Tong Wins 2024 IEEE Signal Processing Society Best Ph.D. Dissertation Award
Tian Tong, who earned his Ph.D. in electrical and computer engineering at Carnegie Mellon University in 2022, has received the 2024 IEEE Signal Processing Society Best Ph.D. Dissertation Award. The award recognizes Ph.D. relevant work in signal processing while stimulating further research in the field.
Tong’s dissertation, “Scaled Gradient Methods for Ill-conditioned Low-rank Matrix and Tensor Estimation,” introduces a new algorithm, called scaled gradient descent (ScaledGD), which provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent.
Many problems encountered in machine learning and signal processing can be formulated as estimating a low-rank object from incomplete, and possibly corrupted, linear measurements; prominent examples include matrix completion and tensor completion. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of gradient descent depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, slows down painstakingly when the problem is ill-conditioned. In addition, a nonsmooth variant of ScaledGD provides further robustness to corruptions by optimizing the least absolute deviation loss. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization.
While enrolled at CMU, Tong was advised by Yuejie Chi, the Sense of Wonder Group Endowed Professor of Electrical and Computer Engineering.
“Tian has made remarkable contributions on developing a new line of algorithms for estimating ill-conditioned low-rank objects that are both computationally and statistically efficient,” says Chi. “I believe that his approaches --- encapsulated by a family of scaled gradient methods --- will be extremely impactful for many years to come.”
Tong will receive one of the Society’s most prestigious awards during IEEE ICASSP 2025 in India.