Preferential Normalizing Flows
This addresses the problem of expert belief elicitation for applications like prior elicitation and reward modeling, offering a flexible approach but with incremental improvements to flow estimation.
The paper tackles the challenge of eliciting high-dimensional probability distributions from experts using only preferential questions like comparisons or rankings, and introduces a method that infers belief densities as normalizing flows with a novel functional prior, demonstrating it on simulated experts and a large language model's prior over a real-world dataset.
Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the expert's belief density as a normalizing flow based solely on preferential questions such as comparing or ranking alternatives. This allows eliciting in principle arbitrarily flexible densities, but flow estimation is susceptible to the challenge of collapsing or diverging probability mass that makes it difficult in practice. We tackle this problem by introducing a novel functional prior for the flow, motivated by a decision-theoretic argument, and show empirically that the belief density can be inferred as the function-space maximum a posteriori estimate. We demonstrate our method by eliciting multivariate belief densities of simulated experts, including the prior belief of a general-purpose large language model over a real-world dataset.