Non-alcoholic fatty liver disease (NAFLD) and the progressive form of non-alcoholic steatohepatitis (NASH) are diseases of major importance with a high unmet medical need. Efficacy studies on novel compounds to treat NAFLD/NASH using disease models are frequently evaluated using established histological feature scores on ballooning, inflammation, steatosis and fibrosis. These features are assessed by a trained pathologist using microscopy and assigned discrete scores. We demonstrate how to automate these scores with convolutional neural networks (CNNs). Whole slide images of stained liver sections are analyzed using two different scales with four CNNs, each specialized for one of four histopathological features. A continuous value is obtained to quantify the extent of each feature, which can be used directly to provide a high resolution readout. In addition, the continuous values can be mapped to obtain the established discrete pathologist-like scores. The automated deep learning-based scores show good agreement with the trainer - a human pathologist.