As machine learning black boxes are increasingly being deployed in critical\ndomains such as healthcare and criminal justice, there has been a growing\nemphasis on developing techniques for explaining these black boxes in a post\nhoc manner. In this work, we analyze two popular post hoc interpretation\ntechniques: SmoothGrad which is a gradient based method, and a variant of LIME\nwhich is a perturbation based method. More specifically, we derive explicit\nclosed form expressions for the explanations output by these two methods and\nshow that they both converge to the same explanation in expectation, i.e., when\nthe number of perturbed samples used by these methods is large. We then\nleverage this connection to establish other desirable properties, such as\nrobustness, for these techniques. We also derive finite sample complexity\nbounds for the number of perturbations required for these methods to converge\nto their expected explanation. Finally, we empirically validate our theory\nusing extensive experimentation on both synthetic and real world datasets.\n