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Singular Learning

Some personal resources for understanding and applying singular learning theory. For more information, please read the textbook by Sumio Watanabe.

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* - [Thesis](https://w3id.org/people/shaoweilin/public/swthesis.pdf) 
  - Algebraic methods for evaluating integrals in Bayesian statistics
* - [Preprint](http://arxiv.org/abs/1003.5338) 
  - Asymptotic approximation of marginal likelihood integrals 
* - [Notes](https://w3id.org/people/shaoweilin/public/useful.pdf) 
  - Useful facts about RLCT 
* - [Slides](https://w3id.org/people/shaoweilin/public/chicago.pdf) 
  - What is singular learning theory? 
* - [Slides](https://w3id.org/people/shaoweilin/public/aim.pdf) 
  - Singular Learning Theory: A view from Algebraic Geometry 
* - [Slides](https://w3id.org/people/shaoweilin/public/curves.pdf) 
  - Computing resolutions: how and why 
* - [Slides](https://w3id.org/people/shaoweilin/public/slc.pdf) 
  - Computing integral asymptotics using toric blow-ups of ideals 
* - [Video](http://www.youtube.com/watch?v=NhdtWnieTgI) 
  - Studying model asymptotics with Singular learning theory 
* - [Website](https://w3id.org/people/shaoweilin/public/rlct.html) 
  - Macaulay2 library for computing RLCTs using Newton polyhedra

Motivic Invariants and Singularities

My slides and problem sets on Singular Learning Theory from the Motivic Invariants and Singularities workshop at the Center for Mathematics at Notre Dame (May 2013).

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* - Statistical Learning Theory
  - [Slides](https://w3id.org/people/shaoweilin/public/cmnd1SLT.pdf)
  - [Problems](https://w3id.org/people/shaoweilin/public/cmnd1prob.pdf)
* - Real Log Canonical Threshold
  - [Slides](https://w3id.org/people/shaoweilin/public/cmnd2RLCT.pdf)
  - [Problems](https://w3id.org/people/shaoweilin/public/cmnd2prob.pdf)
* - Singularities in Graphical Models
  - [Slides](https://w3id.org/people/shaoweilin/public/cmnd3GM.pdf)
  - [Problems](https://w3id.org/people/shaoweilin/public/cmnd3prob.pdf)
* - Blow-ups and Zeta Functions
  - [Notes](https://w3id.org/people/shaoweilin/public/cmnd4notes.pdf)
  -