We describe a general method for building cascade classifiers from part-based deformable models such as pictorial structures. We focus primarily on the case of star-structured models and show how a simple algorithm based on partial hypothesis pruning can speed up object detection by more than one order of magnitude without sacrificing detection accuracy. In our algorithm, partial hypotheses are pruned with a sequence of thresholds. In analogy to probably approximately correct (PAC) learning, we introduce the notion of probably approximately admissible (PAA) thresholds. Such thresholds provide theoretical guarantees on the performance of the cascade method and can be computed from a small sample of positive examples. Finally, we outline a cascade detection algorithm for a general class of models defined by a grammar formalism. This class includes not only tree-structured pictorial structures but also richer models that can represent each part recursively as a mixture of other parts.