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Training (learning): a discriminator is built by using all the input variables. Then, the parameters are iteratively modified by comparing the discriminant output to the true label of the dataset (supervised machine learning algorithms, we will use two of them). This phase is crucial: one should tune the input variables and the parameters of the algorithm!
- As an alternative, algorithms that group and find patterns in the data according to the observed distribution of the input data are called unsupervised learning.
- A good habit is training multiple models with various hyperparameters on a “reduced” training set ( i.e. the full training set minus the so-called validation set), and then select the model that performs best on the validation set.
- Once, the validation process is over, you can re-train the best model on the full training set (including the validation set), and this gives you the final model.
Test: once the training has been performed, the discriminator score is computed in a separated, independent dataset for both
and
.
- A comparison is made between test and training classifier and their performances (in terms of ROC curves) are evaluated.
- If the test fails and the performance of the test and training are different, this could be a symptom of overtraining and our model can be considered not good!
Introduction to the physics problem
In this section you will find the following subsections:
- Particle Physics basic concepts: the Standard Model and the Higgs boson
you may skip it you have already basics knowledge about Particle Physics (cross-section,decay channels,Standard Model definitions, etc.). - Data exploration:
it is important that you pay attention to this section in order to understand all the next steps of the exercise.
Particle Physics basic concepts: the Standard Model and the Higgs boson
If everything went well until now, let's have a look at the physics we are interested in!
The Standard Model of elementary particles represents our knowledge of the microscopic world. It describes the matter constituents (quarks and leptons) and their interactions (mediated by bosons), which are the electromagnetic, the weak, and the strong interactions.
Among all these particles, the Higgs boson still represents a very peculiar case. It is the second heaviest known elementary particle (mass of 125 GeV) after the top quark (175 GeV).
The ideal instrument for measuring the Higgs boson properties is a particle collider. The Large Hadron Collider (LHC), situated nearby Geneva, between France and Switzerland, is the largest proton-proton collider ever built on Earth. It consists of a 27 km circumference ring, where proton beams are smashed at a center-of-mass energy of 13 TeV (99.999999% of the speed of light). At the LHC, 40 Million collisions / second occurs, providing an enormous amount of data. Thanks to these data, ATLAS and CMS experiments discovered the missing piece of the Standard Model, the Higgs boson, in 2012.
During a collision, the energy is so high that protons are "broken" into their fundamental components, i.e. quarks and gluons, which can interact together, producing particles that we don't observe in our everyday life, such as the top quark. The production of a top quark is, by the way, a relatively "rare" phenomenon, since there are other physical processes that occur more often, such as those initiated by strong interaction, producing lighter quarks (such as up, down, strange quarks). In high-energy physics, we speak about the cross-section of a process. We say that the top quark production has a smaller cross-section than one of the productions of light quarks.
The experimental consequence is that distinguishing the decay products of a top quark from a light quark can be extremely difficult, due to the quite larger probability to occur of the latter phenomenon.
Experimental signature of Higgs boson in a particle detector
Let's first understand what are the experimental signatures and how the detectors work at the LHC experiment. As an example, this is a sketch of the Compact Muon Solenoid (CMS) detector.
A collider detector is organized in layers: each layer is able to distinguish and measure different particles and their properties. For example, the silicon tracker detects each particle that is charged. The electromagnetic calorimeter detects photons and electrons. The hadronic calorimeter detects hadrons (such as protons and neutrons). The muon chambers detect muons (that have a long lifetime and travel through the inner layers).
Our physics problem consists in detecting the so-called “golden decay channel” which is one of the possible Higgs boson's decays: its name is due to the fact that it has the clearest and cleanest signature of all the possible Higgs boson's decay modes. The decay chain is sketched here: the Higgs boson decays into Z boson pairs, which in turn decay into a lepton pair (in the picture, muon-antimuon or electron-positron pairs). In this exercise, we will use only datasets concerning the
decay channel and the datasets about the 4e channel are given to you to be analyzed as an optional exercise. At the LHC experiments, the decay channel 2e2mu is also widely analyzed.
How to execute it
Use Googe Colab
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