MLForum.png) +![disco_method](../images/doublediscoNN.png) +Source: CMS [AN-22-101](https://cms.cern.ch/iCMS/analysisadmin/cadilines?line=MLG-23-003) for MLG-23-003. -Source: [ABCD Disco with MDMM](https://indico.cern.ch/event/1330198/contributions/5599632/attachments/2727547/4740694/presentation_MLForum.pdf) (ML Forum) Many thanks to Kevin Pedro for his input on this section and the previous one. ## Parametric Cut @@ -51,10 +51,10 @@ In the randomization method, a generator-level di-higgs invariant mass was rando In the end, oversampling, especially when combined with input variable corrections, provided a sizable performance gain (5.6%) over the randomization method. This gain is determined from ROC curves made for each training iteration (even/odd or odd/event) and each method. The performance loss is also a 5% improvement over the randomization method. -For more information on these methods, see the HIG-21-002 [ML forum presentation](https://indico.cern.ch/event/818774/contributions/3420466/attachments/1840727/3019731/ML_Forum_talk_May8_2019.pdf)). +For more information on these methods, see the [HIG-21-002](https://arxiv.org/pdf/2206.10268.pdf). Below are some example BDT output scores for the $2\ell ss$ and $3 \ell$ channels for this analysis. -![mass_param_BDT](../images/ML_Forum_talk_May8_2019.png) -Source: HIG-21-002 ML forum presentation +![mass_param_BDT](../images/hig21002_bdtscores.png) +Source: [HIG-21-002](https://arxiv.org/pdf/2206.10268.pdf) So far we have seen decorrelation achieved by using inputs that are decorrelated for the classifier and regularizing the output to penalize learning correlations. Another approach can be to learn decorrelation by maximizing performance metrics that more closely align with the sensitivity of the analysis, like in [this paper](https://link.springer.com/article/10.1007/JHEP03(2021)291) and their corresponding Python-based package, [ThickBrick](https://prasanthcakewalk.gitlab.io/thickbrick/). In this case, the authors study the dependence of the event selection threshold on the signal purity in a given bin of the distribution of an observable. They demonstrate that the threshold increases with signal purity, "implying that the threshold is stronger in the x-'bins' of higher purity." This parametric event selection threshold "naturally leads to decorrelation of the event selection criteria from the event variable x." The failure to incorporate the dependencies on observable distributions is framed as a misalignment between the ML-based selector and the sensitivity of the physics analysis. A demo of their package, ThickBrick, was given at [PyHEP2020](https://www.youtube.com/watch?v=rM19CoMNkfA).