Philipp Windischhofer

Lukas Heinrich, Siddharth Mishra-Sharma, Chris Pollard et al.

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure, where "local" parameters impact individual events and "global" parameters influence the entire dataset. We introduce practical approaches for frequentist and Bayesian dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via a hierarchical forward model. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model's hierarchical structure can lead to significantly tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics and cosmology.

Chris Pollard, Philipp Windischhofer

Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of interest. However, the fidelity of these simulators is not always sufficient for all scientific purposes, necessitating the construction of ad-hoc corrections to "calibrate" the simulation and ensure that its output is a faithful representation of reality. In this paper, we leverage methods from transportation theory to construct such corrections in a systematic way. We use a neural network to compute minimal modifications to the individual samples produced by the simulator such that the resulting distribution becomes properly calibrated. We illustrate the method and its benefits in the context of experimental particle physics, where the need for calibrated stochastic simulators is particularly pronounced.

Philipp Windischhofer, Miha Zgubic, Daniela Bortoletto

Analyses of collider data, often assisted by modern Machine Learning methods, condense a number of observables into a few powerful discriminants for the separation of the targeted signal process from the contributing backgrounds. These discriminants are highly correlated with important physical observables; using them in the event selection thus leads to the distortion of physically relevant distributions. We present a novel method based on a differentiable estimate of mutual information, a measure of non-linear dependency between variables, to construct a discriminant that is statistically independent of a number of selected observables, and so manages to preserve their distributions in the event selection. Our strategy is evaluated in a realistic setting, the analysis of the Standard Model Higgs boson decaying into a pair of bottom quarks. Using the distribution of the invariant mass of the di-b-jet system to extract the Higgs boson signal strength, our method achieves state-of-the-art performance compared to other decorrelation techniques, while significantly improving the sensitivity of a similar, cut-based, analysis published by ATLAS.