Rank estimation for (approximately) low-rank matrices.

In observational data analysis, e.g., causal inference, one often encounters data sets that are noisy and incomplete, but come from inherently "low rank" (or correlated) systems. Examples include user ratings of movies/products and term frequency matrices for documents amongst others. In such analysis, estimating the approximate rank of the data sets serves an important function of delineating the signal from the noise. In this paper, we propose a technique to estimate the rank of observational data matrices, compare it to previously proposed techniques, and make a specific methodological contribution of improving the algorithmic parameter estimation in the robust synthetic control method in [1].