Welcome to STAT 217!
Basic Information
Course Number and Course Name |
STAT 217: Topics in high-dimensional statistics: methods from statistical physics |
Instructor / TF |
|
Email |
|
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)
- 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)
- Week 7, Mar 8, Section 6: Conditioning and Bolthausen’s Lemma (Handout)
- 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)
- Week 10, Mar 29, Section 8: Universality and Lindeberg’s approach (Handout)
- 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
- MLE for Community Detection and Minimum Bisection
- Planted Clique and the AKS spectral algorithm
|
Back to TEACHING
|