TY - GEN

T1 - Lp-testing

AU - Berman, Piotr

AU - Raskhodnikova, Sofya

AU - Yaroslavtsev, Grigory

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We initiate a systematic study of sublinear algorithms for approximately testing properties of real-valued data with respect to Lp distances. Such algorithms distinguish datasets which either have (or are close to having) a certain property from datasets which are far from having it with respect to Lp distance. For applications involving noisy realvalued data, using Lp distances allows algorithms to withstand noise of bounded L p norm. While the classical property testing framework developed with respect to Hamming distance has been studied extensively, testing with respect to Lp distances has received little attention. We use our framework to design simple and fast algorithms for classic problems, such as testing monotonicity, convexity and the Lipschitz property, and also distance approximation to monotonicity. In particular, for functions over the hypergrid domains [n]d, the complexity of our algorithms for all these properties does not depend on the linear dimension n. This is impossible in the standard model. Most of our algorithms require minimal assumptions on the choice of sampled data: either uniform or easily samplable random queries suffice. We also show connections between the Lp-testing model and the standard framework of property testing with respect to Hamming distance. Some of our results improve existing bounds for Hamming distance.

AB - We initiate a systematic study of sublinear algorithms for approximately testing properties of real-valued data with respect to Lp distances. Such algorithms distinguish datasets which either have (or are close to having) a certain property from datasets which are far from having it with respect to Lp distance. For applications involving noisy realvalued data, using Lp distances allows algorithms to withstand noise of bounded L p norm. While the classical property testing framework developed with respect to Hamming distance has been studied extensively, testing with respect to Lp distances has received little attention. We use our framework to design simple and fast algorithms for classic problems, such as testing monotonicity, convexity and the Lipschitz property, and also distance approximation to monotonicity. In particular, for functions over the hypergrid domains [n]d, the complexity of our algorithms for all these properties does not depend on the linear dimension n. This is impossible in the standard model. Most of our algorithms require minimal assumptions on the choice of sampled data: either uniform or easily samplable random queries suffice. We also show connections between the Lp-testing model and the standard framework of property testing with respect to Hamming distance. Some of our results improve existing bounds for Hamming distance.

UR - http://www.scopus.com/inward/record.url?scp=84904304303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904304303&partnerID=8YFLogxK

U2 - 10.1145/2591796.2591887

DO - 10.1145/2591796.2591887

M3 - Conference contribution

AN - SCOPUS:84904304303

SN - 9781450327107

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 164

EP - 173

BT - STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing

PB - Association for Computing Machinery

T2 - 4th Annual ACM Symposium on Theory of Computing, STOC 2014

Y2 - 31 May 2014 through 3 June 2014

ER -