Question
Rina Foygel Barber et al. 2023 introduces methods for conformal prediction that do not rely on this assumption and defines the coverage gap to quantify loss in quality relative to when this assumption is met. For 10 points each:
[10m] Name this property of a sequence of random variables whose joint distribution is invariant under their permutation. This property is notably possessed by Pólya urn models and sampling without replacement.
ANSWER: exchangeability [accept word forms; prompt on word forms interchangeable]
[10e] Two answers required. Exchangeability is similar to, and implied by, these two commonly assumed properties of observations. You can give the three-letter acronym for these two properties that is often written above a tilde.
ANSWER: independent AND identically distributed [or i·i·d]
[10h] Exchangeability is justified as an assumption for many statistical models by this statement. By this statement, random variables are exchangeable if and only if they are conditionally independent with respect to a latent variable.
ANSWER: de Finetti’s representation theorem [prompt on representation theorem]
<David Bass, Other Science - Mathematics>
Summary
| 2023 Chicago Open | 08/05/2023 | Y | 9 | 10.00 | 89% | 11% | 0% |
Data
| Curse you, Periplus the Platypus! | BHSU | 0 | 10 | 0 | 10 |
| Evans Hall destruction awaiters | wave2: trimming membership codes 9655377758gp | 0 | 10 | 0 | 10 |
| I would prefer not to | Don't be Afraid, the Clown's Afraid Too | 0 | 10 | 0 | 10 |
| The Plague (anime)" was redirected to: "Oran High School Host Club | remembrance of lost time | 0 | 10 | 0 | 10 |
| Saint Peter Andre 3000 | The anti-STOON-dahl cabal (the tall Keyal et al.) | 0 | 0 | 0 | 0 |
| Teach Us to Outgrow Our Ladness | In Search of Things Past | 0 | 10 | 0 | 10 |
| The Canadians | Quasicrystal Silence | 0 | 10 | 0 | 10 |
| The Catastrophic Implosion of Packet Sub | I prefer really not to speak. If I speak I’m in big trouble | 10 | 10 | 0 | 20 |
| Hang et al., Robert Browning | [moderator voice] yes that is so tenpointscore! is your team feeling bonuspilled? | 0 | 10 | 0 | 10 |