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Such a structure is also called Feedforward Multilayer Perceptron (MLP, see the picture).

The output of the Image Removed node k_th node of the Image Removed layers n_th layers is computed as the weighted average of the input variables, with weights that are subject to optimization via training.

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Then a bias or threshold parameter Image Removed is w₀ is applied. This bias accounts for the random noise, in the sense that it measures how well the model fits the training set (i.e. how much the model is able to correctly predict the known outputs of the training examples.) The output of a given node is: .

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During training we optimize the loss function, i.e. reduce the error between actual and predicted values. Since we deal with a binary classification problem, the Image Removed can y_true can take on just two values, Image Removed y_true = 0 (for hypothesis Image RemovedH₁) and = 1 (for hypothesis Image RemovedH₀).

A popular algorithm to optimize the weights consists of iteratively modifying the weights after each training observation or after a bunch of training observations by doing a minimization of the loss function.

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Question to students: What happens if you switch to the Image Removed decay 4e decay channel? You can submit your model (see the ML challenge below) for this physical process as well!

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• You can participate as a single participant or as a team
• The winner is the one scoring the best AUC in the challenge samples!
• In the next box, you will find some lines of code for preparing an output csv file, containing your y_predic for this new dataset!
• Choose a meaningful name for your result csv file (i.e. your name, or your team name, the model used for the training phase, and the decay channel - 4Image Removed or 4Image Removed 4μ or 4e - but avoid to submit results.csv)
• Download the csv file and upload it here: https://recascloud.ba.infn.it/index.php/s/CnoZuNrlr3x7uPI
• You can submit multiple results, paying attention to name them accordingly (add the version number, such as v1, v34, etc.)
• You can use this exercise as a starting point (train over constituents)
• We will consider your best result for the final score.
• The winner will be asked to present the ML architecture!

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