Let's Think Var-by-Var: Large Language Models Enable Ad Hoc Probabilistic Reasoning

TL;DR

This paper introduces a framework that leverages large language models to generate and optimize probabilistic models for answering common sense and guesstimation questions, demonstrating competitive performance with baseline methods.

Contribution

The authors propose a novel method that extracts variables and constraints from LLMs to construct ad hoc probabilistic models for reasoning tasks.

Findings

LLMs can propose relevant variables for probabilistic reasoning.

Joint optimization improves constraint satisfaction despite noisy inputs.

Framework performs comparably to direct prompting baselines on real-world data.

Abstract

A hallmark of intelligence is the ability to flesh out underspecified situations using "common sense." We propose to extract that common sense from large language models (LLMs), in a form that can feed into probabilistic inference. We focus our investigation on $\textit{guesstimation}$ questions such as "How much are Airbnb listings in Newark, NJ?" Formulating a sensible answer without access to data requires drawing on, and integrating, bits of common knowledge about how $\texttt{Price}$ and $\texttt{Location}$ may relate to other variables, such as $\texttt{Property Type}$. Our framework answers such a question by synthesizing an $\textit{ad hoc}$ probabilistic model. First we prompt an LLM to propose a set of random variables relevant to the question, followed by moment constraints on their joint distribution. We then optimize the joint distribution $p$ within a log-linear family to maximize the overall constraint satisfaction. Our experiments show that LLMs can successfully be prompted to propose reasonable variables, and while the proposed numerical constraints can be noisy, jointly optimizing for their satisfaction reconciles them. When evaluated on probabilistic questions derived from three real-world tabular datasets, we find that our framework performs comparably to a direct prompting baseline in terms of total variation distance from the dataset distribution, and is similarly robust to noise.