high-dim
Test the many with the blood of few
It is 1943, and the Army must screen millions of inductees for syphilis with a blood test costly per run — one-test-per-man is unaffordable arithmetic. The saving fact is sparsity: only a small fraction of samples are positive. Pool the blood: test combined samples, and let a negative pool clear its whole group at a stroke while positives trigger refinement. Design the pooling scheme — group sizes from prevalence, adaptive versus fixed designs, error tolerance when the assay itself is imperfect — and prove how close to the information-theoretic minimum number of tests you can get. Get it wrong and screening either bankrupts the program or misses carriers; the same mathematics returns whenever tests are scarce and positives are rare, from DNA libraries to pandemic surveillance.
Who this problem belongs to
The two figures whose methods fit it best, out of 61 in contention.
Donoho's compressed sensing program, while developed decades after 1943, formalizes the exact mathematical principle underlying this problem's pooled blood testing: a sparse signal, here the small fraction of positive samples, can be recovered from far fewer measurements, here pooled tests, than the number of individuals, provided the measurement design (pooling scheme) satisfies the right recovery conditions. His later explicit historical framing of group testing as an early instance of sparse-signal recovery ties his own theoretical machinery directly back to Dorfman's 1943 army screening problem this scenario describes. His information-theoretic analysis of how close a sparse-recovery scheme can get to the theoretical minimum number of measurements is precisely what this problem asks for. His score reflects that his framework is the modern theoretical lens this exact historical episode is now understood through.
Nowak's research directly engages group testing and pooled sparse recovery as a named research topic: his papers on adaptive group testing and compressed sensing explicitly analyze how pooling designs, both fixed and sequentially adaptive, can identify a small number of positive items among many using near-information-theoretic-minimum numbers of tests, exactly this problem's central technical demand. His active-learning background gives him particular authority on the adaptive-versus-fixed design tradeoff this problem raises, since adaptively choosing which pools to test next based on earlier results is a core active-learning strategy. His work also treats imperfect assay error explicitly, matching this problem's demand to handle 'error tolerance when the assay itself is imperfect.' His score reflects that group testing is squarely inside his own published research area, not merely an adjacent parallel.
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
61 figures are scored on this problem. Draw it in a battle to see where you land.