Oblivious subspace embeddings have proven to be an essential ingredient for approximately solving numerical linear algebra problems, such as regression and low-rank approximation.
While for p = 2 there are nearly optimal tradeoffs in terms of the dimension, distortion, and sparsity, for the important case of 1 <= p < 2, much less was known. In this talk I will present our recent results on lp oblivious subspace embeddings, including (i) nearly optimal lower bounds and (ii) new constructions for sparse lp oblivious subspace embeddings.
Oblivious subspace embeddings are crucial for distributed and streaming environments, as well as entrywise lp low rank approximation. Our results give improved algorithms for these applications.