Jiaze Qiu
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STAT 217 | Spring 2023

Topics in high-dimensional statistics: methods from statistical physics

Welcome to STAT 217!

Basic Information

Course Number and Course Name
​STAT 171: 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
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Contact

Jiaze Qiu
Science Center 316.07
One Oxford Street
Cambridge, MA 02138
jiazeqiu@g.harvard.edu
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