#  Seminar: Sitan Chen (University of California, Berkeley): "Learning Polynomial Transformations" 

 



####  calendar\_today Date and Time 

 **May 10, 2022** 

 09:30AM - 09:30AM EDT 

####  pin\_drop Location 

 **https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09**  



 

 



 

   ![Sitan Chen](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/sitan_chen.jpeg?itok=8kNg6m_Q) 

 

  
Speaker: Sitan Chen (UC Berkeley)  
**Title:** Learning Polynomial Transformations  
**Abstract:** Generative models like variational auto-encoders, generative adversarial networks, and flow-based models have exploded in popularity as extraordinarily effective ways of modeling real-world data. At their heart, these models attempt to learn a parametric transformation of a simple, low-dimensional distribution into a complex, high-dimensional one. Yet despite their immense practical impact, very little is known about the learnability of such distributions from a theoretical perspective.  
This talk concerns arguably the most natural incarnation of this problem: given samples from the pushforward of the Gaussian under an unknown polynomial *p*: ℝ*r* → ℝ*d*, can we approximately recover *p* (up to trivial symmetries)? I'll present the first polynomial-time algorithms for this task. These results leverage the sum-of-squares hierarchy, which has emerged from the theoretical computer science community in recent years as a powerful algorithmic tool for solving a number of high-dimensional statistical problems. Along the way, I will also highlight an intriguing connection to tensor ring decomposition, a popular variant of the matrix product state ansatz.  
Based on joint work with Jerry Li, Yuanzhi Li, and Anru Zhang.

 

 

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