Instruction-following LLMs have recently allowed systems to discover hidden concepts from a collection of unstructured documents based on a natural language description of the purpose of the discovery (i.e., goal). Still, the quality of the discovered concepts remains mixed, as it depends heavily on LLM's reasoning ability and drops when the data is noisy or beyond LLM's knowledge. We present Instruct-LF, a goal-oriented latent factor discovery system that integrates LLM's instruction-following ability with statistical models to handle large, noisy datasets where LLM reasoning alone falls short. Instruct-LF uses LLMs to propose fine-grained, goal-related properties from documents, estimates their presence across the dataset, and applies gradient-based optimization to uncover hidden factors, where each factor is represented by a cluster of co-occurring properties. We evaluate latent factors produced by Instruct-LF on movie recommendation, text-world navigation, and legal document categorization tasks. These interpretable representations improve downstream task performance by 5-52% than the best baselines and were preferred 1.8 times as often as the best alternative, on average, in human evaluation.