I will take my PhD qualifying exam on January 17, 2024. The exam consists of a presentation of my research so far and plans for future work. On this page, you can read a bit more about the research that I'll be presenting.
The presentation covers the following work (see my list of publications if you want more information):
Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition. This paper (which appeared at NeurIPS 2023) explains how to draw samples according to the leverage score distribution of a column-wise Kronecker product of several matrices efficiently. We apply this method to efficiently decompose massive sparse tensors.
Distributed-Memory Randomized Algorithms for Sparse CP Decomposition. We extend the methods from the first paper to the distributed-memory parallel setting and optimize them to avoid processor-to-processor communication. We decompose the Reddit tensor with around 4.7 billion nonzeros in under two minutes on four Perlmutter CPU nodes!
Distributed-Memory Sparse Kernels for Machine Learning. The methods above deal with tensor decomposition / factorization. This work deals instead with sparse matrix completion, a related problem where only a subset of entries are observed. We recast the factorization problem to use the Sampled-Dense-Dense Matrix Multiplication (SDDMM) kernel and Sparse-Times-Dense Matrix Multiplication (SpMM) kernel and develop dual communication-avoiding formulations for both.