A major challenge in cancer treatment is predicting the clinical response to anticancer drugs for each individual patient. For complex diseases, such as cancer, characterized by high inter-patient variance, the implementation of precision medicine approaches is dependent upon understanding the disease process at the molecular level. While the omics era provides unique opportunities to dissect the molecular features of diseases, the ability to apply it to targeted therapeutic efforts is hindered by both the massive size and diverse nature of the omic data. Recent advances with Deep Learning Neural Networks (DLNN), suggests that DLNN could be trained on large data sets to efficiently predict therapeutic responses. We present the application of Association Rule Mining (Market Basket Analysis) in combination with Deep Learning to integrate and extract knowledge in the form of easily interpretable rules from the molecular profiles of 689 cancer cell lines and predict pharmacological responses to 139 anti-cancer drugs. The proposed algorithm achieved superior classification and outperformed Random Forests which currently represents the state-of-the-art classification process. Finally, the in silico pipeline presented introduces a novel strategy for identifying drug combinations with high therapeutic potential. For the first time, we demonstrate that DLNN trained on a large pharmacogenomic data set can effectively predict the therapeutic response of specific drugs in specific cancer types, from a large panel of both drugs and cancer cell lines. These findings serve as a proof of concept for the application of DLNN to predict therapeutic responsiveness, a milestone in precision medicine.