Having access to ever-increasing amount of data presents us with both new opportunities and challenges. It enables researchers to perform statistical inferences that were either data-demanding or simply impossible due to lack of data. On the contrary, it is crucial to extract representative features of the data instead being overwhelmed.
These two intertwined aspects lead to the two main thrusts that I will focus on in this talk: data-demanding statistical inference vs. data summarization. For the former theme, I will talk understanding non-stationarity from a spectral perspective, which in general requires more data compared with time-domain approaches. I will focus on our new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley.
We provide the bias/variance/resolution tradeoff analysis of our improved estimate and further propose a non-parametric stationarity test. The usefulness of the stationarity test will be illustrated through causal inference and change detection. For the latter theme, I will briefly talk about two projects. One is on how to perform distributed hypothesis testing via interactive communication. We characterize the optimal tradeoff between the testing performance and the communication rates and show that interaction is helpful for distributed hypothesis testing problems. The other one is on pseudo-random matrix constructions without compromising key statistical properties such as Wigner's semi-circular law. We show for an n by n matrix, the needed randomness can be greatly reduced from n^2 to about log(n).
Yu Xiang is a postdoctoral fellow in the John A. Paulson School of Engineering and Applied Sciences at Harvard University. Prior to this, he obtained his Ph.D. and M.S. in electrical and computer engineering from University of California, San Diego in 2015 and 2010, respectively. He received his B.S. with highest distinction from the school of telecommunication engineering at Xidian University, Xi'an, China, in 2008. His research centers around statistical signal processing, information theory, machine learning and their applications to neuroscience and computational biology.
For more information, please contact Shucheng Yu at [email protected]