# Chris Liaw CMS Award Blurb
## Christopher Liaw (University of Toronto)

Christopher Liaw is an outstanding researcher whose work has contributed fundamentally to mathematical foundations of machine learning. His dissertation addresses two important problems in theoretical machine learning.

*The first problem* is on identifying the sample complexity of learning mixtures of Gaussians -- a long-standing open problem, with previous solutions requiring extra assumptions. Working together with several collaborators, Christopher Liaw gave a precise characterization with minimal assumptions. Moreover, this work developed a new tool for distribution learning, which has since been applied to give the sample complexity for learning other classes of distributions. This resulted in a "best paper award" at NeurIPS 2018, an extraordinary distinction.

On *another line* focusing on online learning, Christopher Liaw considers online predictions with expert advice, which is a classic model in learning theory. The problem is to find an optimal algorithm to choose a probability distribution over $n$ experts where at each day each expert receives a reward and the algorithm receives the expected reward under the chose distribution. The goal is that, at all times, the total reward earned by the algorithm so far must nearly equal the maximum total reward of any expert by that time. It has been known for decades that there is an algorithm whose reward is only $O(\sqrt{t \ln n})$ smaller than the best expert's reward and this is optimal up to constants. The open question of finding the optimal constant has been posed as early as 1997. Liaw's work (joint with Harvey, Perkins, and Randhawa) resolved this question exactly for $n=2$.

Liaw completed his PhD at the University of British Columbia in 2020 under the spervision of Nicholas Harvey. He has received several awards including a NeurIPS Best Paper Award as well as CGS-M, CGS-D and PDF fellowships from NSERC. He has an excellent publication record with three journal papers and ten papers in computer science conferences. He is currently a postdoctoral fellow in University of Toronto.