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We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximation-size tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancy-based approaches on axis-aligned range queries.

Streaming interactive proofs (SIPs) are a framework to reason about outsourced computation, where a data owner (the verifier) outsources a computation to the cloud (the prover), but wishes to verify the correctness of the solution provided by the cloud service. In this paper we present streaming interactive proofs for problems in data analysis. We present protocols for clustering and shape fitting problems, as well as an improved protocol for rectangular matrix multiplication. The latter can in turn be used to verify k eigenvectors of a (streamed) n × n matrix.In general our solutions use polylogarithmic rounds of communication and polylogarithmic total communication and verifier space. For special cases (when optimality certificates can be verified easily), we present constant round protocols with similar costs. For rectangular matrix multiplication and eigenvector verification, our protocols work in the more restricted annotated data streaming model, and use sublinear (but not polylogarithmic) communication.

Abstract-Device-free or non-cooperative localization uses the changes in signal strength measured on links in a wireless network to estimate a person's position in the network area. Existing methods provide an instantaneous coordinate estimate via radio tomographic imaging or location fingerprinting. In this paper, we explore the problem of, after a person has exited the area of the network, how can we estimate their path through the area? We present two methods which use recent line crossings detected by the network's links to estimate the person's path through the area. We assume that the person took a linear path and estimate the path's parameters. One method formulates path estimation as a line stabbing problem, and another method is a linear regression formulation. Through simulation we show that the line stabbing approach is more robust to false detections, but in the absence of false detections, the linear regression method provides superior performance.

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