Transduction, the ability to include query-specific examples in the prompt at inference time, is one of the emergent abilities of large language models (LLMs). In this work, we propose a framework for adaptive prompt design called active transductive inference (ATI). We design the LLM prompt by adaptively choosing few-shot examples for a given inference query. The examples are initially unlabeled and we query the user to label the most informative ones, which maximally reduces the uncertainty in the LLM prediction. We propose two algorithms, GO and SAL, which differ in how the few-shot examples are chosen. We analyze these algorithms in linear models: first GO and then use its equivalence with SAL. We experiment with many different tasks and show that GO and SAL outperform other methods for choosing few-shot examples in the LLM prompt at inference time.