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Summary Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variance. We show that this fact is implied by an ordering among conditional variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.

Discretized conformal prediction for efficient distribution‐free inference

https://doi.org/10.1002/sta4.173

Chen, Wenyu; Chun, Kelli‐Jean; Barber, Rina Foygel (February 2018, Stat)

In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training and test data are assumed to be exchangeable. However, these methods bear a heavy computational cost—and, to be carried out exactly, the regression algorithm would need to be fitted infinitely many times. In practice, the conformal prediction method is run by simply considering only a finite grid of finely spaced values for the response variable. This paper develops discretized conformal prediction algorithms that are guaranteed to cover the target value with the desired probability and that offer a trade‐off between computational cost and prediction accuracy. Copyright © 2018 John Wiley & Sons, Ltd.

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