Welcome to STAT 217!

Basic Information

Course Number and Course Name	​STAT 217: Topics in high-dimensional statistics: methods from statistical physics
Instructor / TF	Subhabrata Sen / Jiaze Qiu
Email	jiazeqiu@g.harvard.edu
Sections (Jiaze)	Wednesdays 7:30 pm - 8:30 pm (ET), Science Center 705.
Office Hours (Jiaze)	Wednesdays 8:30 pm - 9:30 pm (ET), Science Center 316.07.

Please feel free to contact me if you have any question. I will try to reply as soon as possible.

​Schedule

• Week 2, Feb 1, Section 1: Lipschitz Concentration and I-MMSE Relationship (Handout, Solution)
  • Gaussian integration by parts
  • I-MMSE relationship for tensor PCA
  • Exponential concentration of the log partition function (free energy)
  • ​Review of basic concepts and the tensor PCA model
• Week 3, Feb 8, Section 2: The sequence model and change of measure calculation (Handout, Solution)
  • Replica symmetric calculations for the sequence model as a special case of Tensor PCA
  • Proof of Equation 1.2.11 in the textbook
• Week 4, Feb 15, Section 3: Guerra Interpolation (Handout, Solution)
  • Proof of the replica symmetric prediction through interpolation: An application of Gaussian integration by parts
  • Nishimori identity
• Week 5, Feb 22, Section 4: Gaussian Comparison Inequalities (Handout, Solution)​
  • An interpolation based proof of the J.P. Kahane lemma
  • Gaussian comparison inequalities
    • Slepian’s inequality
    • Gordon’s inequality
    • Sudakov-Fernique inequality
• Week 6, Mar 1, Section 5: Cavity Method for Spiked Matrices (Handout, Solution)​​
• Week 7, Mar 8, Section 6: Conditioning and Bolthausen’s Lemma (Handout, Solution)​
  
  • A conditioning lemma​
    
  • ​An iterative construction of AMP
    
• Week 8, spring break.
• Week 9, Mar 22, Section 7: One-step replica symmetry breaking (1RSB) (Handout, Solution)​
• Week 10, Mar 29, Section 8: Universality and Lindeberg’s approach (Handout, Solution)​
  • ​Telescope sum and Lindeberg’s idea
    
  • Universality in Sherrington-Kirkpatrick (S-K) model
    
• Week 11, Apr 5, Section 9: Detection v.s. Recovery (Handout, Solution)​
  • ​Contiguity
    
  • Detection boundary for Gaussian Wigner Spiked Matrix Model
    
• Week 12, Apr 12, Section 10: Community Detection and Planted Clique (Handout, Solution)
  
  • MLE for Community Detection and Minimum Bisection
    
  • Planted Clique and the AKS spectral algorithm
    

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