Research map / Learning theory and algorithms / Prediction and decision losses
Phase Transitions in the Pooled Data Problem
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Tighten the noiseless converse using a genie-aided bound | Noiseless pooled data · Noiseless pooled data | number of tests required for exact recovery: \frac{p}{\log p}\cdot\frac{1}{2}f(1) -> \frac{p}{\log p}\cdot\max_{r\in\{1,\dotsc,d-1\}}f(r) | Helped |
| Add Gaussian noise with SNR = (\log p)^{\Theta(1)} | Pooled data · Noisy pooled data | necessary number of tests: \Theta\Big(\frac{p}{\log p}\Big) -> \Omega\Big(\frac{p}{\log\log p}\Big) | Hurt |
| Add Gaussian noise at constant SNR | Pooled data · Noisy pooled data | necessary number of tests: \Theta\Big(\frac{p}{\log p}\Big) -> \Omega\big(p\log p\big) | Hurt |
| Use Bernoulli(q) tests with q = o(1), while q and 1-q behave as \omega(\frac{1}{p}) | Noiseless pooled data with Bernoulli testing · Noiseless pooled data | necessary number of tests: \log p -> \log (pq(1-q)) | Hurt |
| Allow up to \qmax = o(p) Hamming errors | Noiseless pooled data · Noiseless approximate recovery | necessary number of tests | No clear effect |
| Allow a fixed positive fraction of Hamming errors | Noiseless pooled data · Noiseless approximate recovery | number of tests | Mixed |
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