Estimation of linear, non-gaussian causal models in the presence of
  confounding latent variables
  The estimation of linear causal models (also known as structural equation
models) from data is a well-known problem which has received much attention in
the past. Most previous work has, however, made an explicit or implicit
assumption of gaussianity, limiting the identifiability of the models. We have
recently shown (Shimizu et al, 2005; Hoyer et al, 2006) that for non-gaussian
distributions the full causal model can be estimated in the no hidden variables
case. In this contribution, we discuss the estimation of the model when
confounding latent variables are present. Although in this case uniqueness is
no longer guaranteed, there is at most a finite set of models which can fit the
data. We develop an algorithm for estimating this set, and describe numerical
simulations which confirm the theoretical arguments and demonstrate the
practical viability of the approach. Full Matlab code is provided for all
simulations.
