Title: We Are Not Your Real Parents: Telling Causal from Confounded using MDL,
Abstract: Given data over variables $(X_1,...,X_m, Y)$ we consider the problem of
finding out whether $X$ jointly causes $Y$ or whether they are all confounded
by an unobserved latent variable $Z$. To do so, we take an
information-theoretic approach based on Kolmogorov complexity. In a nutshell,
we follow the postulate that first encoding the true cause, and then the
effects given that cause, results in a shorter description than any other
encoding of the observed variables.
The ideal score is not computable, and hence we have to approximate it. We
propose to do so using the Minimum Description Length (MDL) principle. We
compare the MDL scores under the models where $X$ causes $Y$ and where there
exists a latent variables $Z$ confounding both $X$ and $Y$ and show our scores
are consistent. To find potential confounders we propose using latent factor
modeling, in particular, probabilistic PCA (PPCA).
Empirical evaluation on both synthetic and real-world data shows that our
method, CoCa, performs very well -- even when the true generating process of
the data is far from the assumptions made by the models we use. Moreover, it is
robust as its accuracy goes hand in hand with its confidence.