Research map / Learning theory and algorithms / Sample complexity
Phase transition for detecting a small community in a large network
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use degree-corrected modeling with degree-matched null and alternative rather than relying on degree differences | Small-community detection in DCBM · Degree-matched alternative | power: κ -> 1 | Helped |
| Use the degree-based chi-square test under degree matching | Small-community detection · Degree-matched alternative | power: power goes to κ | Hurt |
| Use SgnQ when |tilde λ1| / sqrt(λ1) diverges | Small-community detection in DCBM · Alternative satisfying the stated signal condition | power: power tends to 1 | Helped |
| Use SgnQ for an SBM with comparable node weights | Small-community detection · N(a-c)/sqrt(cn) → ∞ | power: power ... tends to 1 | Helped |
| Use signed scan when sqrt(N)(a-c)/sqrt(c log(n)) diverges | Small-community detection · DCBM | sum of type-I and type-II errors: tends to 0 | Helped |
| Use EST with ω/(1-β) < v/e < δ | Small-community detection · SBM with N=n^(1-β), a=n^(-ω), c=n^(-δ) | sum of type-I and type-II errors: tends to 0 | Helped |
| Treat the degree-based chi-square signal as non-robust when expected degrees are matched | Small-community detection · DCBM degree-matched alternative | power: power ... goes to κ | Hurt |
| Use SgnQ instead of the signed scan for polynomial-time detection when N >> sqrt(n) | Small-community detection · DCBM | detection threshold | Helped |
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