Exchangeability
A statistical concept denoting that the joint probability distribution of a set of random variables is unchanged when the order of the variables is altered. It is the underlying assumption for the validity of the binomial model.
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Under the exchangeability assumption, the full-sample posterior probability depends only on the multiplicities of the samples and the complete frequency profile.
In AI evaluation, the probability that strict majority voting over N exchangeable runs still errs equals the binomial tail probability E(N, p) = P(Binomial(N, p) >= ceil(N/2)), where p is the probability that a single run errs.
Exchangeability is the only structural assumption required for the binomial tail probability formula to hold; it is weaker than independent and identical distribution, allowing correlation between runs (such as a shared random seed pool, machine, or data snapshot).
In actual evaluation, randomizing the run order or resampling the seed for each configuration is a necessary prerequisite for guaranteeing exchangeability and thus using the binomial tail probability formula.
The coverage guarantee of conformal prediction is built on the premise of data exchangeability.
Time series data exhibit temporal dependencies, trends, and autocorrelation structures, and therefore almost inevitably violate the exchangeability assumption.
The distribution-free nature of conformal prediction requires only the exchangeability assumption, meaning the order of data points does not affect their joint distribution.
Exchangeability is a weaker requirement than independent and identically distributed (i.i.d.), requiring only that any permutation of the data points has the same joint probability distribution.
All Facts (8)
Under the exchangeability assumption, the full-sample posterior probability depends only on the multiplicities of the samples and the complete frequency profile.
50%UnverifiedIn AI evaluation, the probability that strict majority voting over N exchangeable runs still errs equals the binomial tail probability E(N, p) = P(Binomial(N, p) >= ceil(N/2)), where p is the probability that a single run errs.
50%UnverifiedExchangeability is the only structural assumption required for the binomial tail probability formula to hold; it is weaker than independent and identical distribution, allowing correlation between runs (such as a shared random seed pool, machine, or data snapshot).
50%UnverifiedIn actual evaluation, randomizing the run order or resampling the seed for each configuration is a necessary prerequisite for guaranteeing exchangeability and thus using the binomial tail probability formula.
50%UnverifiedThe coverage guarantee of conformal prediction is built on the premise of data exchangeability.
50%UnverifiedTime series data exhibit temporal dependencies, trends, and autocorrelation structures, and therefore almost inevitably violate the exchangeability assumption.
50%UnverifiedThe distribution-free nature of conformal prediction requires only the exchangeability assumption, meaning the order of data points does not affect their joint distribution.
50%UnverifiedExchangeability is a weaker requirement than independent and identically distributed (i.i.d.), requiring only that any permutation of the data points has the same joint probability distribution.
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