With the better availability of healthcare data, such as Electronic Health Records (EHR), more and more data analytics methodologies are developed aiming at digging insights from them to improve the quality of care delivery. There are many challenges on analyzing EHR, such as high dimensionality and event sparsity. Moreover, different from other application domains, the EHR analysis algorithms need to be highly interpretable to make them clinically useful. This makes representation learning from EHRs of key importance. In this paper, we propose an algorithm called Predictive Task Guided Tensor Decomposition (TaGiTeD), to analyze EHRs. Specifically, TaGiTeD learns event interaction patterns that are highly predictive for certain tasks from EHRs with supervised tensor decomposition. Compared with unsupervised methods, TaGiTeD can learn effective EHR representations in a more focused way. This is crucial because most of the medical problems have very limited patient samples, which are not enough for unsupervised algorithms to learn meaningful representations form. We apply TaGiTeD on real world EHR data warehouse and demonstrate that TaGiTeD can learn representations that are both interpretable and predictive.