Automated Statistical Model Discovery with Language Models

Statistical model discovery involves a challenging search over a vast space of models subject to domain-specific modeling constraints. Efficiently searching over this space requires human expertise in modeling and the problem domain. Motivated by the domain knowledge and programming capabilities of large language models (LMs), we introduce a method for language model driven automated statistical model discovery. We cast our automated procedure within the framework of Box's Loop: the LM iterates between proposing statistical models represented as probabilistic programs, acting as a modeler, and critiquing those models, acting as a domain expert. By leveraging LMs, we do not have to define a domain-specific language of models or design a handcrafted search procedure, key restrictions of previous systems. We evaluate our method in three common settings in probabilistic modeling: searching within a restricted space of models, searching over an open-ended space, and improving classic models under natural language constraints (e.g., this model should be interpretable to an ecologist). Our method matches the performance of previous systems, identifies models on par with human expert designed models, and extends classic models in interpretable ways. Our results highlight the promise of LM driven model discovery.

Gaussian process surrogate models for neural networks

The lack of insight into deep learning systems hinders their systematic design. In science and engineering, modeling is a methodology used to understand complex systems whose internal processes are opaque. Modeling replaces a complex system with a simpler surrogate that is more amenable to interpretation. Drawing inspiration from this, we construct a class of surrogate models for neural networks using Gaussian processes. Rather than deriving the kernels for certain limiting cases of neural networks, we learn the kernels of the Gaussian process empirically from the naturalistic behavior of neural networks. We first evaluate our approach with two case studies inspired by previous theoretical studies of neural network behavior in which we capture neural network preferences for learning low frequencies and identify pathological behavior in deep neural networks. In two further practical case studies, we use the learned kernel to predict the generalization properties of neural networks.