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PreprintCC BY 4.0HAL

Extreme change-point detection

  • Kevin Bleakley
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Abstract

We examine rules for predicting whether a point in ℝ generated from a 50-50 mixture of two different probability distributions came from one distribution or the other, given limited (or no) information on the two distributions, and, as clues, one point generated randomly from each of the two distributions. We prove that nearest-neighbor prediction does better than chance when we know the two distributions are Gaussian densities without knowing their parameter values. We conjecture that this result holds for general probability distributions and, furthermore, that the nearest-neighbor rule is optimal in this setting, i.e., no other rule can do better than it if we do not know the distributions or do not know their parameters, or both.

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Cite

BibTeXRIS
BibTeX
@misc{bleakley2026extreme,
  title = {{Extreme change-point detection}},
  author = {Kevin Bleakley},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  eprint = {2403.19237},
  archivePrefix = {arXiv},
  url = {https://inria.hal.science/hal-04523912v3},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Extreme change-point detection
AU  - Kevin Bleakley
PY  - 2026
DA  - 2026/10/15
PB  - HAL
UR  - https://inria.hal.science/hal-04523912v3
AB  - We examine rules for predicting whether a point in ℝ generated from a 50-50 mixture of two different probability distributions came from one distribution or the other, given limited (or no) information on the two distributions, and, as clues, one point generated randomly from each of the two distributions. We prove that nearest-neighbor prediction does better than chance when we know the two distributions are Gaussian densities without knowing their parameter values. We conjecture that this result holds for general probability distributions and, furthermore, that the nearest-neighbor rule is optimal in this setting, i.e., no other rule can do better than it if we do not know the distributions or do not know their parameters, or both.
ER  -