We study the problem of applying adaptive filters for approximate query processing in a distributed stream environment. We propose filter bound assignment protocols with the objective of reducing communication cost. Most previous works focus on value-based queries (e.g., average) with numerical error tolerance. In this paper, we cover entity-based queries (e.g., a nearest neighbor query returns object names rather than a single value). In particular, we study non-value-based tolerance (e.g., the answer to the nearest-neighbor query should rank third or above). We investigate different non-value-based error tolerance definitions and discuss how they are applied to two classes of entity-based queries: non-rankbased and rank-based queries. Extensive experiments show that our protocols achieve significant savings in both communication overhead and server computation.