...
- one that contains events distributed according to the null (in our case signal - there exist other conventions in actual physics analyses) hypothesis
H0 ;
- another one according to the alternative (in our case background) hypothesis
H1 .
Then the algorithm must learn how to classify new datasets (the test dataset in our case).
This means that we have the same set of features (random variables) with their own distribution on the and
hypothesesH0 and H1 hypotheses.
To obtain a good ML classifier with high discriminating power, we will follow the following steps:
...
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
- 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!
...
Our physics problem consists in detecting the so-called “golden decay channel” 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 4µ 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.
...
- electrically-charged leptons (electrons or muons, denoted with
l)
- particle jets (collimated streams of particles originating from quarks or gluons, denoted with
j).
For each object, several kinetic variables are measured:
- the momentum transverse to the beam direction (
pt)
- two angles
θ (polar) and
Φ (azimuthal) - see picture below for the CMS reference frame used.
- for convenience, at hadron colliders, the pseudorapidity
η, defined as
is η=-ln(tan(η/2)) is used instead of the polar angle
We will use some of them for training our Machine Learning algorithms.
...