| Abstract: |
| Probabilistic conditioning concerns the identification of the distribution of a random variable X given a random variable Y. It is a cornerstone of science and engineering applications where modeling uncertainty is key. This problem has traditionally been addressed in machine learning by directly learning the conditional distribution of a fixed joint distribution. Instead, this talk solves the conditioning problem by identifying a single operator that maps any joint density to its conditional, thus amortizing over joint-conditional pairs. The talk establishes that density-to-density conditioning can be approximated to arbitrary accuracy by neural operators. The proof relies on new stability estimates for the conditioning operator over suitable classes of densities. Numerical experiments that train neural operators to condition a class of Gaussian mixtures illustrate the promise of the new framework. |
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