Preferential Normalizing Flows
Keywords: normalizing flow, elicitation, random utility models, prior distribution
TL;DR: We show how normalising flows can be fitted for preferential data representing expert's choices between a set of alternatives, as a function-space maximum a posteriori estimate with a novel functional prior.
Abstract: 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.
Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)
Submission Number: 6060
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