  Machine learning practitioners often face significant challenges in formally
integrating their prior knowledge and beliefs into predictive models, limiting
the potential for nuanced and context-aware analyses. Moreover, the expertise
needed to integrate this prior knowledge into probabilistic modeling typically
limits the application of these models to specialists. Our goal is to build a
regression model that can process numerical data and make probabilistic
predictions at arbitrary locations, guided by natural language text which
describes a user's prior knowledge. Large Language Models (LLMs) provide a
useful starting point for designing such a tool since they 1) provide an
interface where users can incorporate expert insights in natural language and
2) provide an opportunity for leveraging latent problem-relevant knowledge
encoded in LLMs that users may not have themselves. We start by exploring
strategies for eliciting explicit, coherent numerical predictive distributions
from LLMs. We examine these joint predictive distributions, which we call LLM
Processes, over arbitrarily-many quantities in settings such as forecasting,
multi-dimensional regression, black-box optimization, and image modeling. We
investigate the practical details of prompting to elicit coherent predictive
distributions, and demonstrate their effectiveness at regression. Finally, we
demonstrate the ability to usefully incorporate text into numerical
predictions, improving predictive performance and giving quantitative structure
that reflects qualitative descriptions. This lets us begin to explore the rich,
grounded hypothesis space that LLMs implicitly encode.
