Data fission: splitting a single data point

• URL: http://arxiv.org/abs/2112.11079v9
• Date: Sun, 10 Dec 2023 19:04:32 GMT
• Title: Data fission: splitting a single data point
• Authors: James Leiner, Boyan Duan, Larry Wasserman, Aaditya Ramdas
• Abstract summary: In this paper, we offer a more general methodology for achieving such a split in finite samples. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on a few applications, such as post-selection inference for trend filtering and other regression problems.
• Score: 27.500860533521713
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Suppose we observe a random vector $X$ from some distribution $P$ in a known family with unknown parameters. We ask the following question: when is it possible to split $X$ into two parts $f(X)$ and $g(X)$ such that neither part is sufficient to reconstruct $X$ by itself, but both together can recover $X$ fully, and the joint distribution of $(f(X),g(X))$ is tractable? As one example, if $X=(X_1,\dots,X_n)$ and $P$ is a product distribution, then for any $m<n$, we can split the sample to define $f(X)=(X_1,\dots,X_m)$ and $g(X)=(X_{m+1},\dots,X_n)$. Rasines and Young (2022) offers an alternative approach that uses additive Gaussian noise -- this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this paper, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on a few prototypical applications, such as post-selection inference for trend filtering and other regression problems.

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