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Model interpretation is essential in data mining and knowledge discovery. It can help understand the intrinsic model working mechanism and check if the model has undesired characteristics. A popular way of performing model interpretation is Instance-wise Feature Selection (IFS), which provides an importance score of each feature representing the data samples to explain how the model generates the specific output. In this paper, we propose a Model-agnostic Effective Efficient Direct (MEED) IFS framework for model interpretation, mitigating concerns about sanity, combinatorial shortcuts, model identifiability, and information transmission. Also, we focus on the following setting: using selected features to directly predict the output of the given model, which serves as a primary evaluation metric for model-interpretation methods. Apart from the features, we involve the output of the given model as an additional input to learn an explainer based on more accurate information. To learn the explainer, besides fidelity, we propose an Adversarial Infidelity Learning (AIL) mechanism to boost the explanation learning by screening relatively unimportant features. Through theoretical and experimental analysis, we show that our AIL mechanism can help learn the desired conditional distribution between selected features and targets. Moreover, we extend our framework by integrating efficient interpretation methods as proper priors to provide a warm start. Comprehensive empirical evaluation results are provided by quantitative metrics and human evaluation to demonstrate the effectiveness and superiority of our proposed method. Our code is publicly available online at https://github.com/langlrsw/MEED.