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A key challenge for decision makers when incorporating black box machine learned models into practice is being able to understand the predictions provided by these models. One proposed set of methods is training surrogate explainer models which approximate the more complex model. Explainer methods are generally classified as either local or global, depending on what portion of the data space they are purported to explain. The improved coverage of global explainers usually comes at the expense of explainer fidelity. One way of trading off the advantages of both approaches is to aggregate several local explainers into a single explainer model with improved coverage. However, the problem of aggregating these local explainers is computationally challenging, and existing methods only use heuristics to form these aggregations. In this paper we propose a local explainer aggregation method which selects local explainers using non-convex optimization. In contrast to other heuristic methods, we use an integer optimization framework to combine local explainers into a near-global aggregate explainer. Our framework allows a decision-maker to directly tradeoff coverage and fidelity of the resulting aggregation through the parameters of the optimization problem. We also propose a novel local explainer algorithm based on information filtering. We evaluate our algorithmic framework on two healthcare datasets---the Parkinson's Progression Marker Initiative (PPMI) data set and a geriatric mobility dataset---which is motivated by the anticipated need for explainable precision medicine. Our method outperforms existing local explainer aggregation methods in terms of both fidelity and coverage of classification and improves on fidelity over existing global explainer methods, particularly in multi-class settings where state-of-the-art methods achieve 70% and ours achieves 90%.