A common problem that appears in collider physics is the inference of a random variable $Y$ given a measurement of another random variable $X$, and the estimation of the uncertainty on $Y$. Additionally, one would like to quantify the extent to which $X$ and $Y$ are related. We present a machine learning framework for performing frequentist maximum likelihood inference with uncertainty estimation and measuring the mutual information between random variables. By using the Donsker-Varadhan representation of the KL divergence, the framework learns the likelihood ratio $p(x|y)/p(x)$. This can be used to calculate the mutual information between $X$ and $Y$. The framework is parameterized using a Gaussian ansatz, which enables a manifest extraction of the maximum likelihood values and uncertainties. All of this can be accomplished in a single training of the model. We then demonstrate our framework for a simple Gaussian example, apply it to a realistic calibration task by calculating jet energy correction (JEC) and jet energy resolution (JER) factors for CMS open data.
|Affiliation||Massachusetts Institute of Technology|
|Academic Rank||PhD Student|