Event(s) on November 2021

• Wednesday, 17th November, 2021

  Title:	Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint
  Speaker:	Prof Gabriele Steidl, Technische Universität Berlin, Germany
  Time/Place:	17:00  -  18:00 Zoom, (Meeting ID: 966 1844 9330)
  Abstract:	Stochastic normalizing flows can overcome topological constraints and improve the expressiveness of normalizing flow architectures by combining deterministic, learnable flow transformations with stochastic sampling methods. We consider stochastic normalizing flows from a Markov chain point of view. In particular, we replace transition densities by general Markov kernels and establish proofs via Radon-Nikodym derivatives which allows to incorporate distributions without densities in a sound way. Further, we generalize the results for sampling from posterior distributions as required in inverse problems. The performance of the proposed conditional stochastic normalizing flow is demonstrated by numerical examples. Joint work with P. Hagemann and J. Hertrich.

  
  

• Tuesday, 23rd November, 2021

  Title:	Homogeneity Pursuit in Single Index Models based Panel Data Analysis
  Speaker:	Wenyang ZHANG, Department of Mathematics, University of York, UK
  Time/Place:	16:00  -  17:00 zoom, https://hkbu.zoom.us/j/98761459009
  Abstract:	Panel data analysis is an important topic in statistics and econometrics. Traditionally, in panel data analysis, all individuals are assumed to share the same unknown parameters, e.g. the same coefficients of covariates when the linear models are used, and the differences between the individuals are accounted for by cluster effects. This kind of modelling only makes sense if our main interest is on the global trend, this is because it would not be able to tell us anything about the individual attributes which are sometimes very important. In this talk, I will present a new modelling approach, based on the single index models embedded with homogeneity, for panel data analysis, which builds the individual attributes in the model and is parsimonious at the same time. I will show a data driven approach to identify the structure of homogeneity, and estimate the unknown parameters and functions based on the identified structure. I will show the asymptotic properties of the resulting estimators. I will also use intensive simulation studies to show how well the resulting estimators work when sample size is finite. Finally, I will apply the proposed modelling idea to a public financial dataset and a UK climate dataset, and show some interesting findings.

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