Measuring causal influence with back-to-back regression: the linear case

Jean-Remi King, Francois Charton, Maxime Oquab, David Lopez-Paz

Abstract: Identifying causes from observations can be particularly challenging when i) potential factors are difficult to manipulate individually and ii) observations are complex and multi-dimensional. To address this issue, we introduce “Back-to-Back” regression (B2B), a method designed to efficiently measure, from a set of co-varying factors, the causal influences that most plausibly account for multidimensional observations. After proving the consistency of B2B and its links to other linear approaches, we show that our method outperforms least-squares regression and cross-decomposition techniques (e.g. canonical correlation analysis and partial least squares) on causal identification. Finally, we apply B2B to neuroimaging recordings of 102 subjects reading word sequences. The results show that the early and late brain representations, caused by low- and high-level word features respectively, are more reliably detected with B2B than with other standard techniques.