Identifying causes solely from observations can be particularly challenging when i) the factors under investigation are difficult to manipulate independently from one-another and ii) observations are high-dimensional. To address this issue, we introduce ''Back-to-Back'' regression (B2B), a linear method designed to efficiently estimate, from a set of correlated factors, those that most plausibly account for multidimensional observations. First, we prove the consistency of B2B, its links to other linear approaches, and show how it can provide a robust, unbiased and interpretable scalar estimate for each factor. Second, we use a variety of simulated data to show that B2B can outperform forward modeling ("encoding"), backward modeling ("decoding") as well as cross-decomposition modeling (i.e.. canonical correlation analysis and partial least squares) on causal identification when the factors and the observations are not orthogonal. Finally, we apply B2B to a hundred magneto-encephalography recordings and to a hundred functional Magnetic Resonance Imaging recordings acquired while subjects performed a one hour reading task. B2B successfully disentangles the respective contribution of collinear factors such as word length, word frequency in the early visual and late associative cortical responses respectively. B2B compared favorably to other standard techniques on this disentanglement. We discuss how the speed and the generality of B2B sets promising foundations to help identify the causal contributions of covarying factors from high-dimensional observations.

中文翻译：

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背靠背回归：从多元观察中解开相关因素的影响

当 i) 所调查的因素难以相互独立地操纵并且 ii) 观察是高维的时，仅从观察中确定原因可能特别具有挑战性。为了解决这个问题，我们引入了“背靠背”回归 (B2B)，这是一种线性方法，旨在从一组相关因素中有效估计最有可能解释多维观察的因素。首先，我们证明了 B2B 的一致性及其与其他线性方法的联系，并展示了它如何为每个因素提供稳健、无偏且可解释的标量估计。其次，我们使用各种模拟数据来表明 B2B 可以胜过正向建模（“编码”）、反向建模（“解码”）以及交叉分解建模（即 当因素和观察值不正交时，典型相关分析和偏最小二乘法）进行因果识别。最后，我们将 B2B 应用于一百个脑磁图记录和一百个功能性磁共振成像记录，同时受试者执行一小时的阅读任务。B2B 成功地解开了早期视觉和晚期联想皮层反应中字长、词频等共线因素的各自贡献。B2B 与其他标准技术在这种解开方面相比具有优势。我们讨论了 B2B 的速度和普遍性如何奠定了有希望的基础，以帮助从高维观察中确定协变因素的因果贡献。