Optimising HEP parameter fits via Monte Carlo weight derivative regression

Valassi (2020) — weight-derivative regression

Result

defines the event-by-event sensitivity $\gamma_i=(1/w_i)\,\partial w_i/\partial\theta$ — the single-parameter score — shows the binned-fit information is $I_\theta=\sum_k s_k\phi_k^2$ with $\phi_k=\langle\gamma\rangle_k$ the cell-mean sensitivity, and argues the optimal partitioning variable is $\gamma$ itself. Defines FIP$_3=I_\theta/I_\theta^{(\rm ideal)}\in[0,1]$ and factors it as FIP$_{\rm efS}\times$FIP$_{\rm shS}\times$FIP$_{\rm shB}$ (efficiency $\times$ signal sharpness $\times$ background sharpness).

Boundary marker

the $d=1$ case of the score-space reduction and of the retained-information identity is established prior art, stated in HEP language. FIP$_3$ is $\eta$ at $s=1$; FIP$_{\rm shS}$ is precisely the sharpness of a hard binning of the score. Boundary of what it does not do: no multivariate score space, no determinant or any matrix criterion, no nuisance profiling, and no optimality theorem for the binning — the partitioning claim is an argument in the scalar case, not a geometric characterisation.

Open attribution question (for a literature session, not settled here)

whether FIP$_3$ constitutes prior art for INFO-D-EFFICIENCY at $s=1$, and FIP$_{\rm shS}$ for the retained-information ratio. Both claims now cite it; neither has been demoted, and no literature_search_status was set. Recorded in reviewed.md.