Research map / Learning theory and algorithms / Sample complexity
Achieving the KS threshold in the general stochastic block model with linearized acyclic belief propagation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Linearized acyclic belief propagation (ABP) with r-nonbacktracking walks (cycle mitigation) versus plain BP on loopy graphs | SBM detection · symmetric and general SBM with linear-size communities | achieves KS threshold (SNR > 1) for detection | Helped |
| Compensating for dominant and smaller eigenvalues of PQ (subtracting multiples of y(t-1) from y(t)) instead of only subtracting the average | ABP for general multi-community SBM · general SBM detection | detection threshold / ability to remove bias | Helped |
| Graph-splitting step: randomly removing a small fraction of edges at the beginning | ABP · general SBM detection proof | proof dependency control | No clear effect |
| Assigning vertices to sets with probabilities scaling linearly with y' entries instead of by sign | ABP final step · general SBM detection | conversion of community-mean differences into detection | Helped |
| Using r=2 nonbacktracking versus larger r backtracking order | ABP · SBM detection | robustness to small loops/triangles | No clear effect |
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