Leonard Schulman

Bijan Mazaheri, Spencer Gordon, Yuval Rabani et al.

An acyclic causal structure can be described with directed acyclic graph (DAG), where arrows indicate the possibility of direct causation. The task of learning this structure from data is known as "causal discovery." Diverse populations or changing environments can sometimes give rise to data that is heterogeneous in the following sense: each population/environment is a "source" which idiosyncratically determines the forms of those direct causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery are able to work around latent confounding in special cases, especially when only few observables are confounded, a global confounder is a difficult challenge. The only known ways to deal with latent global confounding involve assumptions that limit the structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identifiable with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying DAG.

Sanjoy Dasgupta, Leonard Schulman

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.