Biases in observational data of treatments pose a major challenge to estimating expected treatment outcomes in different populations. An important technique that accounts for these biases is reweighting samples to minimize the discrepancy between treatment groups. We present a novel reweighting approach that uses bi-level optimization to alternately train a discriminator to minimize classification error, and a balancing weights generator that uses exponentiated gradient descent to maximize this error. This approach borrows principles from generative adversarial networks (GANs) to exploit the power of classifiers for measuring two-sample divergence. We provide theoretical results for conditions in which the estimation error is bounded by two factors: (i) the discrepancy measure induced by the discriminator; and (ii) the weights variability. Experimental results on several benchmarks comparing to previous state-of-the-art reweighting methods demonstrate the effectiveness of this approach in estimating causal effects.
We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in approach that rejects data points with a decision that disagrees with the new policy, leading to high variance estimates and ineffective learning. We propose a new, balance-based approach that too makes the data look like the new policy but does so directly by finding weights that optimize for balance between the weighted data and the target policy in the given, finite sample, which is equivalent to minimizing worst-case or posterior conditional mean square error. Our policy learner proceeds as a two-level optimization problem over policies and weights. We demonstrate that this approach markedly outperforms existing ones both in evaluation and learning, which is unsurprising given the wider support of balance-based weights. We establish extensive theoretical consistency guarantees and regret bounds that support this empirical success. Increasingly complex generative models are being used across the disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to perform likelihood-based statistical inference. We consider here a likelihood-free framework where inference is done by identifying parameter values which generate simulated data adequately resembling the observed data. A major difficulty is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models.  Abstract Matched sampling is a method for selecting units from a large reservoir of potential controls to produce a control group of modest size that is similar to a treated group with respect to the distribution of observed covariates. We illustrate the use of multivariate matching methods in an observational study of the effects of prenatal exposure to barbiturates on subsequent psychological development. A key idea is the use of the propensity score as a distinct matching variable. We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations of the method as well as empirical results using both fully connected architectures to learn complex relationships and convolutional architectures to handle image confounders, showing how this new method can enable strong causal analyses in these challenging settings. This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications. We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg. a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.