Fast exact conformalization of the lasso using piecewise linear homotopy
Fast exact conformalization of the lasso using piecewise linear homotopy
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DOI：
10.1093/biomet/asz046
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发表时间：
2019-12-01
期刊：
影响因子：
2.7
通讯作者：
Lei, J.
中科院分区：
文献类型：
--
作者：
Lei, J.
保形预测是一种通用的方法，它可以将几乎任何点预测器转换为预测集。结果集保留了标准假设下原始估计量的良好统计特性，并保证有效的平均覆盖率，即使模型被错误指定。在现代应用中应用保形预测的主要挑战是有效的计算，因为它通常需要在整个输出空间上进行穷举搜索。在本文中，我们开发了一个精确的和计算效率高的一致的套索和弹性网。该方法利用了一种新的分段线性同伦的拉索解扰动下的一个单一的输入样本点。作为副产品，我们提供了一个更简单，更合理的在线套索算法，这可能是独立的利益。我们的推导还揭示了一个有趣的准确性稳定性权衡共形推理，这是类似于传统的参数估计的偏差方差权衡。新算法的实际性能在合成和真实的数据的例子证明。
Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set retains the good statistical properties of the original estimator under standard assumptions, and guarantees valid average coverage even when the model is mis-specified. A main challenge in applying conformal prediction in modern applications is efficient computation, as it generally requires an exhaustive search over the entire output space. In this paper we develop an exact and computationally efficient conformalization of the lasso and elastic net. The method makes use of a novel piecewise linear homotopy of the lasso solution under perturbation of a single input sample point. As a by-product, we provide a simpler and better-justified online lasso algorithm, which may be of independent interest. Our derivation also reveals an interesting accuracy-stability trade-off in conformal inference, which is analogous to the bias-variance trade-off in traditional parameter estimation. The practical performance of the new algorithm is demonstrated in both synthetic and real data examples.