This is the academic homepage of Yang Liu (I publish under Yang P. Liu). Pursue a degree in the fields of Finanical, Pure, Applied, … The Probabilistic Estimates of the Largest Strictly Convex p-singular Value of Pregaussian Random Matrices. I am fascinated by the question of how much we are able to uncover in a weakly supervised setting (e.g., noisy supervision, low-quality/biased training inputs, etc). [name] = yangpliu. I also am interested in geometric functional analysis and combinatorics (CV). Liuzhou, China. My research is supported by the National Defense Science and Engineering Graduate (NDSEG) Fellowship. Yang Liu's interests include logic, decision theory, foundations of probability, philosophy of ai. Office: 380-T Yang Liu is a philosopher at University of Cambridge. Placement Criteria for Entry-Level Mathematics Courses at UGA; Advanced Placement Credit; Transfer Credit; Slideshow. Dissertation/Thesis Title: Non-Convex Optimization for Linear System with Pregaussian Matrices and Recovery from Multiple Measurements. March 17, 2016 by Louis Y. Liu Leave a comment. Dr. Yang Liu, an Assistant Professor of Mathematics, received his Ph.D. in Mathematics from the University of Georgia in the U.S. and previously his M.S. Moreover, we parametrize the Grassmannian in an elementary linear algebra approach, and give a characterization on the image of the (ab solute value) co- sine transform on the space of distributions on the Grassman nian , by computing the coefficients in the Legendre series expansion o f distributions. We appreciate your financial support. In this paper, we study the decay of the smallest singular value of submatrices that consist of bounded column vectors. These results provide probabilistic description or picture on the behaviors of the largest p -singular values of random matrices in probability for p> 1. satisfying are modified Dirac delta functions. Follow. ), Written Qualifying Examination Study Guide, Past Mathematics Department Award Winners, Placement Criteria for Entry-Level Mathematics Courses at UGA. In September 2018, I started a PhD at Stanford University in mathematics, and am advised by Aaron Sidford. 2015, 2017 Putnam N2 (top 25 out of over 4000 students) Research Interests . Photo: Research. I am interested in theoretical computer science at large, especially algorithm design. Create a free website or blog at WordPress.com. The infinity norm is often used as a model in analysis and geometry, not for continuous scenarios, but for the discrete or singular scenarios. Before attending Stanford, I graduated from MIT in May 2018. In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value , when the number of rows of the matrices becomes very large. But it is unknown yet what exactly the function is, because the invariance yields that , but this doesn’t produce an appropriate function in the general expression for the complex infinity norm. A problem is what function would satisfy, if one parametrizes by the Hopf coordinates, One can show that the function is actually some function independent of and by the invariance of the complex norm under action, so it can be denoted as . Based on the results in probabilistic estimates on the largest q-singular value, we also give probabilistic estimates on the smallest q-singular value for pre-Gaussian random matrices.
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