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通过置换增广回归构造线性模型的保形检验AI 解读

Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through…

局部化保形预测：保形预测的广义推断框架AI 解读

Summary We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample, and can be combined with different conformal scores. The proposed framework enjoys an assumption-free finite sample marginal coverage guarantee, and it also offers additional local coverage guarantees under suitable assumptions. We…

分类问题中的预测与离群点检测AI 解读

Abstract We consider the multi-class classification problem when the training data and the out-of-sample test data may have different distributions and propose a method called BCOPS (balanced and conformal optimized prediction sets). BCOPS constructs a prediction set C(x) as a subset of class labels, possibly empty. It tries to optimize the out-of-sample performance, aiming to include the correct class and to detect outliers x as often as possible. BCOPS returns no…

基因扰动实验的强信号检测：具有功效保证与 FDR 控制的自适应方法AI 解读

The perturbation of a transcription factor should affect the expression levels of its direct targets. However, not all genes showing changes in expression are direct targets. To increase the chance of detecting direct targets, we propose a modified two-group model where the null group corresponds to genes which are not direct targets, but can have small nonzero effects. We model the behavior of genes from the null set by a Gaussian distribution with unknown variance τ 2 . To…

图上分段常数信号的近似 ℓ₀ 惩罚估计AI 解读

We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_{0}$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical risk guarantees are achieved by the $\alpha$-expansion algorithm which computes an approximate minimizer in polynomial time. We establish that for graphs with small average vertex degree, these guarantees are minimax rate-optimal over…