S&DS 684: Statistical inference on graphs

Yihong Wu, Yale University, Spring 2023

Lecture notes

Lecture schedule

Jan 17 Introduction (slides), max clique in Erdos-Renyi graphs (Chap 1.2)
Jan 24 Greedy algorithm (1.3), planted clique model, statistical limits, (iterated) degree test (Chap 2.1-2.4)
Jan 31 Spectral Method and basic random matrix theory I (Chap 3-4)
Feb 7 Spectral Method and basic random matrix theory II (Chap 4-5)
Feb 14 SDP relaxation for planted clique, robustness (Chap 6.1-6.2)
Feb 21 Rounding of SDP, Convexified MLE (nuclear norm), planted partition model (Chap 6.3, 7.1)
Feb 28 Detection threshold of SBM, cycle-counting statistic, counting cycles in sparse graphs (Chap 7.1, 7.2)
Mar 7 Correlated recovery of sparse SBM, belief propagation and non-backtracking matrix (Chap 8.1, 9)
Mar 14 Spring break I 😄
Mar 21 Spring break II 😂
Mar 28 Belief propagation and non-backtracking matrix II (Chap 9)
Apr 4 SDP relaxation for exact and approximate recovery in SBM (Chap 10 and 12)
Apr 11 Planted Hamiltonian problem and LP relaxation (slides)
Apr 18 Graph matching I: IT analysis and simple algorithms (slides)
Apr 25 Graph matching II: spectral method and QP relaxation (slides)