L2 Sensitivity

Understanding how each dataset influences a model is critical, especially when combining multiple datasets, where conflicting signals can obscure important patterns. That’s why it’s essential to evaluate dataset impact even after a model has been built.

Recently, a new technique called L2 sensitivity was developed to measure how much each dataset influences a model’s fit (link to study). In essence, it checks how much the model’s error (χ² goodness-of-fit) changes when a PDF parameter is adjusted by one standard deviation.

However, the standard L2 sensitivity method only works if the dataset is already part of the model’s analysis, which means it can’t directly evaluate brand-new or external data.

To solve that problem, I developed a more flexible procedure that applies L2 sensitivity to any dataset, even if it’s not part of the original model. I integrated this solution into the open-source xFitter tool and validated it with real data (as documented in my publication at arXiv).

Files related to the L2 sensitivity extraction method can be found here.

Baseline Comparison

I verified my method by comparing its results to an earlier study on how datasets affect proton PDFs. My results closely matched the prior study’s findings, confirming that my approach works reliably.

There were a few minor differences because I defined the chi-squared metric slightly differently and handled heavy-quark data in another way. These technical details only caused small changes in the L2 sensitivity results (as a function of the parton’s momentum fraction x).