Statistical inference in physics is often based on samples from a generator (sometimes referred to as a ``forward model") that emulate experimental data and depend on parameters of the underlying theory. Modern machine learning has supercharged this workflow to enable high-dimensional and unbinned analyses to utilize much more information than ever before. We propose a general framework for describing the integration of machine learning with generators called Generator Based Inference (GBI). A well-studied special case of this setup is Simulation Based Inference (SBI) where the generator is a physics-based simulator. In this work, we examine other methods within the GBI toolkit that use data-driven methods to build the generator. In particular, we focus on resonant anomaly detection, where the generator describing the background is learned from sidebands. We show how to perform machine learning-based parameter estimation in this context with data-derived generators. This transforms the statistical outputs of anomaly detection to be directly interpretable and the performance on the LHCO community benchmark dataset establishes a new state-of-the-art for anomaly detection sensitivity.

We present R-ANODE, a new method for data-driven, model-agnostic resonant anomaly detection that raises the bar for both performance and interpretability. The key to R-ANODE is to enhance the inductive bias of the anomaly detection task by fitting a normalizing flow directly to the small and unknown signal component, while holding fixed a background model (also a normalizing flow) learned from sidebands. In doing so, R-ANODE is able to outperform all classifier-based, weakly-supervised approaches, as well as the previous ANODE method which fit a density estimator to all of the data in the signal region instead of just the signal. We show that the method works equally well whether the unknown signal fraction is learned or fixed, and is even robust to signal fraction misspecification. Finally, with the learned signal model we can sample and gain qualitative insights into the underlying anomaly, which greatly enhances the interpretability of resonant anomaly detection and offers the possibility of simultaneously discovering and characterizing the new physics that could be hiding in the data.