Can Generative AI Solve Your In-Context Learning Problem? A Martingale Perspective
This addresses the challenge of assessing generative AI models for in-context learning problems, such as medical diagnosis, but is incremental as it builds on existing Bayesian model criticism approaches.
This work tackles the problem of estimating when a conditional generative model can solve an in-context learning problem by developing a statistical method called the generative predictive p-value, which enables posterior predictive checks without requiring explicit likelihood or posterior sampling. The method is empirically evaluated on synthetic tasks using large language models, showing it can determine model suitability based on generated queries and response log probabilities.
This work is about estimating when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. An in-context learning (ICL) problem comprises a CGM, a dataset, and a prediction task. The CGM could be a multi-modal foundation model; the dataset, a collection of patient histories, test results, and recorded diagnoses; and the prediction task to communicate a diagnosis to a new patient. A Bayesian interpretation of ICL assumes that the CGM computes a posterior predictive distribution over an unknown Bayesian model defining a joint distribution over latent explanations and observable data. From this perspective, Bayesian model criticism is a reasonable approach to assess the suitability of a given CGM for an ICL problem. However, such approaches -- like posterior predictive checks (PPCs) -- often assume that we can sample from the likelihood and posterior defined by the Bayesian model, which are not explicitly given for contemporary CGMs. To address this, we show when ancestral sampling from the predictive distribution of a CGM is equivalent to sampling datasets from the posterior predictive of the assumed Bayesian model. Then we develop the generative predictive $p$-value, which enables PPCs and their cousins for contemporary CGMs. The generative predictive $p$-value can then be used in a statistical decision procedure to determine when the model is appropriate for an ICL problem. Our method only requires generating queries and responses from a CGM and evaluating its response log probability. We empirically evaluate our method on synthetic tabular, imaging, and natural language ICL tasks using large language models.