Title: Geometric methods in advanced statistical inference

Speaker:  Prof. Xing Qiu ( University of Rochester )

Location:  Tencent Conference

Meeting Number: 886 9329 7132

Paaword: 1207

Lecture One：A review of statistical inference

Time:  Dec.7 2020--Dec.9 2020 , PM: 21:30-23:00

Lecture Two：Invariant and equivariant statistical models

Time:  Dec.10 2020--Dec.12 2020 , PM: 21:30-23:00

Lecture Three：Introduction to Lie groups [8/24]

Time:  Dec.13 2020--Dec.15 2020 , PM: 21:30-23:00

Lecture Four：Using general linear group to speedup dynamic network analysis

Time:  Dec.16 2020--Dec.18 2020 , PM: 21:30-23:00

Lecture Five：Applications of geometric methods to real world statistical problems

Time:  Dec.19 2020--Dec.20 2020 , PM: 21:30-23:00

Lecture Six：Future directions in geometric methods for statistical models  

Time:  Dec.21 2020--Dec.22 2020 , PM: 21:30-23:00

Inviter: Prof. Jun Yang

Introdution:

      We propose to study the statistical analysis on manifold by the method of symmetry. Many useful manifolds are symmetric under certain Lie group actions. From the statistical perspective, if we have a statistical model that is invariant or equivariant under a Lie group transformation, we can first study the properties of the corresponding Lie algebra, which is a linear space therefore easy to study, and then use the exponential map to translate these properties back to the original Lie group hence the original statistical model. We can also use Lie groups to construct maximal invariant, and use it as an efficient dimension reduction method.