Filtering with Abstract Particles

By using particles, beam search and sequential Monte Carlo can approximate distributions in an extremely flexible manner. However, they can suffer from sparsity and inadequate coverage on large state spaces. We present a new filtering method for discrete spaces that addresses this issue by using “abstract particles,” each of which represents an entire region of state space. These abstract particles are combined into a hierarchical decomposition, yielding a compact and flexible representation. Empirically, our method outperforms beam search and sequential Monte Carlo on both a text reconstruction task and a multiple object tracking task.