Research map / Graph learning / Graph algorithms and clustering
The Edge Density Barrier: Computational-Statistical Tradeoffs in Combinatorial Inference
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use weak edge density mu (rather than strong edge density mu') to characterize the computational lower bound when queries are polynomially constrained | Clique detection, nearest neighbor graph, 3-clique vs s-clique testing · Testing in Gaussian graphical models under oracle computational model | signal strength threshold | Mixed |
| Large gap between poly-time threshold and information-theoretic threshold when mu << mu' | Clique detection · Empty graph vs s-clique | ratio mu/mu' | Hurt |
| Entrywise test (pairwise statistics, O(d^2) queries) used for signals that are spread out | Empty graph vs s-clique · Gaussian graphical model testing | detection threshold | Helped |
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