Exact Non-Oblivious Performance of Rademacher Random Embeddings
It addresses the gap between theory and practice in random projection methods, offering incremental improvements for data analysis applications.
This paper tackles the performance analysis of Rademacher random projections by establishing novel statistical guarantees that are numerically sharp and non-oblivious to input data, resulting in improved bounds for sparse or low-spread data.
This paper revisits the performance of Rademacher random projections, establishing novel statistical guarantees that are numerically sharp and non-oblivious with respect to the input data. More specifically, the central result is the Schur-concavity property of Rademacher random projections with respect to the inputs. This offers a novel geometric perspective on the performance of random projections, while improving quantitatively on bounds from previous works. As a corollary of this broader result, we obtained the improved performance on data which is sparse or is distributed with small spread. This non-oblivious analysis is a novelty compared to techniques from previous work, and bridges the frequently observed gap between theory and practise. The main result uses an algebraic framework for proving Schur-concavity properties, which is a contribution of independent interest and an elegant alternative to derivative-based criteria.