Welcome to STAT 217!
Basic Information
Course Number and Course Name |
STAT 171: Topics in high-dimensional statistics: methods from statistical physics |
Instructor / TF |
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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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