5 research outputs found
Adaptive Estimation in Weighted Group Testing
Abstract-We consider a generalization of the problem of estimating the support size of a hidden subset S of a universe U from samples. This framework falls under the group testing [1] and the conditional sampling model
Estimation of Sparsity via Simple Measurements
We consider several related problems of estimating the 'sparsity' or number
of nonzero elements in a length vector by observing only
, where is a predesigned test matrix
independent of , and the operation varies between problems.
We aim to provide a -approximation of sparsity for some constant
with a minimal number of measurements (rows of ). This framework
generalizes multiple problems, such as estimation of sparsity in group testing
and compressed sensing. We use techniques from coding theory as well as
probabilistic methods to show that rows are sufficient
when the operation is logical OR (i.e., group testing), and nearly this
many are necessary, where is a known upper bound on . When instead the
operation is multiplication over or a finite field
, we show that respectively and measurements are necessary and sufficient.Comment: 13 pages; shortened version presented at ISIT 201