Estimating the true extent of the outbreak was one of the major challenges in combating COVID-19 outbreak early on. Our inability in doing so, allowed unreported/undetected in- fections to drive up disease spread in numerous regions in the US and worldwide. Accurately identifying the true magnitude of infections still remains a major challenge, despite the use of surveillance-based methods such as serological studies, due to their costs and biases. In this paper, we propose an information theoretic approach to accurately estimate the unreported infections. Our approach, built on top of an existing ordinary differential equations based epi- demiological model, aims to deduce an optimal parameterization of the epidemiological model and the true extent of the outbreak which "best describes" the observed reported infections. Our experiments show that the parameterization learned by our framework leads to a better estimation of unreported infections as well as more accurate forecasts of the reported infec- tions compared to the baseline parameterization. We also demonstrate that our framework can be leveraged to simulate what-if scenarios with non-pharmaceutical interventions. Our results also support earlier findings that a large majority of COVID-19 infections were unreported and non-pharmaceutical interventions indeed helped in mitigating the COVID-19 outbreak.