Posterior replicas and conditional information in Gaussian regression
For a signal with density bounded by L relative to uniform probability on $S^{d-1}$, we bound the information in a finite message W formed from exact Gaussian measurements, conditional on an independent projection revealed only to the analyst. For explicit row counts proportional to d , the bound is $O(H(W)/d+d+\log(2+\log L))$. Consequently, a finite-state learner with $o(d^2)$ persistent bits and a deterministic sample horizon needs $\Omega(d\log(1/\epsilon))$ fresh noiseless Gaussian measurements for constant-probability angular accuracy $0\lt \epsilon\le1/10$ under the uniform…
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/Posterior-replicas-and-conditional-information-in-Gaussian-regression
curl -X POST /api/v1/records/openai-math/Posterior-replicas-and-conditional-information-in-Gaussian-regression/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Posterior-replicas-and-conditional-information-in-Gaussian-regression/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'