A commonly applied approach for estimating causal effects from observational data is to apply weights which render treatments independent of observed pre-treatment covariates. Recently emphasis has been placed on deriving balancing weights which explicitly target this independence condition. In this work we introduce permutation weighting, a method for estimating balancing weights using a standard binary classifier (regardless of cardinality of treatment). A large class of probabilistic classifiers may be used in this method; the choice of loss for the classifier implies the particular definition of balance. We bound bias and variance in terms of the excess risk of the classifier, show that these disappear asymptotically, and demonstrate that our classification problem directly minimizes imbalance. Additionally, hyper-parameter tuning and model selection can be performed with standard cross-validation methods. Empirical evaluations indicate that permutation weighting provides favorable performance in comparison to existing methods.

Estimation of importance sampling weights for off-policy evaluation of contextual bandits often results in imbalance—a mismatch between the desired and the actual distribution of state-action pairs after weighting. In this work we present balanced off-policy evaluation (B-OPE), a generic method for estimating weights which minimize this imbalance. Estimation of these weights reduces to a binary classification problem regardless of action type. We show that minimizing the risk of the classifier implies minimization of imbalance to the desired counterfactual distribution. In turn, this is tied to the error of the off-policy estimate, allowing for easy tuning of hyperparameters. We provide experimental evidence that B-OPE improves weighting-based approaches for offline policy evaluation in both discrete and continuous action spaces.

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new algorithm that requires conditioning only on small sets of variables. The proposed algorithm, which is essentially a modified version of the PC-Algorithm, offers significant gains in both computational complexity and estimation accuracy. In particular, it results in more efficient and accurate estimation in large networks containing hub nodes, which are common in biological systems. We prove the consistency of the proposed algorithm, and show that it also requires a less stringent faithfulness assumption than the PC-Algorithm. Simulations in low and high-dimensional settings are used to illustrate these findings. An application to gene expression data suggests that the proposed algorithm can identify a greater number of clinically relevant genes than current methods.

Directed acyclic graphs (DAGs) are commonly used to represent causal relations within a large number of random variables. Estimating DAGs from observational data is a difficult task, it is often impossible to uniquely determine edge direction. The skeleton of the graph, where directions are removed from edges, is often estimated instead. We consider the task of estimating the skeleton of a potentially high-dimensional DAG consisting of Gaussian random variables. A drawback of existing methods is that a prohibitively large number of conditional independence relations need to be tested for. By exploiting properties of common random graph families, we develop a new algorithm that requires conditioning only on small sets of variables. By extending previous theoretical results for undirected graphs to the setting of directed graphs, we prove the consistency of our algorithm, and demonstrate improvements over the state-of-the-art alternative in low and high-dimensional simulation settings. We conclude by applying our proposed algorithm on a real gene expression data set.