Given data over variables (X 1 , ..., X m , Y ) we consider the problem of nding 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 rst encoding the true cause, and then the e ects given that cause, results in a shorter description than any other encoding of the observed variables. e 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 nd 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, C C , 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 con dence.

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Access to a representative sample from the population is an assumption that underpins all of machine learning. Selection effects can cause observations to instead come from a subpopulation, by which our inferences may be subject to bias. It is therefore important to know whether or not a sample is affected by selection effects. We study under which conditions we can identify selection bias and give results for both parametric and non-parametric families of distributions. Based on these results we develop two practical methods to determine whether or not an observed sample comes from a distribution subject to selection bias. Through extensive evaluation on synthetic and real world data we verify that our methods beat the state of the art both in detecting as well as characterizing selection bias.