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Causal inference with observational data has drawn attention across various fields. These observational studies typically use matching methods which find matched pairs with similar covariate values. However, matching methods may not directly achieve covariate balance, a measure of matching effectiveness. As an alternative, the Balance Optimization Subset Selection (BOSS) framework, which seeks optimal covariate balance directly, has been proposed. This paper extends BOSS by estimating and decomposing a treatment effect as a combination of heterogeneous treatment effects from a partitioned set. Our method differs from the traditional propensity score subclassification method in that we find a subset in each subclass using BOSS instead of using the stratum determined by the propensity score. Then, by conducting a bootstrap hypothesis test on each component, we check the statistical significance of these treatment effects. These methods are applied to a dataset from the National Supported Work Demonstration (NSW) program which was conducted in the 1970s. By examining the statistical significance, we show that the program was not significantly effective to a specific subgroup composed of those who were already employed. This differs from the combined estimate—the NSW program was effective when considering all the individuals. Lastly, we provide results that are obtained when these steps are repeated with sub-samples.

Observational data are prevalent in many fields of research, and it is desirable to use this data to make causal inferences. Because this data is nonrandom, additional assumptions are needed in order to construct unbiased estimators for causal effects. The standard assumption is strong ignorability, though it is often impossible to achieve the level of covariate balance that it requires. As such, researchers often settle for lesser balance levels within their datasets. However, these balance levels are generally insufficient to guarantee an unbiased estimate of the treatment effect without further assumptions. This article presents several extensions to the strong ignorability assumption that address this issue. Under these additional assumptions, specific levels of covariate balance are both necessary and sufficient for the treatment effect estimate to be unbiased. There is a trade-off, however: as balance decreases, stronger assumptions are required to guarantee estimator unbiasedness. These results unify parametric and nonparametric adjustment methods for causal inference and are actualized by the Balance Optimization Subset Selection framework, which identifies the best level of balance that can be achieved within a dataset.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

The cyclic best-first search (CBFS) strategy is a recent search strategy that has been successfully applied to branch-and-bound algorithms in a number of different settings. CBFS is a modification of best-first search (BFS) that places search tree subproblems into contours which are collections of subproblems grouped in some way, and repeatedly cycles through all non-empty contours, selecting one subproblem to explore from each. In this article, the theoretical properties of CBFS are analyzed for the first time. CBFS is proved to be a generalization of all other search strategies by using a contour definition that explores the same sequence of subproblems as any other search strategy. Further, a bound is proved between the number of subproblems explored by BFS and the number of children generated by CBFS, given a fixed branching strategy and set of pruning rules. Finally, a discussion of heuristic contour-labeling functions is provided, and proof-of-concept computational results for mixed-integer programming problems from the MIPLIB 2010 database are shown. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 64–82, 2017

Customers today are faced with a plethora of choices of products to buy and consume. The sheer volume of choices can be daunting, and customers forced to sift through the products are likely to become dissatisfied. Retailers have the ability to solve this problem by providing customers with recommendations of products that are likely to be of interest to each specific customer. This can be done by profiling each customer and identifying products that similar customers like. This paper presents a balance optimization approach, where customers are characterized and matched as groups. By identifying and analyzing a group of customers who have shown positive reactions to a specific product, we propose a technique to find a comparable group who we hypothesize will show a similar positive reaction. This allows for the creation of targeted advertisements, mailing lists, and other material to recommend products to customers. The methodology is tested using a Netflix dataset, where we are able to show a statistically significant improvement on the mean rating of selected users over random selection of 0.384 when the ratings are on a scale of 0–5.

The NCAA basketball tournament attracts over 60 million people who fill out a bracket to try to predict the outcome of every tournament game correctly. Predictions are often made on the basis of instinct, statistics, or a combination of the two. This paper proposes a technique to select round-of-64 upsets in the tournament using a Balance Optimization Subset Selection model. The model determines which games feature match-ups that are statistically most similar to the match-ups in historical upsets. The technique is then applied to the tournament in each of the 13 years from 2003 to 2015 in order to select two games as potential upsets each year. Of the 26 selected games, 10 (38.4%) were actual upsets, which is more than twice as many as the expected number of correct selections when using a weighted random selection method.

To make causal inferences from observational data, researchers have often turned to matching methods. These methods are variably successful. We address issues with matching methods by redefining the matching problem as a subset selection problem. Given a set of covariates, we seek to find two subsets, a control group and a treatment group, so that we obtain optimal balance, or, in other words, the minimum discrepancy between the distributions of these covariates in the control and treatment groups. Our formulation captures the key elements of the Rubin causal model and translates nicely into a discrete optimization framework.