We consider the problem of estimating causal DAG models from a mix of
observational and interventional data, when the intervention targets are
partially or completely unknown. This problem is highly relevant for example in
genomics, since gene knockout technologies are known to have off-target
effects. We characterize the interventional Markov equivalence class of DAGs
that can be identified from interventional data with unknown intervention
targets. In addition, we propose a provably consistent algorithm for learning
the interventional Markov equivalence class from such data. The proposed
algorithm greedily searches over the space of permutations to minimize a novel
score function. The algorithm is nonparametric, which is particularly important
for applications to genomics, where the relationships between variables are
often non-linear and the distribution non-Gaussian. We demonstrate the
performance of our algorithm on synthetic and biological datasets. Links to an
implementation of our algorithm and to a reproducible code base for our
experiments can be found at this https URL

针对部分或完全未知的干预目标的混合观测和干预数据的因果 DAG 模型估计问题，本文提出一个算法来寻找干预马可夫等价类，此算法采用贪心策略在排列空间中搜索以最小化新的分数函数，同时该算法是无参数的，因此适用于非线性关系和非高斯分布的情况，性能表现已被验证。

基于置换的因果结构学习（未知干预目标）

Permutation-Based Causal Structure Learning with Unknown Intervention  Targets

This paper introduces a nonparametric algorithm for bootstrapping a
stationary random field and proves certain consistency properties of the
algorithm for the case of mixing random fields. The motivation for this paper
comes from relating a heuristic texture synthesis algorithm popular in computer
vision to general nonparametric bootstrapping of stationary random fields. We
give a formal resampling scheme for the heuristic texture algorithm and prove
that it produces a consistent estimate of the joint distribution of pixels in a
window of certain size under mixing and regularity conditions on the random
field. The joint distribution of pixels is the quantity of interest here
because theories of human perception of texture suggest that two textures with
the same joint distribution of pixel values in a suitably chosen window will
appear similar to a human. Thus we provide theoretical justification for an
algorithm that has already been very successful in practice, and suggest an
explanation for its perceptually good results.

本文介绍了一种非参数算法，用于引导一个平稳随机场，并证明了这种算法对混合随机场的一些一致性特性，为计算机视觉中一种通用的非参数引导平稳随机场的启发式纹理合成算法提供了正式的重采样方案，并证明它在混合和正则条件下能够产生像素联合分布的一致估计，而对每一个窗口中的像素值的联合分布是本文的研究关注点，因为纹理的人类感知理论表明，在一个合适的选择窗口内，拥有相同像素值联合分布的两个纹理将看起来相似，因此我们提供了一个算法的理论证明，这个算法在实践中已经非常成功，并为其感知效果的好处提供了解释。