I am aware of the problem of low rank approximation of matrices which has been studied in various models of computation. My question is the following:
What is the status of approximating rank of a matrix in these models (e.g., communication complexity, query complexity, streaming etc)? Here the goal is to output a number which is approximately the rank of the matrix. Is there a paper(s) which presents the state-of-the-art regarding this?
A quick Google search points only to the papers involving low rank approximation. The exact rank problem, however, has high lower bound (in randomized communication complexity) which follows from a reduction from singularity problem (i.e., whether a matrix is of full rank or not).