monofacts-estimator-error-bounds-within-o-1-sqrt-n
IN premise — summaries/2026/08/24/kalai-2023-hallucination-inevitable-s1-introduction.md
Created 2026-08-24T17:10:59+00:00
The Good-Turing/MonoFacts estimator dMF = |{f : count(f) = 1 in x_train}| / n estimates the true missing mass p(U) within Õ(1/√n) with high probability, per McAllester and Schapire (2000).
Summary
Counting how many items you have seen exactly once (relative to your total samples) gives you a trustworthy estimate of the fraction of the world you simply haven't encountered yet. The practical upshot is that the system can quantify its own blind spots, and the estimate tightens predictably as more data comes in, so the system knows both what it is missing and how much confidence to place in that number.