We consider the problem of estimating the counterfactual joint distribution
of multiple quantities of interests (e.g., outcomes) in a multivariate causal
model extended from the classical difference-in-difference design. Existing
methods for this task either ignore the correlation structures among dimensions
of the multivariate outcome by considering univariate causal models on each
dimension separately and hence produce incorrect counterfactual distributions,
or poorly scale even for moderate-size datasets when directly dealing with such
multivariate causal model. We propose a method that alleviates both issues
simultaneously by leveraging a robust latent one-dimensional subspace of the
original high-dimension space and exploiting the efficient estimation from the
univariate causal model on such space. Since the construction of the
one-dimensional subspace uses information from all the dimensions, our method
can capture the correlation structures and produce good estimates of the
counterfactual distribution. We demonstrate the advantages of our approach over
existing methods on both synthetic and real-world data.

我们提出了一种方法，通过利用原始高维空间的鲁棒一维潜在子空间，并利用在该空间上的单变量因果模型的高效估计，同时减轻了多变量因果模型中存在的问题，从而捕捉了相关结构并产生了反事实分布的良好估计。

多元因果模型中可扩展的反事实分布估计

Scalable Counterfactual Distribution Estimation in Multivariate Causal  Models

Financial correlation matrices measure the unsystematic correlations between
stocks. Such information is important for risk management. The correlation
matrices are known to be ``noise dressed''. We develop a new and alternative
method to estimate this noise. To this end, we simulate certain time series and
random matrices which can model financial correlations. With our approach,
different correlation structures buried under this noise can be detected.
Moreover, we introduce a measure for the relation between noise and
correlations. Our method is based on a power mapping which efficiently
suppresses the noise. Neither further data processing nor additional input is
needed.

本文提出了一种基于功率映射的新型方法来估计金融相关性矩阵中的噪声，能够有效地探测出不同的相关结构，并引入了一种旨在评估噪声与相关性之间关系的度量，无需进一步的数据处理或附加输入。